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 strai...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.展开更多
Let F be a meromorphic functions family on the unit disc Δ, If for every (the zeros of f is a multiplicity of at least k) and if then and ( ), then F is normal on Δ.
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)。
文摘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.
文摘Let F be a meromorphic functions family on the unit disc Δ, If for every (the zeros of f is a multiplicity of at least k) and if then and ( ), then F is normal on Δ.
