组合悬臂板的非线性振动响应

为研究电机升高片,发动机凸肩叶片的非线性振动特征,将其简化成组合悬臂板模型,应用弹性薄板理论,推导出考虑阻尼、几何大变形的三个互相耦合的非线性振动微分方程.再使用Galerkin法获得广义坐标中的非线性方程组,采取Runge-Kutta数值分析方法获得了组合悬臂板非线性振动响应和幅频特性曲线.结果表明:由于几何非线性因素对系统的影响,非线性的振动响应小于线性振动响应;非线性共振频率大于固有频率,但仍在组合板各阶固有频率附近;非线性幅频特性曲线具有多值性和跳跃性,其形状与激振力大小有关.

Nonlinear Vibration Response of Combination Cantilever Plates

Considering the shrouded blades of aeronautic engine and roll's lifting motor tray as combination cantilever plates,three coupled nonlinear differential equations of motion of cantilever plates are derived from the theory of thin elastic plate with the effects of damping and geometric large-amplitude vibration taken into account.Then,the Galerkin method is introduced to obtain nonlinear equations in the generalized coordinates.The nonlinear vibration response of combination cantilever plates is analyzed by the Runge-Kutta numerical method to obtain the frequency-response curves.The results show that the geometrical nonlinear effect on the system makes the nonlinear vibration response less than linear one,and the nonlinear resonant frequency is slightly higher than the nature frequencies of each of the combination cantilever plates.The nonlinear frequency-response curve shows the multi-value and jumping characteristic,and its shape relates to the amplitude of exciting force.