智能悬臂梁横向振动的行波解  

WAVE PROPAGATION SOLUTION OF SMART CANTILEVER BEAMS TRANSVERSE VIBRATION

作　　者：郭兰满[1] 黄迪山[1] 唐亮[1] 朱晓锦[1] 

机构地区：[1]上海大学机电工程与自动化学院,上海200072

出　　处：《机械强度》2011年第6期815-821,共7页Journal of Mechanical Strength

基　　金：国家自然科学基金重大研究计划资助(90716027)~~

摘　　要：介绍智能梁的行波建模方法及其横向振动固有频率的计算方法。行波建模方法主要步骤包括,①求出Timoshenko梁横向振动方程的谐波解。②根据弯曲波的传播特性,给出弯曲波的传递关系;在智能梁上截面尺寸改变处和边界处,根据其连续条件和平衡条件,给出波的反射关系和透射关系。③通过联立智能梁内所有的传递、反射、透射关系,求得整体智能梁的特征方程。文中以智能悬臂梁为算例,通过解析法(包括Timoshenko梁模型和Euler-Bernoulli梁模型)与有限元法得到横向振动频率的比较,验证行波建模方法的有效性。此外,为考虑压电片材料对智能梁整体模型的影响,引入等效弹性模量。A smart beam is modeled by a wave propagation method,and is used for computing the natural frequency and mode of transverse vibration.The wave propagating modeling contains three steps.Firstly,a general solution in the form of harmonic is given from the governing equation of Timoshenko beam vibration.Secondly,in accordance with traveling manner of elastic bending wave,transfer matrices are determined.Also,the reflection and transmission incited by harmonic disturbance on those cross-section discontinuities and boundaries are derived respectively.Finally,all of these matrices are combined into the equation reflecting the global characteristic of the smart beam.Examples of cantilever beam are presented to illustrate the valid of wave propagation modeling by comparing analytical solutions of Timosheko beam with a FEA（finite element analysis） solution.To consider different materials in the smart beam where the foundational material is mixed with some piezoelectric components,an equivalent elastic modulus was applied in the model of smart beam as a whole.

关 键 词：行波法 TIMOSHENKO梁 智能梁 横向振动 

分 类 号：TH113[机械工程—机械设计及理论] O325[理学—一般力学与力学基础]