梁的强迫振动问题Green函数解及应用研究综述

Review of Green Function Solutions and Applications for Forced Vibration of Beams

工程系统中梁结构经常处于各种激励的作用,因而梁结构在这种环境下不可避免地发生着各种各样的强迫振动.在梁结构发生振动的过程中,其自身会受到的温度、湿度、电磁场、裂纹等众多内外部因素的影响,而众多内外部因素就构成梁的多物理场耦合环境.在多场耦合环境下,Green函数法作为一种解析方法在研究梁的多场耦合振动问题方面具有优势,有利于讨论力、电、热、裂纹等因素作用下梁的振动特性和多场耦合特性.Green函数法相比于模态叠加法,优点在于能够得到完整且精度较高的解析解,具有收敛性好,运算快的特点.本文主要阐述Green函数在梁的强迫振动、热力耦合振动、力电耦合振动、裂纹梁振动等研究问题上取得了大量的理论和工程研究成果.本文以裂纹为内因,热、力、电为外因进行分类,阐述了在内外因影响下梁的强迫振动问题Green函数解的研究现状,从而让读者进一步系统性的了解Green函数法在振动领域中的广泛应用,以及了解该方法本身的特色和优势奠定基础.

Beam structures in engineering system are usually suffered by various complex loads,and these loads induces many kinds of forced vibration of beam structures in this environment inevitably.When forced vibrations are occurred,these forced vibrations are affected by many factors such as temperature,humidity,electromagnetic field,cracks,etc.,and these factors constitute multi-physical fields of beam structures.In multi-physical fields'environment,as a good analytical mathematical tool,the Green's function method has advantages to solve multi-field coupled forced vibrations of beam structures,and has good performances to discuss vibration characteristics and coupled characteristics of beam structures under actions of external forces,electricity,heat and cracks are discussed.Compared with modal superposition method,the Green's function method has advantages that it can obtain complete and high precision analytical solution,and has characteristics of good convergence and fast operation.This paper mainly reviewed a large number of theoretical and engineering research results of the Green's function method on research problems of forced vibrations,thermodynamic coupled vibrations,electro-mechanical coupled vibrations,cracked beam vibrations,and so on.