Limit cycle oscillations （LCOs） as well as nonlinear aeroelastic analysis of a 3-DOF aeroelastic airfoil motion with cubic restoring moments in the pitch degree of freedom are investigated. Aeroelastic equations of ...Limit cycle oscillations （LCOs） as well as nonlinear aeroelastic analysis of a 3-DOF aeroelastic airfoil motion with cubic restoring moments in the pitch degree of freedom are investigated. Aeroelastic equations of an airfoil with control surface in an incompressible potential flow are presented in the time domain. The harmonic balance （HB） method is utilized to calculate the LCO frequency and amplitude for the airfoil. Also the semi-analytical method has revealed the presence of stable and unstable limit cycles, along with stability reversal in the neighborhood of a Hopf bifurcation. The system response is determined by nu- merically integrating the governing equations using a standard Runge-Kutta algorithm and the obtained results are compared with the HB method. Also the results by the third order HB （HB3） method for control surface are consistent with the other numerical solution. Finally, by combining the numerical and the HB methods, types of bifiarcation, be it supercritical, subcritical, or diver- gent flutter area are identified.展开更多
压电俘能器能够为自然界中低功率的微机电系统持续供能.为了模拟机翼的沉浮-俯仰二自由度运动和有效俘获气动弹性振动能量,本文提出一种新颖的翼型颤振压电俘能器.基于非定常气动力模型,推导翼型颤振压电俘能器流-固-电耦合场的数学模型...压电俘能器能够为自然界中低功率的微机电系统持续供能.为了模拟机翼的沉浮-俯仰二自由度运动和有效俘获气动弹性振动能量,本文提出一种新颖的翼型颤振压电俘能器.基于非定常气动力模型,推导翼型颤振压电俘能器流-固-电耦合场的数学模型.建立有限元模型,模拟机翼的沉浮-俯仰二自由度运动,获得机翼附近的涡旋脱落和流场特性.搭建风洞实验系统,制作压电俘能器样机.利用实验验证理论和仿真模型的正确性,仿真分析压电俘能器结构参数对其气动弹性振动响应和俘获性能的影响.结果表明:理论分析、仿真模拟和实验研究获得的输出电压具有较好的一致性,验证建立数学和仿真模型的正确性.仿真分析获得机翼附近的压力场变化云图,表明交替的压力差驱动机翼发生二自由度沉浮-俯仰运动.当风速超过颤振起始速度时,压电俘能器发生颤振,并表现为极限环振荡.当偏心距为0.3和风速为16 m/s时,可获得最大输出电压为17.88 V和输出功率为1.278 m W.功率密度为7.99 m W/cm^(3),相比较于其他压电俘能器,能实现优越的俘获性能.研究结果对设计更高效的翼型颤振压电俘能器提供重要的指导意义.展开更多
This paper studies the application of mathematical models to analyze the vortex-induced vibrations of the tendons of a given TLP along the Indian coastline, by using an analytical approach, using MATLAB. The tendon is...This paper studies the application of mathematical models to analyze the vortex-induced vibrations of the tendons of a given TLP along the Indian coastline, by using an analytical approach, using MATLAB. The tendon is subjected to a steady current load, which causes vortex-shedding downstream, leading to cross-flow vibrations. The magnitude of the excitation(lift and drag coefficients) depends on the vortex-shedding frequency. The resulting vibration is studied for possible resonant behavior. The excitation force is quantified empirically, the added mass by potential flow hydrodynamics, and the vibration by normal mode summation method. Non-linear viscous damping of the water is considered. The non-linear oscillations are studied by the phase-plane method, investigating the limit-cycle oscillations. The stable/unstable regions of the dynamic behavior are demarcated. The modal contribution to the total deflection is studied to establish the possibility of resonance of one of the wet modes with the vortex-shedding frequency.展开更多
A typical airfoil section system with freeplay is investigated in the paper. The classic quasi-steady flow model is applied to calculate the aerodynamics, and a piecewise-stiffness model is adopted to characterize the...A typical airfoil section system with freeplay is investigated in the paper. The classic quasi-steady flow model is applied to calculate the aerodynamics, and a piecewise-stiffness model is adopted to characterize the non- linearity of the airfoil section＇s freeplay. There are two crit- ical speeds in the system, i.e., a lower critical speed, above which the system might generate limit cycle oscillation, and an upper critical one, above which the system will flutter. Then a Poincar6 map is constructed for the limit cycle os- cillations by using piecewise-linear solutions with and with- out contact in the system. Through analysis of the Poincar6 map, a series of equations which can determine the frequen- cies of period-1 limit cycle oscillations at any flight veloc- ity are derived. Finally, these analytic results are compared to the results of numerical simulations, and a good agree- ment is found. The effects of freeplay value and contact stiffness ratio on the limit cycle oscillation are also analyzed through numerical simulations of the original system. More- over, there exist multi-periods limit cycle oscillations and even complicated ＂chaotic＂ oscillations may occur, which are usually found in smooth nonlinear dynamic systems.展开更多
文摘Limit cycle oscillations （LCOs） as well as nonlinear aeroelastic analysis of a 3-DOF aeroelastic airfoil motion with cubic restoring moments in the pitch degree of freedom are investigated. Aeroelastic equations of an airfoil with control surface in an incompressible potential flow are presented in the time domain. The harmonic balance （HB） method is utilized to calculate the LCO frequency and amplitude for the airfoil. Also the semi-analytical method has revealed the presence of stable and unstable limit cycles, along with stability reversal in the neighborhood of a Hopf bifurcation. The system response is determined by nu- merically integrating the governing equations using a standard Runge-Kutta algorithm and the obtained results are compared with the HB method. Also the results by the third order HB （HB3） method for control surface are consistent with the other numerical solution. Finally, by combining the numerical and the HB methods, types of bifiarcation, be it supercritical, subcritical, or diver- gent flutter area are identified.
