The nonlinear behavior of fixed parabolic shallow arches subjected to a vertical uniform load is inves- tigated to evaluate the in-plane buckling load. The virtual work principle method is used to establish the non-li...The nonlinear behavior of fixed parabolic shallow arches subjected to a vertical uniform load is inves- tigated to evaluate the in-plane buckling load. The virtual work principle method is used to establish the non-linear equilibrium and buckling equations. Analytical solutions for the non-linear in-plane sym- metric snap-through and antisymmetric bifurcation buckling loads are obtained. Based on the least square method, an approximation for the symmetric buckling load of fixed parabolic arch is proposed to simplify the solution process. And the relation between modified slenderness and buckling modes are discussed. Comparisons with the results of finite element analysis demonstrate that the solutions are accurate. A cable-arch structure is presented to improve the in-plane stability of parabolic arches. The comparison of buckling loads between cable-arch systems and arches only show that the effect of cables becomes more evident with the increase of arch’s modified slenderness.展开更多
Floating oscillating bodies constitute a large class of wave energy converters, especially for offshore deployment. Usually the Power-Take-Off（PTO） system is a directly linear electric generator or a hydraulic motor...Floating oscillating bodies constitute a large class of wave energy converters, especially for offshore deployment. Usually the Power-Take-Off（PTO） system is a directly linear electric generator or a hydraulic motor that drives an electric generator. The PTO system is simplified as a linear spring and a linear damper. However the conversion is less powerful with wave periods off resonance. Thus, a nonlinear snap-through mechanism with two symmetrically oblique springs and a linear damper is applied in the PTO system. The nonlinear snap-through mechanism is characteristics of negative stiffness and double-well potential. An important nonlinear parameter γ is defined as the ratio of half of the horizontal distance between the two springs to the original length of both springs. Time domain method is applied to the dynamics of wave energy converter in regular waves. And the state space model is used to replace the convolution terms in the time domain equation. The results show that the energy harvested by the nonlinear PTO system is larger than that by linear system for low frequency input. While the power captured by nonlinear converters is slightly smaller than that by linear converters for high frequency input. The wave amplitude, damping coefficient of PTO systems and the nonlinear parameter γ affect power capture performance of nonlinear converters. The oscillation of nonlinear wave energy converters may be local or periodically inter well for certain values of the incident wave frequency and the nonlinear parameter γ, which is different from linear converters characteristics of sinusoidal response in regular waves.展开更多
A modified snap-through mechanism is used in an electromagnetic energy harvester to improve its effectiveness. It mainly comprises three springs that are configured so that the potential energy of the system has two s...A modified snap-through mechanism is used in an electromagnetic energy harvester to improve its effectiveness. It mainly comprises three springs that are configured so that the potential energy of the system has two stable equilibrium points. In particular, the small vibration behavior of the harvester around one of the equilibriums is of interest. A multi-scale method(MSM) is used to analyze the frequency response curve. Two snap-through mechanisms are considered. One has both horizontal and vertical springs. The other has only horizontal springs. The frequency response curves of these two classes are compared under the same excitation and electric loading conditions. The latter exhibits more bending of the frequency response curve than the former one. The results are also validated by some numerical work. The averaged power subject to the Gaussian white noise is calculated numerically, and the results demonstrate that bi-stable energy harvesting with only horizontal springs can outperform the mechanism with both horizontal and vertical springs for the same distance between two equilibriums.展开更多
Nonlinear solution of reinforced concrete structures, particularly complete load-deflection response, requires tracing of the equilibrium path and proper treatment of the limit and bifurcation points. In this regard, ...Nonlinear solution of reinforced concrete structures, particularly complete load-deflection response, requires tracing of the equilibrium path and proper treatment of the limit and bifurcation points. In this regard, ordinary solution techniques lead to instability near the limit points and also have problems in case of snap-through and snap-back. Thus they fail to predict the complete load-displacement response. The arc-length method serves the purpose well in principle, received wide acceptance in finite element analysis, and has been used extensively. However modifications to the basic idea are vital to meet the particular needs of the analysis. This paper reviews some of the recent developments of the method in the last two decades, with particular emphasis on nonlinear finite element analysis of reinforced concrete structures.展开更多
