提出一种用于求解任意边界条件下带有任意集中质量的连续多跨梁的自振特性的方法。求解过程为:运用改进的傅里叶级数法(Improved Fourier Series Method,IFSM)确定梁的位移形函数,通过Rayleigh-Ritz法得到梁的拉格朗日方程,然后利用Hami...提出一种用于求解任意边界条件下带有任意集中质量的连续多跨梁的自振特性的方法。求解过程为:运用改进的傅里叶级数法(Improved Fourier Series Method,IFSM)确定梁的位移形函数,通过Rayleigh-Ritz法得到梁的拉格朗日方程,然后利用Hamilton原理得到频率特征矩阵,通过求解广义特征值求得自振频率及位移振型。随后,对所提出的方法的收敛性和精度进行讨论,与现有文献中的方法对比,该方法具有计算精度较高、收敛性好、收敛速度快等特点。讨论不同边界条件下截断数、跨数以及频率阶数之间的关系。最后通过工程中的实际案例说明该方法的实用性,与现有文献对比可知,其精度可达99.9%以上,由此验证了该方法的可靠性以及适用性。该方法易于通过编程实现快速计算,可为工程运用提供便捷有效的理论支撑。展开更多
The dynamic vibration absorber with inerter and grounded stiffness(IGDVA)is used to control a two-scale system subject to a weak periodic perturbation.The vibration suppression effect is remarkable.The amplitude of th...The dynamic vibration absorber with inerter and grounded stiffness(IGDVA)is used to control a two-scale system subject to a weak periodic perturbation.The vibration suppression effect is remarkable.The amplitude of the main system coupled with absorber is significantly reduced,and the high frequency vibration completely disappears.First,through the slow-fast analysis and stability theory,it is found that the stability of the autonomous system exerts a notable regulating effect on the vibration response of the non-autonomous system.After adding the dynamic vibrator absorber,the center in the autonomous system changes to an asymptotically stable focus,consequently suppressing the vibration in the non-autonomous system.Further research reveals that the parameters of the absorber affect the real parts of the eigenvalues of the autonomous system,thereby regulating the stability of the system.Transitioning from a qualitative standpoint to a quantitative approach,a comparison of the solutions before and after the introduction of the dynamic absorber reveals that,when the grounded stiffness ratio and the mass ratio of the dynamic absorber are not equal,the high-frequency part in the analytical solution disappears.As a result,this leads to a reduction in the amplitude of the trajectory,achieving a vibration reduction effect.展开更多
文摘提出一种用于求解任意边界条件下带有任意集中质量的连续多跨梁的自振特性的方法。求解过程为:运用改进的傅里叶级数法(Improved Fourier Series Method,IFSM)确定梁的位移形函数,通过Rayleigh-Ritz法得到梁的拉格朗日方程,然后利用Hamilton原理得到频率特征矩阵,通过求解广义特征值求得自振频率及位移振型。随后,对所提出的方法的收敛性和精度进行讨论,与现有文献中的方法对比,该方法具有计算精度较高、收敛性好、收敛速度快等特点。讨论不同边界条件下截断数、跨数以及频率阶数之间的关系。最后通过工程中的实际案例说明该方法的实用性,与现有文献对比可知,其精度可达99.9%以上,由此验证了该方法的可靠性以及适用性。该方法易于通过编程实现快速计算,可为工程运用提供便捷有效的理论支撑。
基金Project supported by the National Natural Science Foundation of China(Nos.12172233 and U1934201)。
文摘The dynamic vibration absorber with inerter and grounded stiffness(IGDVA)is used to control a two-scale system subject to a weak periodic perturbation.The vibration suppression effect is remarkable.The amplitude of the main system coupled with absorber is significantly reduced,and the high frequency vibration completely disappears.First,through the slow-fast analysis and stability theory,it is found that the stability of the autonomous system exerts a notable regulating effect on the vibration response of the non-autonomous system.After adding the dynamic vibrator absorber,the center in the autonomous system changes to an asymptotically stable focus,consequently suppressing the vibration in the non-autonomous system.Further research reveals that the parameters of the absorber affect the real parts of the eigenvalues of the autonomous system,thereby regulating the stability of the system.Transitioning from a qualitative standpoint to a quantitative approach,a comparison of the solutions before and after the introduction of the dynamic absorber reveals that,when the grounded stiffness ratio and the mass ratio of the dynamic absorber are not equal,the high-frequency part in the analytical solution disappears.As a result,this leads to a reduction in the amplitude of the trajectory,achieving a vibration reduction effect.
