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

作　　者：Hai QING Huidiao SONG 

机构地区：[1]State Key Laboratory of Mechanics and Control for Aerospace Structures,Nanjing University of Aeronautics and Astronautics,Nanjing 210016,China

出　　处：《Applied Mathematics and Mechanics(English Edition)》2023年第5期773-786,共14页应用数学和力学（英文版）

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

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 environment.Hamilton's principle is used to derive the differential governing equations and corresponding boundary conditions.The integral relations between the strain and the nonlocal stress are converted into a differential form with constitutive constraints.The size-dependent axial thermal stress due to the variation of the environmental temperature is derived explicitly.The Laplace transformation is utilized to obtain the explicit expression for the bending deflection and moment.Considering 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 ratio.The 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.

关 键 词：damping vibration size effect integral nonlocal stress gradient model standard viscoelastic model Laplace transformation 

分 类 号：O175.6[理学—数学]