Dynamic Response of Fractional-Order Viscoelastic High-Order Shear Beam Based on Nonlocal Strain Gradient Elasticity

作     者：Yuqian Xu Peijun Wei Yuqian Xu;Peijun Wei

作者机构：Department of Applied MechanicsUniversity of Science and Technology BeijingBeijing 100083China 

出 版 物：《Acta Mechanica Solida Sinica》 (固体力学学报（英文版）)

年 卷 期：2023年第36卷第6期

页      面：875-883页

核心收录：

学科分类：07[理学] 0805[工学-材料科学与工程（可授工学、理学学位）] 0802[工学-机械工程] 0701[理学-数学] 0801[工学-力学（可授工学、理学学位）] 0702[理学-物理学] 070101[理学-基础数学] 

基　　金：supported by the National Natural Science Foundation of China(Grant Nos.12072022,11872105,and 11911530176) the Fundamental Research Funds for the Central Universities(FRF-BR-18-008B,FRF-TW-2018-005) 

主　　题：Nonlocal strain gradient Higher-order beam Fractional-order derivatives Viscoelasticity Laplace transform Mittag–Leffler function 

摘      要：The dynamic behavior of a viscoelastic high-order shear microbeam is studied based on a new constitutive model which incorporates size effects and viscoelasticity *** size effects are modeled by the nonlocal gradient elasticity,while viscoelastic effects are modeled by fractional-order *** constitutive relation and the equations of motion are both differential equations with fractional-order *** on the Laplace transform and inverse transform,the analytical solution of the dynamic response under a step load is obtained in terms of the Mittag–Leffler *** order to verify the reliability of the analytical solution,a comparison with the numerical solution is also *** on the numerical results,the effects of the nonlocal parameter,strain gradient parameter,fractional-order parameter,and viscosity coefficient on the dynamic response of the viscoelastic microbeam are *** is found that the influences of the fractional order and the coefficient of viscosity on the dynamic response of the microbeam are very different,although both are related to the viscoelastic behavior.