Pasternak地基梁受迫振动行波解  

Forced vibration of beam on Pasternak foundation: A wave evolution analysis

作　　者：丁虎[1] 陈立群[1,2] 

机构地区：[1]上海市应用数学和力学研究所,上海200072 [2]上海大学力学系,上海200444

出　　处：《中国科学：物理学、力学、天文学》2013年第4期564-571,共8页Scientia Sinica Physica,Mechanica & Astronomica

基　　金：国家杰出青年科学基金(编号:10725209);国家自然科学基金(批准号:10932006);上海市青年科技启明星计划(编号:11QA1402300);上海市教育委员会科研创新项目(编号:12YZ028);上海市重点学科建设项目(编号:S30106)

摘　　要：通过弹性波在梁结构中的反射、透射和传播,研究了Pasternak地基Euler梁在简谐集中载荷激励下响应.分别总结了Pasternak地基梁和有限长度弹性梁振动的波传播分析的研究进展.推导了Pasternak地基梁上外力和力矩作用点处的入射波与外力和力矩的矩阵关系.结合这些矩阵以及波在梁中的传播矩阵和边界处的反射矩阵,通过波列封闭原则给出了一种简洁、系统地分析任意激励频率下梁横向响应的方法.考虑两种经典边界条件,通过扫描简谐激励频率,给出了地基梁的频率响应.并由共振关系给出Pasternak地基梁的固有频率以及模态.通过数值算例比较了地基剪切模量对地基梁的频率响应的影响.This paper concerns wave reflection, transmission, and propagation in beam on Pasternak foundation with wave analysis of vibrations. The advance in a beam placed on a Pasternak foundation and wave propagation method for finite-length beam are respectively reviewed. The matrix relations for beams resting on foundation between the injected waves and externally applied forces and moments are derived. These matrices can be combined with the propagation matrix and the reflection matrices at boundaries to provide a concise and systematic approach to forced vibration analysis of beams resting on foundation subjected to a temporally harmonic force. Two types of the conventional boundary conditions are investigated. Forced response of beams is obtained via sweeping frequency of harmonic force and the wave-train closure principle. From the results, the natural frequencies and mode shapes are calculated. The research in the influence of shear modulus of foundation is provided with illustrations.

关 键 词：波传播 梁 Pasternak基础 受迫响应 共振 

分 类 号：TU470[建筑科学—结构工程]