梁式结构受移动荷载作用非平稳随机振动的DQ-PEM方法  

DQ-PEM for non-stationary random vibration analysis of beam structures under moving loads

作　　者：张琼[1] 杜永峰[1,2] 朱前坤[1,2] ZHANG Qiong;DU Yong-feng;ZHU Qian-kun(Institute of Earthquake Protection and Disaster Mitigation,Lanzhou University of Technology,Lanzhou 730050,China;International Research Base on Seismic Mitigation and Isolation of Gansu Province,Lanzhou University of Technology,Lanzhou 730050,China)

机构地区：[1]兰州理工大学防震减灾研究所,兰州730050 [2]兰州理工大学甘肃省减震隔震国际合作研究基地,兰州730050

出　　处：《计算力学学报》2022年第4期413-419,共7页Chinese Journal of Computational Mechanics

基　　金：国家自然科学基金(51868046,51668042,52168041)资助项目。

摘　　要：针对梁式结构受移动荷载作用的非平稳随机振动问题,提出了一种综合利用微分求积法和虚拟激励法DQ-PEM的新方法。梁式结构受移动荷载作用的振动控制方程为含Dirac函数的偏微分方程,利用微分求积(DQ)-积分求积法(IQ)法将其振动控制方程转化为不含Dirac函数的常微分方程。同时,将表示荷载位置变化的Dirac函数视为移动荷载的非平稳化函数,再结合虚拟激励法的思想,可得梁式结构在确定性荷载作用下的虚拟响应,进而得到其非平稳随机响应。通过工程算例验证了该方法的准确性与有效性,并进一步讨论了不同速度和不同边界条件下梁式结构受移动荷载作用的随机振动问题。The DQ-PEM method for non-stationary random vibration of beam structures subjected to moving loads is proposed, which combines differential quadrature method and pseudo-excitation method.Generally, the vibration control equation of beam structures subjected to moving loads is a partial differential equation containing the Dirac function.First, the DQ-IQ hybrid method is used to transform the equation into ordinary differential equations that do contain the Dirac function.Simultaneously, the Dirac function representing the change of load position is also regarded as the non-stationary function of moving loads.Then, combined with the pseudo-excitation method, the pseudo-response of a beam structure subjected to a deterministic load can be obtained, and finally its non-stationary random response can be obtained.The accuracy and validity of the method are verified by engineering examples.The random vibration of beam structures subjected to moving loads at different velocities and boundary conditions is further discussed.

关 键 词：梁式结构 移动荷载 虚拟响应 非平稳随机振动 DQ-PEM方法 

分 类 号：O324[理学—一般力学与力学基础]