轴向运动正六边形板的自由振动

本文研究了在轴向运动激励下正六边形薄板的横向自由振动问题。应用Reddy三阶剪切变形板理论刻画板的力学状态,采用6节点三角形单元离散求解域,利用虚功原理建立系统的动力学有限元方程。数值算例选取2种典型布置形式,并分别考虑固支和简支2种边界条件。通过求解系统方程得到了前四阶固有频率,经与ANSYS计算结果对比,验证了本研究方法的准确性。研究发现,速度通过离心力和科氏力影响系统固有振动,且速度与各阶频率反相关。正六边形板的第二和第三阶振动分别有2种模态,速度为零时其固有频率相同,但随着速度的增大逐渐分离。本文揭示的若干动力学现象可为轴向运动正六边形薄板的设计和优化提供参考。

Free Vibration on Regular Hexagonal Thin Plates in Axial Motion

The transverse free vibration of a regular hexagonal thin plate under axial motion excitation was studied. In order to account for the effect of transverse shear deformation, Reddy''s third-order shear deformation plate theory was applied, and 6-node triangular elements were used to discretize the domain. The dynamic finite element equation of the system was established by virtual work principle. In the numerical example, two typical layout forms were selected, and two boundary conditions of fixed support and simple support were considered. The first four order natural frequencies were obtained by solving the system equation numerically. The accuracy of the proposed method was verified by comparing with ANSYS results. It was found that the velocity affects the natural vibration of the system through centrifugal force and Coriolis force, and the velocity is inversely correlated with each order frequency. In addition, it was found that the second and third order frequencies of the regular hexagonal plate have two modes respectively. When the speed is zero, the natural frequencies are the same, but with the increase of the speed, the corresponding frequencies of the two modes gradually separate. Some dynamic phenomena revealed can provide reference for the design and optimization of axially moving regular hexagonal thin plates.