基于微分变换法的变截面梁振动研究及有限元数值模拟

Vibration Research and Finite Element Numerical Simulation of Variable Section Beam Based on Differential Transformation Method

基于微分变换法推导出圆形变截面材料棒横振动偏微分方程的级数解,由简支边界条件,确定出级数解的各项系数,并得到一阶固有频率和振型;利用有限元分析软件Abaqus 6.14进行建模,通过其动力学模态分析获得了一阶固有频率和振型图;二者对比结果表明,基于微分变换法求解变截面梁振动偏微分方程求解具有较高的精度。

The series solution of the partial differential equation of the transverse vibration of a circularly variable cross-section material is derived based on the differential transformation method(DTM).The coefficients of the series solution are determined by the simple boundary condition,and the first-order natural frequency and mode shape are obtained.The finite element analysis software Abaqus 6.14 was modeled,and the first-order natural frequency and mode shape were obtained by its dynamic modal analysis.The comparison results show that the DTM is effective for solving the differential partial equations of variable cross-section beams.