分数阶粘弹性Pasternak地基上四边固支板的自由振动  

Free Vibration of Fully Clamped Rectangular Plate on Fractional Viscoelastic Pasternak Foundations

作　　者：宋鹏飞 魏培君 周小利[1,3] 毕晓东[1] SONG Pengfei;WEI Peijun;ZHOU Xiaoli;BI Xiaodong(Collegeof Civil Engineering,Hebei University of Engineering,Handan 056038,Hebei,China;Department of Applied Mechanics,University of Science and Technology,Beijing 100083,China;The Center for Computational Mechanics and Engineering Applications,Hebei University of Engineering,Handan 056038,Hebei,China)

机构地区：[1]河北工程大学土木工程学院,河北邯郸056038 [2]北京科技大学应用力学系,北京100083 [3]河北工程大学计算力学与工程应用研究中心,河北邯郸056038

出　　处：《力学季刊》2022年第3期681-690,共10页Chinese Quarterly of Mechanics

基　　金：国家自然科学基金(12072022);河北省教育厅项目(QN2018061)。

摘　　要：本文研究了分数阶粘弹性Pasternak地基上四边固支薄板的自由振动问题.通过引入分数阶导数,将传统整数阶粘弹性模型修正为分数阶导数粘弹性模型,增强了模型的灵活性.基于所提出的分数阶粘弹性Pasternak地基模型,导出相应的应力-应变本构关系的复弹性模量.在此基础上进一步研究Pasternak地基上四边固支矩形板的固有频率对粘弹性地基的依赖特性.在数值算例中,计算了分数阶粘弹性地基上四边固支板的前四阶复固有频率,以及双轴对称、双轴反对称、一轴对称另外一轴反对称等不同振动模态下的振型图.基于数值结果讨论了粘弹性地基分数阶参数及粘性参数对复数固有频率及振动衰减的影响规律.In this paper,the free vibration problem of fully clamped rectangular thin plate on fractional viscoelastic Pasternak foundation is studied.Specifically,fractional derivative is introduced to transform the traditional integer viscoelastic model into the fractional derivative viscoelastic model,which has enhanced flexibility.Based on the proposed fractional viscoelastic Pasternak foundation model,the corresponding complex elastic modulus of the stress-strain constitutive relationship is derived.Further,the dependence of the natural frequency of fully clamped plate on the viscoelastic foundation is studied.In the numerical examples,the complex-valued natural frequencies and the vibrational modes with biaxial symmetry,biaxial antisymmetry,one axial symmetry while the other axial antisymmetry features of the fully clamped rectangular thin plate on the fractional viscoelastic foundation are calculated.Based on numerical results,the influence laws of the fractional order parameter and the viscosity parameter on the complex natural frequency and the vibration attenuation of the rectangular plate are discussed.

关 键 词：粘弹性地基 四边固支板 分数阶导数 复模量 复固有频率 

分 类 号：O326[理学—一般力学与力学基础]