轴向运动正三角形Mindlin板的自由振动

Free Vibration of Axially Moving Equilateral Regular Triangle Mindlin Plate

基于Mindlin板理论和有限元法研究了轴向运动正三角形板的自由振动问题.利用虚功原理推导轴向运动正三角形板横向自由振动的有限元方程,在三边简支边界条件下研究系统自由振动特性.算例部分,针对两种常见布置形式,首先求解板无轴向速度时的前四阶固有频率,并将其与ANSYS软件计算结果对比,证实了所给方法的准确性;随后重点探讨了速度和布置形式对前四阶固有频率的实部和虚部的影响.结果显示:速度与板受到的离心力与科氏力密切相关,在这两种力的共同作用下,速度越大,固有频率越小;第二阶振动对应不同的模态,低速时频率相同,高速时频率发散;布置形式对振动有一定影响.

Based on Mindlin plate theory and finite element method,the free vibration of axially moving equilateral triangle plates is studied.The principle of virtual work is used to derive the finite element equation of transverse free vibration of an equilateral triangle plate moving axially and study the free vibration characteristics of the system under the condition of three-sided simply-supported boundary.In the calculation part,aiming at two common layout forms,the first four order natural frequencies of the non-axial velocity of the plate are solved,and the results are compared with the calculation results of ANSYS software to verify the accuracy of the proposed method.Then the effects of velocity and layout forms on the real and imaginary parts of the first four natural frequencies are discussed.The results show that the velocity is closely related to the centrifugal force and Coriolis force on the plate.Under the combined action of these two forces,the higher the velocity,the lower the natural frequency.The second order vibration corresponds to different modes,with the same frequency at low speed and divergent frequency at high speed.The layout form has certain influence on vibration.