Multi-stable origami structures and metamaterials possess unique advantages and could exhibit multiple stable three-dimensional configurations,which have attracted widespread research interest and held promise for app...Multi-stable origami structures and metamaterials possess unique advantages and could exhibit multiple stable three-dimensional configurations,which have attracted widespread research interest and held promise for applications in many fields.Although a great deal of attention has been paid to the design and application of multi-stable origami structures,less knowledge is available about the transition sequence among different stable configurations,especially in terms of the fundamental mechanism and the tuning method.To fill this gap,with the multi-stable dual-cell stacked Miura-ori chain as a platform,this paper explores the rules that govern the configuration transition and proposes effective methods for tuning the transition sequence.Specifically,by correlating the energy evolution,the transition paths,and the associated force-displace-ment profiles,we find that the critical extension/compression forces of the component cells play a critical role in governing the transition sequence.Accordingly,we summarize the rules for predicting the transition sequence:the component cell that first reaches the critical force during quasi-static extension or compression will be the first to undergo a configuration switch.Based on these findings,two methods,i.e.,a design method based on crease-stiffness assignment and an online method based on internal pressure regulation,are proposed to tune the stability profile and the transition sequence of the multi-stable origami structure.The crease-stiffness design approach,although effective,cannot be employed for online tuning once the prototype has been fabricated.The pressure-based approach,on the other hand,has been shown experimentally to be effective in adjusting the constitutive force-displacement profiles of the component cells and,in turn,tuning the transition sequence according to the summarized rules.The results of this study will advance the state of the art of origami mechanics and promote the engineering applications of multi-stable origami metamaterials.展开更多
The buckling behavior of single layer space structure is very sensitive. The joint rigidity, moreover, is one of the main factors of stability which may determine the entire failure behavior. Thus, the reasonable stif...The buckling behavior of single layer space structure is very sensitive. The joint rigidity, moreover, is one of the main factors of stability which may determine the entire failure behavior. Thus, the reasonable stiffness of joint system, which is neither total pin assumption nor perfect fix condition, is very important to apply to the real single layer space one. Therefore, the purpose of this work was to investigate the buckling behavior of single layer space structure, using the development of the upgraded stiffness matrix for the joint rigidity. To derive tangential stiffness matrix, a displacement function was assumed using translational and rotational displacement at the node. The geometrical nonlinear analysis was simulated not only with perfect model but also with imperfect one. As a result, the one and two free nodal numerical models were investigated using derived stiffness matrix. It was figured out that the buckling load increases in proportion to joint rigidity with rise-span ratio. The stability of numerical model is very sensitive with the initial imperfection, responding of bifurcation in the structure.展开更多
Flexoelectricity is present in nonuniformly deformed dielectric materials and has size-dependent properties, making it useful for microelectromechanical systems. Flexoelectricity is small compared to piezoelectricity;...Flexoelectricity is present in nonuniformly deformed dielectric materials and has size-dependent properties, making it useful for microelectromechanical systems. Flexoelectricity is small compared to piezoelectricity;therefore, producing a large-scale flexoelectric effect is of great interest. In this paper, we explore a way to enhance the flexoelectric effect by utilizing the snap-through instability and a stiffness gradient present along the length of a curved dielectric plate. To analyze the effect of stiffness profiles on the plate, we employ numerical parameter continuation. Our analysis reveals a nonlinear relationship between the effective electromechanical coupling coefficient and the gradient of Young’s modulus. Moreover, we demonstrate that the quadratic profile is more advantageous than the linear profile. For a dielectric plate with a quadratic profile and a modulus gradient of − 0.9, the effective coefficient can reach as high as 15.74 pC/N, which is over three times the conventional coupling coefficient of piezoelectric material. This paper contributes to our understanding of the amplification of flexoelectric effects by harnessing snapping surfaces and stiffness gradient design.展开更多
The snap-through behaviors and nonlinear vibrations are investigated for a bistable composite laminated cantilever shell subjected to transversal foundation excitation based on experimental and theoretical approaches....The snap-through behaviors and nonlinear vibrations are investigated for a bistable composite laminated cantilever shell subjected to transversal foundation excitation based on experimental and theoretical approaches.An improved experimental specimen is designed in order to satisfy the cantilever support boundary condition,which is composed of an asymmetric region and a symmetric region.The symmetric region of the experimental specimen is entirely clamped,which is rigidly connected to an electromagnetic shaker,while the asymmetric region remains free of constraint.Different motion paths are realized for the bistable cantilever shell by changing the input signal levels of the electromagnetic shaker,and the displacement responses of the shell are collected by the laser displacement sensors.The numerical simulation is conducted based on the established theoretical model of the bistable composite laminated cantilever shell,and an off-axis three-dimensional dynamic snap-through domain is obtained.The numerical solutions are in good agreement with the experimental results.The nonlinear stiffness characteristics,dynamic snap-through domain,and chaos and bifurcation behaviors of the shell are quantitatively analyzed.Due to the asymmetry of the boundary condition and the shell,the upper stable-state of the shell exhibits an obvious soft spring stiffness characteristic,and the lower stable-state shows a linear stiffness characteristic of the shell.展开更多
