运动梯形板的自由振动

Free vibration on trapezoid plates with motion

以往对运动二维结构动力学的研究局限于矩形板,且运动效应仅关注单一方向,故研究了梯形板固有振动的运动效应,分别考察了两个方向上的运动速度对固有振动的影响。从Minldin板理论出发,将预应力统一到系统势能,应用虚功原理建立了双向运动梯形板的控制方程,其中运动效应体现为科氏力项和离心力项。为应对控制方程在梯形边界情况下的求解挑战,采用8节点等参坐标变换技术将求解域映射为矩形,进而利用微分求积法将控制方程离散为代数方程组。数值结果以四边固支的边界条件为例,与ANSNYS结果对比证实了该方法的准确性。研究发现:运动效应对梯形板振动有削弱作用,且与速度方向密切相关;预应力与振动频率正相关,且与模态相关。

In the past,the study of the dynamics of moving two-dimensional structures was limited to rectangular plates,and the motion effect was only concerned only on a single direction.In this paper,the motion effect of natural vibration of trapezoidal plate is studied,and the influence of velocity in two directions on natural vibration is investigated.Based on the theory of Minldin plate,the governing equation of bidirectional moving trapezoid plate is established by applying the principle of virtual work.The motion effect is Coriolis force term and centrifugal force term.In order to deal with the challenge of solving the governing equations with trapezoidal boundary,the 8-node isorametric coordinate transformation technology is used to transform the solution domain into a rectangle,and then the governing equations are discretized into algebraic equations by differential quadrature method.The numerical results are compared with the ANSNYS results to verify the accuracy of the proposed method in the boundary of four edges fixed.It is found that the motion effect weakens the vibration of trapezoidal plate,and it is closely related to the velocity direction.Pre-stress is positively correlated with vibration frequency and mode.