Thermoelastic wave and thermal shock based on dipolar gradient elasticity and fractional-order generalized thermoelasticity

Abstract

In the current work, the thermoelastic wave propagation and the thermal shock problems are studied based on the dipolar gradient elasticity and fractional order generalized thermoelasticity in order to take into account the microstructure effect and the thermal effect at a small scale. First, the fractional-order governing equations for coupled thermoelastic wave propagation are derived and the effects of microstructure parameters and fractional order on the dispersion and the attenuation are discussed; next, the transient problems by the thermal shock and the mechanical shock on the surface of half-space are studied. The Laplace transformation method and the state transfer equation method are used to solve this problem. The numerical results for the temperature, the displacement, the stress and the high order stress distributions are provided and shown graphically. The effects of the fractional order and the microstructure parameter on the thermoelastic behavior are investigated. Some interesting phenomenons and conclusions are presented at last.

Keyword:

• Gradient elasticity
• generalized thermoelasticity
• fractional older differential
• thermoelastic wave
• Thermal shock

Disclosure statement

All authors (Yueqiu Li, PeijunWei, Peng Zhang, Xiaowei Gao) declare that they have no conflict of interest or financial conflicts to disclose.

Additional information

Funding

This work was supported by National Natural Science Foundation of China [Grant Numbers 11872105, 11911530176, 12072022]; Heilongjiang Natural Science Fund [Grant Number LH2019A026]; Fundamental Research Funds for the Central Universities [Grant Number FRF-TW-2018-005, FRF-BR-18-008B]; Basic business special in Heilongjiang province department of education [Grant Number 135509123].