The chaotic dynamic snap-through and complex nonlinear vibrations are investigated in a rectangular asymmetric cross-ply bistable composite laminated cantilever shell,in cases of 1:2 inter-well internal resonance and ...The chaotic dynamic snap-through and complex nonlinear vibrations are investigated in a rectangular asymmetric cross-ply bistable composite laminated cantilever shell,in cases of 1:2 inter-well internal resonance and primary resonance.The transverse foundation excitation is applied to the fixed end of the structure,and the other end is in a free state.The first-order approximate multiple scales method is employed to perform the perturbation analysis on the dimensionless two-degree-of-freedom ordinary differential motion control equation.The four-dimensional averaged equations are derived in both polar and rectangular coordinate forms.Deriving from the obtained frequency-amplitude and force-amplitude response curves,a detailed analysis is conducted to examine the impacts of excitation amplitude,damping coefficient,and tuning parameter on the nonlinear internal resonance characteristics of the system.The nonlinear softening characteristic is exhibited in the upper stable-state,while the lower stable-state demonstrates the softening and linearity characteristics.Numerical simulation is carried out using the fourth-order Runge-Kutta method,and a series of nonlinear response curves are plotted.Increasing the excitation amplitude further elucidates the global bifurcation and chaotic dynamic snap-through characteristics of the bistable cantilever shell.展开更多
The dynamic model of a bistable laminated composite shell simply supported by four corners is further developed to investigate the resonance responses and chaotic behaviors.The existence of the 1:1 resonance relations...The dynamic model of a bistable laminated composite shell simply supported by four corners is further developed to investigate the resonance responses and chaotic behaviors.The existence of the 1:1 resonance relationship between two order vibration modes of the system is verified.The resonance response of this class of bistable structures in the dynamic snap-through mode is investigated,and the four-dimensional(4D)nonlinear modulation equations are derived based on the 1:1 internal resonance relationship by means of the multiple scales method.The Hopf bifurcation and instability interval of the amplitude frequency and force amplitude curves are analyzed.The discussion focuses on investigating the effects of key parameters,e.g.,excitation amplitude,damping coefficient,and detuning parameters,on the resonance responses.The numerical simulations show that the foundation excitation and the degree of coupling between the vibration modes exert a substantial effect on the chaotic dynamics of the system.Furthermore,the significant motions under particular excitation conditions are visualized by bifurcation diagrams,time histories,phase portraits,three-dimensional(3D)phase portraits,and Poincare maps.Finally,the vibration experiment is carried out to study the amplitude frequency responses and bifurcation characteristics for the bistable laminated composite shell,yielding results that are qualitatively consistent with the theoretical results.展开更多
The deformation and snap-through behaviour of a thin-walled elastic spherical shell statically compressed on a flat surface or impacted against a fiat surface are studied the- oretically and numerically in order to es...The deformation and snap-through behaviour of a thin-walled elastic spherical shell statically compressed on a flat surface or impacted against a fiat surface are studied the- oretically and numerically in order to estimate the influence of the dynamic effects on the response. A table tennis ball is considered as an example of a thin-walled elastic shell. It is shown that the increase of the impact velocity leads to a variation of the deformed shape thus resulting in larger de- formation energy. The increase of the contact force is caused by both the increased contribution of the inertia forces and contribution of the increased deformation energy. The contact force resulted from deformation/inertia of the ball and the shape of the deformed region are calcu- lated by the proposed theoretical models and compared with the results from both the finite element analysis and some previously obtained experimental data. Good agreement is demonstrated.展开更多
Three-dimensional(3D)mesostructures with distinct compressive deformation behaviors and tunable mechanical responses have gained increasing interest in recent years.3D cage-shaped mesostructures are representative fra...Three-dimensional(3D)mesostructures with distinct compressive deformation behaviors and tunable mechanical responses have gained increasing interest in recent years.3D cage-shaped mesostructures are representative framework structures widely exploited in 3D flexible electronics,owing to their unique cellular geometry and unusual mechanical responses.The snap-through behavior of cage-shaped mesostructures could potentially result in the performance degradation of electronics,while it could also be harnessed to design reconfigurable electronics.Due to the complicated deformation modes and random characteristics in experiments,the snap-through behavior of cage-shaped mesostructures remains largely unexplored,espe-cially in terms of probability-based analyses.In this work,we present a systematic study on the configuration evolution and snap-through of 3D cage-shaped mesostructures under out-of-plane compressions.Experimental and computational studies show the existence of two distinct deformation modes associated with the snap-through,which is controlled by the energy barrier based on the energetic analyses.Phase diagrams of the deformation modes decode how key geometric parameters and assembly strain affect the snap-through.Compressive experiments based on periodic arrays(10 × 10)of mesostructures provided a large amount of deformation data,allowing for statistical analyses of the snap-through behavior.These results provide new insights and useful guidelines for the design of 3D reconfigurable devices and multistable metamaterials based on 3D cage-shaped mesostructures.展开更多
