Flexural waves in thermoelastic higher-order shear micro-plate modelled by spatiotemporal fractional differential

An orthotropic higher-order shear micro-plate model is established with consideration the small-scale effect and the thermoelastic coupling effects to study the dispersion and attenuation of flexural waves in the present work. The nonlocal elasticity and the strain gradient elasticity are incorporated to lead the nonlocal strain gradient model to reflect the size effect. The generalized thermoelasticity (non-Fourier heat conduction) is introduced to reflect the history-dependent feature of heat conduction. Furthermore, the integer order derivatives are replaced by the fractional derivatives of Caputo-type to get a more refined model which can extend the range of application of model and provide more exquisite description of the spatial nonlocal behavior and temporal memory behavior at small scale. In addition, the nonlocal characteristic length and the memory characteristic length as new small scale parameters are first introduced in the present model to focus on describing the short-range nonlocal and the short-term memory behavior. A detailed parameter study is performed and the effects of nonlocal characteristic length, strain gradient characteristic length, the memory characteristic length and the spatiotemporal fractional order on the dispersion and attenuation of thermoelastic coupled flexural waves are discussed based on the numerical results.