A novel oscillator structure, bimorph piezoelectric cantilever beam with two-stepped variable thicknesses,is proposed to improve the energy harvestingperformance of the vibration energy harvester (VEH) under low-frequ...A novel oscillator structure, bimorph piezoelectric cantilever beam with two-stepped variable thicknesses,is proposed to improve the energy harvestingperformance of the vibration energy harvester (VEH) under low-frequency vibration environment. Firstly, the piezoelectric cantilever is segmented to obtain the energy functions based on the Euler-Bernoulli beam assumptions, and the Galerkin approach is utilized to discretize the energy functions. Applying boundary conditions and continuity conditions enforced at separation locations, the electromechanical coupled governing equations for the piezoelectric energy harvesterareintroduced by means of the Lagrange equations. Furthermore, the steady state response expressions are obtained for harmonic base excitations at arbitrary frequencies. Numerical results are computed and the effects ofthe lengths-ratio, thicknesses-ratio,end thicknessand load resistance on the output voltage, harvested power and power density are discussed. Moreover, to verify thecorrectness ofanalytical results, the finite element method (FEM)simulationis also conducted to analyze performance of the proposed VEH, where a good agreement is presented. All the results show thatthe present oscillator structureis moreefficient than the conventional uniform beam structure, specifically, for vibration energy harvesting in low-frequency environment.展开更多
Since the 1960 s, mining science and technology in China has experienced two technical innovations, i.e.the ‘‘Masonry Beam Theory(MBT)" and ‘‘Transfer Rock Beam Theory(TRBT)". Based on those theories, th...Since the 1960 s, mining science and technology in China has experienced two technical innovations, i.e.the ‘‘Masonry Beam Theory(MBT)" and ‘‘Transfer Rock Beam Theory(TRBT)". Based on those theories, the conventional mining method(being called the 121 mining method) was established, consisting of excavating two tunnels with a pillar left for mining a working panel. However, with increasing mining depth,engineering geological disasters in the underground caverns have been frequently encountered. In addition, the use of the coal-pillar mining results in a large amount of coal resources unexploited. In order to address the problems above, the ‘‘Roof Cut Short-Arm Beam Theory(RCSBT), being called the 110 mining method)" was proposed by He Manchao in 2008. The 110 mining method features the mining of one coal seam panel, excavating necessarily only one roadway tunnel and leaving no pillars. Realization of the 110 mining method includes the following steps:(1) directional pre-splitting roof cutting,(2) supporting the roof by using high Constant Resistance Large Deformation bolt/cable(CRLD), and(3) blocking gangue by hydraulic props. This paper presents an overview of the principles, techniques and application of the 110 mining method. Special emphasis is placed on the numerical simulation of the geostress distribution found in the mining panel using the 110 method compared to that of the 121 method. In addition, the stress distribution on the ‘‘short beam" left by the roof cutting when performing the 110 method was also investigated using both numerical simulation and theoretical formulation.展开更多
The model and analysis of the cantilever beam adhesion problem under the action of electrostatic force are given. Owing to the nonlinearity of electrostatic force, the analytical solution for this kind of problem is...The model and analysis of the cantilever beam adhesion problem under the action of electrostatic force are given. Owing to the nonlinearity of electrostatic force, the analytical solution for this kind of problem is not available. In this paper, a systematic method of generating polynomials which are the exact beam solutions of the loads with di?erent distributions is provided. The polynomials are used to approximate the beam displacement due to electrostatic force. The equilibrium equation o?ers an answer to how the beam deforms but no information about the unstuck length. The derivative of the functional with respect to the unstuck length o?ers such information. But to compute the functional it is necessary to know the beam deformation. So the problem is iteratively solved until the results are converged. Galerkin and Newton-Raphson methods are used to solve this nonlinear problem. The e?ects of dielectric layer thickness and electrostatic voltage on the cantilever beam stiction are studied. The method provided in this paper exhibits good convergence. For the adhesion problem of cantilever beam without electrostatic voltage, the analytical solution is available and is also exactly matched by the computational results given by the method presented in this paper.展开更多
基金The authors gratefully acknowledge the support of the National Natural Science Foundation of China (Grants 11672008 and 11272016).
文摘A novel oscillator structure, bimorph piezoelectric cantilever beam with two-stepped variable thicknesses,is proposed to improve the energy harvestingperformance of the vibration energy harvester (VEH) under low-frequency vibration environment. Firstly, the piezoelectric cantilever is segmented to obtain the energy functions based on the Euler-Bernoulli beam assumptions, and the Galerkin approach is utilized to discretize the energy functions. Applying boundary conditions and continuity conditions enforced at separation locations, the electromechanical coupled governing equations for the piezoelectric energy harvesterareintroduced by means of the Lagrange equations. Furthermore, the steady state response expressions are obtained for harmonic base excitations at arbitrary frequencies. Numerical results are computed and the effects ofthe lengths-ratio, thicknesses-ratio,end thicknessand load resistance on the output voltage, harvested power and power density are discussed. Moreover, to verify thecorrectness ofanalytical results, the finite element method (FEM)simulationis also conducted to analyze performance of the proposed VEH, where a good agreement is presented. All the results show thatthe present oscillator structureis moreefficient than the conventional uniform beam structure, specifically, for vibration energy harvesting in low-frequency environment.
文摘Since the 1960 s, mining science and technology in China has experienced two technical innovations, i.e.the ‘‘Masonry Beam Theory(MBT)" and ‘‘Transfer Rock Beam Theory(TRBT)". Based on those theories, the conventional mining method(being called the 121 mining method) was established, consisting of excavating two tunnels with a pillar left for mining a working panel. However, with increasing mining depth,engineering geological disasters in the underground caverns have been frequently encountered. In addition, the use of the coal-pillar mining results in a large amount of coal resources unexploited. In order to address the problems above, the ‘‘Roof Cut Short-Arm Beam Theory(RCSBT), being called the 110 mining method)" was proposed by He Manchao in 2008. The 110 mining method features the mining of one coal seam panel, excavating necessarily only one roadway tunnel and leaving no pillars. Realization of the 110 mining method includes the following steps:(1) directional pre-splitting roof cutting,(2) supporting the roof by using high Constant Resistance Large Deformation bolt/cable(CRLD), and(3) blocking gangue by hydraulic props. This paper presents an overview of the principles, techniques and application of the 110 mining method. Special emphasis is placed on the numerical simulation of the geostress distribution found in the mining panel using the 110 method compared to that of the 121 method. In addition, the stress distribution on the ‘‘short beam" left by the roof cutting when performing the 110 method was also investigated using both numerical simulation and theoretical formulation.
文摘The model and analysis of the cantilever beam adhesion problem under the action of electrostatic force are given. Owing to the nonlinearity of electrostatic force, the analytical solution for this kind of problem is not available. In this paper, a systematic method of generating polynomials which are the exact beam solutions of the loads with di?erent distributions is provided. The polynomials are used to approximate the beam displacement due to electrostatic force. The equilibrium equation o?ers an answer to how the beam deforms but no information about the unstuck length. The derivative of the functional with respect to the unstuck length o?ers such information. But to compute the functional it is necessary to know the beam deformation. So the problem is iteratively solved until the results are converged. Galerkin and Newton-Raphson methods are used to solve this nonlinear problem. The e?ects of dielectric layer thickness and electrostatic voltage on the cantilever beam stiction are studied. The method provided in this paper exhibits good convergence. For the adhesion problem of cantilever beam without electrostatic voltage, the analytical solution is available and is also exactly matched by the computational results given by the method presented in this paper.