Double-clamped bistable buckled beams demonstrate great versatility in various fields such as robotics,energy harvesting,and microelectromechanical system(MEMS).However,their design often requires time-consuming and e...Double-clamped bistable buckled beams demonstrate great versatility in various fields such as robotics,energy harvesting,and microelectromechanical system(MEMS).However,their design often requires time-consuming and expensive computations.In this work,we present a method to easily and rapidly design bistable buckled beams subjected to a transverse point force.Based on the Euler–Bernoulli beam theory,we establish a theoretical model of bistable buckled beams to characterize their snapthrough properties.This model is verified against the results from a finite element analysis(FEA)model,with maximum discrepancy less than 7%.By analyzing and simplifying our theoretical model,we derive explicit analytical expressions for critical behavioral values on the force-displacement curve of the beam.These behavioral values include critical force,critical displacement,and travel,which are generally sufficient for characterizing the snapthrough properties of a bistable buckled beam.Based on these analytical formulas,we investigate the influence of a bistable buckled beam's key design parameters,including its actuation position and precompression,on its critical behavioral values,with our results validated by FEA simulations.Our analytical method enables fast and computationally inexpensive design of bistable buckled beams and can guide the design of complicated systems that incorporate bistable mechanisms.展开更多
This study investigated characteristics of bifurcation and critical buckling load by shape imperfection of space truss,which were sensitive to initial conditions.The critical point and buckling load were computed by t...This study investigated characteristics of bifurcation and critical buckling load by shape imperfection of space truss,which were sensitive to initial conditions.The critical point and buckling load were computed by the analysis of the eigenvalues and determinants of the tangential stiffness matrix.The two-free-nodes example and star dome were selected for the case study in order to examine the nodal buckling and global buckling by the sensitivity to the eigen buckling mode and the analyses of the influence,and characteristics of the parameters as defined by the load ratio of the center node and surrounding node,as well as rise-span ratio were performed.The sensitivity to the imperfection of the initial shape of the two-free-nodes example,which occurs due to snapping at the critical point,resulted in bifurcation before the limit point due to the buckling mode,and the buckling load was reduced by the increase in the amount of imperfection.The two sensitive buckling patterns of the numerical model are established by investigating the displaced position of the free nodes,and the asymmetric eigenmode greatly influenced the behavior of the imperfection shape whether it was at limit point or bifurcation.Furthermore,the sensitive mode of the two-free-nodes example was similar to the in-extensional basis mechanism of a simplified model.The star dome,which was used to examine the influence among several nodes,indicated that the influence of nodal buckling was greater than that of global buckling as the rise-span ratio was higher.Besides,global buckling is occurred with reaching bifurcation point as the value of load ratio was higher,and the buckling load level was about 50%-70% of load level at limit point.展开更多
Dielectric elastomer actuators have attracted growing interest for soft robot due to their large deformation and fast response.However,continuous high-voltage loading tends to cause the electric breakdown of the actua...Dielectric elastomer actuators have attracted growing interest for soft robot due to their large deformation and fast response.However,continuous high-voltage loading tends to cause the electric breakdown of the actuator due to heat accumulation,and viscoelasticity complicates precise control.The snap-through bistability of the Venus flytrap is one of the essential inspirations for bionic structure,which can be adopted to improve the shortcoming of dielectric elastomer actuators and develop a new actuation structure with low energy consumption,variable configuration,and multi-mode actuation.Hence,in this paper,the structural design principles of electroactive bistable actuators are first presented based on the total potential energy of the structure.Following that,a feasible design parameter region is provided,the influence of crucial parameters on the actuation stroke,trigger voltage,and actuation charge are discussed.Finally,according to the coupling relationship between the bending stiffness and the bistable property of the actuator,the adjusting methods of bistable actuation are explored.A qualitative experiment was performed to verify the feasibility and correctness of the bistable design methodology and the actuation regulation strategy.This study provides significant theoretical guidance and technical support for developing and applying dielectric elastomer actuators with multi-mode,high-performance,and long-life characteristics.展开更多
基金Supported by the National Natural Science Foundation of China (Grant No. 50478075)Scientific Research Foundation of Graduate School of Southeast University (Grant No. YBJJ0817)
文摘The nonlinear behavior of fixed parabolic shallow arches subjected to a vertical uniform load is inves- tigated to evaluate the in-plane buckling load. The virtual work principle method is used to establish the non-linear equilibrium and buckling equations. Analytical solutions for the non-linear in-plane sym- metric snap-through and antisymmetric bifurcation buckling loads are obtained. Based on the least square method, an approximation for the symmetric buckling load of fixed parabolic arch is proposed to simplify the solution process. And the relation between modified slenderness and buckling modes are discussed. Comparisons with the results of finite element analysis demonstrate that the solutions are accurate. A cable-arch structure is presented to improve the in-plane stability of parabolic arches. The comparison of buckling loads between cable-arch systems and arches only show that the effect of cables becomes more evident with the increase of arch’s modified slenderness.
