Nonlocal stress gradient formulation for damping vibration analysis of viscoelastic microbeam in thermal environment

作     者：Hai QING Huidiao SONG Hai QING;Huidiao SONG

作者机构：State Key Laboratory of Mechanics and Control for Aerospace StructuresNanjing University of Aeronautics and AstronauticsNanjing 210016China 

出 版 物：《Applied Mathematics and Mechanics(English Edition)》 (应用数学和力学（英文版）)

年 卷 期：2023年第44卷第5期

页      面：773-786页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：Project supported by the National Natural Science Foundation of China(No.12172169) 

主　　题：damping vibration size effect integral nonlocal stress gradient model standard viscoelastic model Laplace transformation 

摘      要：An integral nonlocal stress gradient viscoelastic model is proposed on the basis of the integral nonlocal stress gradient model and the standard viscoelastic model,and is utilized to investigate the free damping vibration analysis of the viscoelastic BernoulliEuler microbeams in thermal *** s principle is used to derive the differential governing equations and corresponding boundary *** integral relations between the strain and the nonlocal stress are converted into a differential form with constitutive *** size-dependent axial thermal stress due to the variation of the environmental temperature is derived *** Laplace transformation is utilized to obtain the explicit expression for the bending deflection and *** the boundary conditions and constitutive constraints,one can get a nonlinear equation with complex coefficients,from which the complex characteristic frequency can be determined.A two-step numerical method is proposed to solve the elastic vibration frequency and the damping *** effects of length scale parameters,viscous coefficient,thermal stress,vibration order on the vibration frequencies,and critical viscous coefficient are investigated numerically for the viscoelastic Bernoulli-Euler microbeams under different boundary conditions.