分数阶黏弹性地基上非贯穿裂纹板的自由振动  

Free Vibration of Non-Through Cracked Plates on Fractional-Order Viscoelastic Foundations

作　　者：王刚 魏培君 周小利[1,3] 张骏[1] WANG Gang;WEI Peijun;ZHOU Xiaoli;ZHANG Jun(College of 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》2025年第1期151-161,共11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：本文研究了分数阶黏弹性地基上非贯穿裂纹板的自由振动问题.首先,引入分数阶导数,建立分数阶黏弹性地基模型.接着针对四边简支板研究含贯穿裂纹情形的自由振动问题,在此基础上将贯穿裂纹推广到非贯穿裂纹.基于能量释放率和应力强度因子的关系得到两种情况下裂纹引起的附加转角,并进一步导出两种情况下裂纹等效扭转弹簧的柔度系数.最终,根据边界条件得到复固有频率.通过具体算例,讨论了黏弹性地基的分数阶系数、黏性系数以及裂纹位置和裂纹深度等参数对复固有频率和振型的影响规律.The free vibration problem of non-through cracked plates on fractional-order viscoelastic foundations is studied in this paper.First,a fractional-order viscoelastic foundation model is introduced to better describe the mechanical behavior of foundation.Next,the free vibration of cracked plate with through crack under the four-edge simply-supported boundary conditions is studied.Further,the through crack situation is generalized to the non-through crack situation.Based on the relation between the energy release rate and the stress instensity factor,the additional rotation angles induced by the crack is obtained,and the compliance coefficients of the crack equivilent rotation spring are derived for both the through and non-through crack situations.Finally,the complex natural frequency are obtained according to the boundary conditions.The numerical examples are provided and the influences of the fractional order coefficient,the viscosity coefficient,crack location and crack depth on the complex natural frequency and mode shape of the cracked plate were discussed.

关 键 词：分数阶 黏弹性地基 裂纹板 非贯穿裂纹 自由振动 

分 类 号：O326[理学—一般力学与力学基础]