基金financially supported by the National Natural Science Foundation of China(Grant No.51239007)the Independent Research Project of State Key Laboratory of Ocean Engineering in Shanghai Jiao Tong University(Grant No.GKZD010023)
文摘Floating oscillating bodies constitute a large class of wave energy converters, especially for offshore deployment. Usually the Power-Take-Off（PTO） system is a directly linear electric generator or a hydraulic motor that drives an electric generator. The PTO system is simplified as a linear spring and a linear damper. However the conversion is less powerful with wave periods off resonance. Thus, a nonlinear snap-through mechanism with two symmetrically oblique springs and a linear damper is applied in the PTO system. The nonlinear snap-through mechanism is characteristics of negative stiffness and double-well potential. An important nonlinear parameter γ is defined as the ratio of half of the horizontal distance between the two springs to the original length of both springs. Time domain method is applied to the dynamics of wave energy converter in regular waves. And the state space model is used to replace the convolution terms in the time domain equation. The results show that the energy harvested by the nonlinear PTO system is larger than that by linear system for low frequency input. While the power captured by nonlinear converters is slightly smaller than that by linear converters for high frequency input. The wave amplitude, damping coefficient of PTO systems and the nonlinear parameter γ affect power capture performance of nonlinear converters. The oscillation of nonlinear wave energy converters may be local or periodically inter well for certain values of the incident wave frequency and the nonlinear parameter γ, which is different from linear converters characteristics of sinusoidal response in regular waves.
基金Project supported by the State Key Program of National Natural Science of China(No.11232009)the National Natural Science Foundation of China(Nos.11502135 and 11572182)the Innovation Program of Shanghai Municipal Education Commission(No.2017-01-07-00-09-E00019)
文摘A modified snap-through mechanism is used in an electromagnetic energy harvester to improve its effectiveness. It mainly comprises three springs that are configured so that the potential energy of the system has two stable equilibrium points. In particular, the small vibration behavior of the harvester around one of the equilibriums is of interest. A multi-scale method(MSM) is used to analyze the frequency response curve. Two snap-through mechanisms are considered. One has both horizontal and vertical springs. The other has only horizontal springs. The frequency response curves of these two classes are compared under the same excitation and electric loading conditions. The latter exhibits more bending of the frequency response curve than the former one. The results are also validated by some numerical work. The averaged power subject to the Gaussian white noise is calculated numerically, and the results demonstrate that bi-stable energy harvesting with only horizontal springs can outperform the mechanism with both horizontal and vertical springs for the same distance between two equilibriums.
文摘Nonlinear solution of reinforced concrete structures, particularly complete load-deflection response, requires tracing of the equilibrium path and proper treatment of the limit and bifurcation points. In this regard, ordinary solution techniques lead to instability near the limit points and also have problems in case of snap-through and snap-back. Thus they fail to predict the complete load-displacement response. The arc-length method serves the purpose well in principle, received wide acceptance in finite element analysis, and has been used extensively. However modifications to the basic idea are vital to meet the particular needs of the analysis. This paper reviews some of the recent developments of the method in the last two decades, with particular emphasis on nonlinear finite element analysis of reinforced concrete structures.
基金supported by the National Key Research and Development Program ofChina(Grant No.2020YFB1312900)the National Natural Science Foundation of China(Grant Nos.12272096,11932015)the Shanghai Pilot Program forBasicResearch-Fudan University 21TQ1400100-22TQ009.