文摘压电俘能器能够为自然界中低功率的微机电系统持续供能.为了模拟机翼的沉浮-俯仰二自由度运动和有效俘获气动弹性振动能量,本文提出一种新颖的翼型颤振压电俘能器.基于非定常气动力模型,推导翼型颤振压电俘能器流-固-电耦合场的数学模型.建立有限元模型,模拟机翼的沉浮-俯仰二自由度运动,获得机翼附近的涡旋脱落和流场特性.搭建风洞实验系统,制作压电俘能器样机.利用实验验证理论和仿真模型的正确性,仿真分析压电俘能器结构参数对其气动弹性振动响应和俘获性能的影响.结果表明:理论分析、仿真模拟和实验研究获得的输出电压具有较好的一致性,验证建立数学和仿真模型的正确性.仿真分析获得机翼附近的压力场变化云图,表明交替的压力差驱动机翼发生二自由度沉浮-俯仰运动.当风速超过颤振起始速度时,压电俘能器发生颤振,并表现为极限环振荡.当偏心距为0.3和风速为16 m/s时,可获得最大输出电压为17.88 V和输出功率为1.278 m W.功率密度为7.99 m W/cm^(3),相比较于其他压电俘能器,能实现优越的俘获性能.研究结果对设计更高效的翼型颤振压电俘能器提供重要的指导意义.
文摘This paper studies the application of mathematical models to analyze the vortex-induced vibrations of the tendons of a given TLP along the Indian coastline, by using an analytical approach, using MATLAB. The tendon is subjected to a steady current load, which causes vortex-shedding downstream, leading to cross-flow vibrations. The magnitude of the excitation(lift and drag coefficients) depends on the vortex-shedding frequency. The resulting vibration is studied for possible resonant behavior. The excitation force is quantified empirically, the added mass by potential flow hydrodynamics, and the vibration by normal mode summation method. Non-linear viscous damping of the water is considered. The non-linear oscillations are studied by the phase-plane method, investigating the limit-cycle oscillations. The stable/unstable regions of the dynamic behavior are demarcated. The modal contribution to the total deflection is studied to establish the possibility of resonance of one of the wet modes with the vortex-shedding frequency.
基金supported by the National Science Fund for Distinguished Young Scholars in China(11225212)the Young Teachers' Funds of Hunan Province,China
文摘A typical airfoil section system with freeplay is investigated in the paper. The classic quasi-steady flow model is applied to calculate the aerodynamics, and a piecewise-stiffness model is adopted to characterize the non- linearity of the airfoil section＇s freeplay. There are two crit- ical speeds in the system, i.e., a lower critical speed, above which the system might generate limit cycle oscillation, and an upper critical one, above which the system will flutter. Then a Poincar6 map is constructed for the limit cycle os- cillations by using piecewise-linear solutions with and with- out contact in the system. Through analysis of the Poincar6 map, a series of equations which can determine the frequen- cies of period-1 limit cycle oscillations at any flight veloc- ity are derived. Finally, these analytic results are compared to the results of numerical simulations, and a good agree- ment is found. The effects of freeplay value and contact stiffness ratio on the limit cycle oscillation are also analyzed through numerical simulations of the original system. More- over, there exist multi-periods limit cycle oscillations and even complicated ＂chaotic＂ oscillations may occur, which are usually found in smooth nonlinear dynamic systems.
