Euler-Bernoulli梁模态公式的修正  

MODIFICATION OF THE MODE SHAPE EXPRESSIONS FOR EULER-BERNOULLI BEAMS

作　　者：毛崎波[1] MAO Qibo(School of Aircraft Engineering,Nanchang Hangkong University,Nanchang 330063,China)

机构地区：[1]南昌航空大学飞行器工程学院,南昌330063

出　　处：《力学与实践》2025年第1期233-237,共5页Mechanics in Engineering

基　　金：国家自然科学基金(12364058,51975266);航空科学基金项目(2020Z073056001)资助。

摘　　要：在机械振动教科书给出Euler-Bernoulli梁的模态表达式中,除了简支梁,一般只能计算前12阶模态。主要原因是由于模态表达式中存在双曲正弦和双曲余弦函数,双曲函数随模态阶数呈指数增加,由此引起的舍入误差导致数值计算时模态形状失真。本文提出对传统的模态表达式进行修正,从而可以精确计算至少前200阶模态。In most vibration text books,the expressions for mode shape functions of Euler-Bernoulli beams in numerical evaluation can only be accurate up to the first 12 modes except for simply-supported boundary condition.The main reason is that these expressions involve the hyperbolic sine and cosine functions,which increase exponentialy as mode index increases.The mode shapes in numerical calculation will distort due to the round-off errors.In this paper,these functions are modified in a different form.With proposed modified expressions,the modes for a vibrating beam can be calculated accurately up to at least the 200th mode.

关 键 词：EULER-BERNOULLI梁 高阶模态 舍入误差 边界条件 模态形状 

分 类 号：O312[理学—一般力学与力学基础]