文摘Multi-stable origami structures and metamaterials possess unique advantages and could exhibit multiple stable three-dimensional configurations,which have attracted widespread research interest and held promise for applications in many fields.Although a great deal of attention has been paid to the design and application of multi-stable origami structures,less knowledge is available about the transition sequence among different stable configurations,especially in terms of the fundamental mechanism and the tuning method.To fill this gap,with the multi-stable dual-cell stacked Miura-ori chain as a platform,this paper explores the rules that govern the configuration transition and proposes effective methods for tuning the transition sequence.Specifically,by correlating the energy evolution,the transition paths,and the associated force-displace-ment profiles,we find that the critical extension/compression forces of the component cells play a critical role in governing the transition sequence.Accordingly,we summarize the rules for predicting the transition sequence:the component cell that first reaches the critical force during quasi-static extension or compression will be the first to undergo a configuration switch.Based on these findings,two methods,i.e.,a design method based on crease-stiffness assignment and an online method based on internal pressure regulation,are proposed to tune the stability profile and the transition sequence of the multi-stable origami structure.The crease-stiffness design approach,although effective,cannot be employed for online tuning once the prototype has been fabricated.The pressure-based approach,on the other hand,has been shown experimentally to be effective in adjusting the constitutive force-displacement profiles of the component cells and,in turn,tuning the transition sequence according to the summarized rules.The results of this study will advance the state of the art of origami mechanics and promote the engineering applications of multi-stable origami metamaterials.
基金Project(12 High-tech Urban C11) supported by High-tech Urban Development Program of Ministry of Land,Transport and Maritime Affairs,Korea
文摘The buckling behavior of single layer space structure is very sensitive. The joint rigidity, moreover, is one of the main factors of stability which may determine the entire failure behavior. Thus, the reasonable stiffness of joint system, which is neither total pin assumption nor perfect fix condition, is very important to apply to the real single layer space one. Therefore, the purpose of this work was to investigate the buckling behavior of single layer space structure, using the development of the upgraded stiffness matrix for the joint rigidity. To derive tangential stiffness matrix, a displacement function was assumed using translational and rotational displacement at the node. The geometrical nonlinear analysis was simulated not only with perfect model but also with imperfect one. As a result, the one and two free nodal numerical models were investigated using derived stiffness matrix. It was figured out that the buckling load increases in proportion to joint rigidity with rise-span ratio. The stability of numerical model is very sensitive with the initial imperfection, responding of bifurcation in the structure.
文摘Flexoelectricity is present in nonuniformly deformed dielectric materials and has size-dependent properties, making it useful for microelectromechanical systems. Flexoelectricity is small compared to piezoelectricity;therefore, producing a large-scale flexoelectric effect is of great interest. In this paper, we explore a way to enhance the flexoelectric effect by utilizing the snap-through instability and a stiffness gradient present along the length of a curved dielectric plate. To analyze the effect of stiffness profiles on the plate, we employ numerical parameter continuation. Our analysis reveals a nonlinear relationship between the effective electromechanical coupling coefficient and the gradient of Young’s modulus. Moreover, we demonstrate that the quadratic profile is more advantageous than the linear profile. For a dielectric plate with a quadratic profile and a modulus gradient of − 0.9, the effective coefficient can reach as high as 15.74 pC/N, which is over three times the conventional coupling coefficient of piezoelectric material. This paper contributes to our understanding of the amplification of flexoelectric effects by harnessing snapping surfaces and stiffness gradient design.
基金Project supported by the National Natural Science Foundation of China(Nos.11832002 and 12072201)。
文摘The snap-through behaviors and nonlinear vibrations are investigated for a bistable composite laminated cantilever shell subjected to transversal foundation excitation based on experimental and theoretical approaches.An improved experimental specimen is designed in order to satisfy the cantilever support boundary condition,which is composed of an asymmetric region and a symmetric region.The symmetric region of the experimental specimen is entirely clamped,which is rigidly connected to an electromagnetic shaker,while the asymmetric region remains free of constraint.Different motion paths are realized for the bistable cantilever shell by changing the input signal levels of the electromagnetic shaker,and the displacement responses of the shell are collected by the laser displacement sensors.The numerical simulation is conducted based on the established theoretical model of the bistable composite laminated cantilever shell,and an off-axis three-dimensional dynamic snap-through domain is obtained.The numerical solutions are in good agreement with the experimental results.The nonlinear stiffness characteristics,dynamic snap-through domain,and chaos and bifurcation behaviors of the shell are quantitatively analyzed.Due to the asymmetry of the boundary condition and the shell,the upper stable-state of the shell exhibits an obvious soft spring stiffness characteristic,and the lower stable-state shows a linear stiffness characteristic of the shell.
