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

doi:10.1007/s10483-023-2933-8

Abstract

Abstract: 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.

Key words: orthotropic higher-order plate, nonlocal strain gradient, thermo-elastic coupling, fractional-order derivative, free vibration

2010 MSC Number:

70J30

Lingkang ZHAO, Peijun WEI, Yueqiu LI. Free vibration of thermo-elastic microplate based on spatiotemporal fractional-order derivatives with nonlocal characteristic length and time. Applied Mathematics and Mechanics (English Edition), 2023, 44(1): 109-124.

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