Free vibration of thermo-elastic microplate based on spatiotemporal fractional-order derivatives with nonlocal characteristic length and time  

作　　者：Lingkang ZHAO Peijun WEI Yueqiu LI 

机构地区：[1]Department of Applied Mechanics,University of Science and Technology Beijing,Beijing 100083,China [2]Department of Mathematics,Qiqihar University,Qiqihar 161006,Heilongjiang Province,China

出　　处：《Applied Mathematics and Mechanics(English Edition)》2023年第1期109-124,共16页应用数学和力学（英文版）

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

摘　　要：A fractional-order thermo-elastic model taking into account the small-scale effects of the thermo-elastic coupled behavior is developed to study the free vibration of a higher-order shear microplate.The nonlocal strain gradient theory is modified with the introduction of the fractional-order derivatives and the nonlocal characteristic length.The Fourier heat conduction is replaced by the non-Fourier heat conduction with the introduction of the fractional order and the memory characteristic time.Numerical calculations are performed to analyze the effects of the nonlocal strain gradient parameters,the spatiotemporal fractional order,the nonlocal characteristic length,and the memory characteristic time on the natural frequencies,the vibration attenuation,and the phase shift between the temperature field and the displacement field.The numerical results show that the new thermo-elastic model with the spatiotemporal fractional order can provide more exquisite descriptions of the thermo-elastic behavior at a small scale.

关 键 词：orthotropic higher-order plate nonlocal strain gradient thermo-elastic coupling fractional-order derivative free vibration 

分 类 号：O327[理学—一般力学与力学基础]