基金Project supported by the National Natural Science Foundation of China(Nos.11832002 and 12072201)。
文摘The chaotic dynamic snap-through and complex nonlinear vibrations are investigated in a rectangular asymmetric cross-ply bistable composite laminated cantilever shell,in cases of 1:2 inter-well internal resonance and primary resonance.The transverse foundation excitation is applied to the fixed end of the structure,and the other end is in a free state.The first-order approximate multiple scales method is employed to perform the perturbation analysis on the dimensionless two-degree-of-freedom ordinary differential motion control equation.The four-dimensional averaged equations are derived in both polar and rectangular coordinate forms.Deriving from the obtained frequency-amplitude and force-amplitude response curves,a detailed analysis is conducted to examine the impacts of excitation amplitude,damping coefficient,and tuning parameter on the nonlinear internal resonance characteristics of the system.The nonlinear softening characteristic is exhibited in the upper stable-state,while the lower stable-state demonstrates the softening and linearity characteristics.Numerical simulation is carried out using the fourth-order Runge-Kutta method,and a series of nonlinear response curves are plotted.Increasing the excitation amplitude further elucidates the global bifurcation and chaotic dynamic snap-through characteristics of the bistable cantilever shell.
基金Project supported by the National Natural Science Foundation of China(Nos.12293000,12293001,11988102,12172006,and 12202011)。
文摘The dynamic model of a bistable laminated composite shell simply supported by four corners is further developed to investigate the resonance responses and chaotic behaviors.The existence of the 1:1 resonance relationship between two order vibration modes of the system is verified.The resonance response of this class of bistable structures in the dynamic snap-through mode is investigated,and the four-dimensional(4D)nonlinear modulation equations are derived based on the 1:1 internal resonance relationship by means of the multiple scales method.The Hopf bifurcation and instability interval of the amplitude frequency and force amplitude curves are analyzed.The discussion focuses on investigating the effects of key parameters,e.g.,excitation amplitude,damping coefficient,and detuning parameters,on the resonance responses.The numerical simulations show that the foundation excitation and the degree of coupling between the vibration modes exert a substantial effect on the chaotic dynamics of the system.Furthermore,the significant motions under particular excitation conditions are visualized by bifurcation diagrams,time histories,phase portraits,three-dimensional(3D)phase portraits,and Poincare maps.Finally,the vibration experiment is carried out to study the amplitude frequency responses and bifurcation characteristics for the bistable laminated composite shell,yielding results that are qualitatively consistent with the theoretical results.
基金supported by the National Natural Science Foundation of China (11032001)
文摘The deformation and snap-through behaviour of a thin-walled elastic spherical shell statically compressed on a flat surface or impacted against a fiat surface are studied the- oretically and numerically in order to estimate the influence of the dynamic effects on the response. A table tennis ball is considered as an example of a thin-walled elastic shell. It is shown that the increase of the impact velocity leads to a variation of the deformed shape thus resulting in larger de- formation energy. The increase of the contact force is caused by both the increased contribution of the inertia forces and contribution of the increased deformation energy. The contact force resulted from deformation/inertia of the ball and the shape of the deformed region are calcu- lated by the proposed theoretical models and compared with the results from both the finite element analysis and some previously obtained experimental data. Good agreement is demonstrated.
基金National Natural Science Foundation of China,12225206,Yihui Zhang,12050004,Yihui Zhang,11921002,Yihui Zhangthe Tsinghua National Laboratory for Information Science and Technology,the Henry Fok Education Foundation,171003,Yihui Zhangthe Institute for Guo Qiang,Tsinghua University,2019GQG1012,Yihui Zhang.
文摘Three-dimensional(3D)mesostructures with distinct compressive deformation behaviors and tunable mechanical responses have gained increasing interest in recent years.3D cage-shaped mesostructures are representative framework structures widely exploited in 3D flexible electronics,owing to their unique cellular geometry and unusual mechanical responses.The snap-through behavior of cage-shaped mesostructures could potentially result in the performance degradation of electronics,while it could also be harnessed to design reconfigurable electronics.Due to the complicated deformation modes and random characteristics in experiments,the snap-through behavior of cage-shaped mesostructures remains largely unexplored,espe-cially in terms of probability-based analyses.In this work,we present a systematic study on the configuration evolution and snap-through of 3D cage-shaped mesostructures under out-of-plane compressions.Experimental and computational studies show the existence of two distinct deformation modes associated with the snap-through,which is controlled by the energy barrier based on the energetic analyses.Phase diagrams of the deformation modes decode how key geometric parameters and assembly strain affect the snap-through.Compressive experiments based on periodic arrays(10 × 10)of mesostructures provided a large amount of deformation data,allowing for statistical analyses of the snap-through behavior.These results provide new insights and useful guidelines for the design of 3D reconfigurable devices and multistable metamaterials based on 3D cage-shaped mesostructures.
基金financial support from the National Science Foundation of the United State (Grants 1752575 and 1644579)
文摘Double-clamped bistable buckled beams demonstrate great versatility in various fields such as robotics,energy harvesting,and microelectromechanical system(MEMS).However,their design often requires time-consuming and expensive computations.In this work,we present a method to easily and rapidly design bistable buckled beams subjected to a transverse point force.Based on the Euler–Bernoulli beam theory,we establish a theoretical model of bistable buckled beams to characterize their snapthrough properties.This model is verified against the results from a finite element analysis(FEA)model,with maximum discrepancy less than 7%.By analyzing and simplifying our theoretical model,we derive explicit analytical expressions for critical behavioral values on the force-displacement curve of the beam.These behavioral values include critical force,critical displacement,and travel,which are generally sufficient for characterizing the snapthrough properties of a bistable buckled beam.Based on these analytical formulas,we investigate the influence of a bistable buckled beam's key design parameters,including its actuation position and precompression,on its critical behavioral values,with our results validated by FEA simulations.Our analytical method enables fast and computationally inexpensive design of bistable buckled beams and can guide the design of complicated systems that incorporate bistable mechanisms.
基金Project (No. 2012-0005418) supported by the Basic Science Re-search Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education,Science and Technology
文摘This study investigated characteristics of bifurcation and critical buckling load by shape imperfection of space truss,which were sensitive to initial conditions.The critical point and buckling load were computed by the analysis of the eigenvalues and determinants of the tangential stiffness matrix.The two-free-nodes example and star dome were selected for the case study in order to examine the nodal buckling and global buckling by the sensitivity to the eigen buckling mode and the analyses of the influence,and characteristics of the parameters as defined by the load ratio of the center node and surrounding node,as well as rise-span ratio were performed.The sensitivity to the imperfection of the initial shape of the two-free-nodes example,which occurs due to snapping at the critical point,resulted in bifurcation before the limit point due to the buckling mode,and the buckling load was reduced by the increase in the amount of imperfection.The two sensitive buckling patterns of the numerical model are established by investigating the displaced position of the free nodes,and the asymmetric eigenmode greatly influenced the behavior of the imperfection shape whether it was at limit point or bifurcation.Furthermore,the sensitive mode of the two-free-nodes example was similar to the in-extensional basis mechanism of a simplified model.The star dome,which was used to examine the influence among several nodes,indicated that the influence of nodal buckling was greater than that of global buckling as the rise-span ratio was higher.Besides,global buckling is occurred with reaching bifurcation point as the value of load ratio was higher,and the buckling load level was about 50%-70% of load level at limit point.
基金the National Key Research and Development Program of China(2019YFB1311600)Natural Science Foundation of China(Grant No.11902248 and 52075411)+1 种基金Shaanxi Key Research and Development Program(2020ZDLGY06-11)the State Key Laboratory for Strength and Vibration of Mechanical Structures(SV2018-KF-08).
文摘Dielectric elastomer actuators have attracted growing interest for soft robot due to their large deformation and fast response.However,continuous high-voltage loading tends to cause the electric breakdown of the actuator due to heat accumulation,and viscoelasticity complicates precise control.The snap-through bistability of the Venus flytrap is one of the essential inspirations for bionic structure,which can be adopted to improve the shortcoming of dielectric elastomer actuators and develop a new actuation structure with low energy consumption,variable configuration,and multi-mode actuation.Hence,in this paper,the structural design principles of electroactive bistable actuators are first presented based on the total potential energy of the structure.Following that,a feasible design parameter region is provided,the influence of crucial parameters on the actuation stroke,trigger voltage,and actuation charge are discussed.Finally,according to the coupling relationship between the bending stiffness and the bistable property of the actuator,the adjusting methods of bistable actuation are explored.A qualitative experiment was performed to verify the feasibility and correctness of the bistable design methodology and the actuation regulation strategy.This study provides significant theoretical guidance and technical support for developing and applying dielectric elastomer actuators with multi-mode,high-performance,and long-life characteristics.
