A differential quadrature framework for fractional-order thermo-electro-mechanical PDEs in piezo-thermoelastic plate

The present study employs the Differential Quadrature Method (DQM) as an efficient numerical strategy for analysing the coupled thermo-electro-mechanical behaviour of a three-dimensional transversely isotropic piezo-thermoelastic plate subjected to non-uniform thermal and electrical boundary conditions in the presence of fractional-order time derivatives and thermal relaxation effects. A three-dimensional generalized fractional model is formulated to describe the coupled thermo-electro-mechanical response, capturing memory-dependent effects that classical integer-order models fail to represent. The governing equations are formulated using generalized fractional thermoelasticity and transformed into state space form under a moving reference frame travelling with a uniform velocity. The material is assumed to move uniformly with respect to the moving reference frame. The governing equations are expressed in state space form and discretized using the Differential Quadrature Method, wherein Chebyshev-Gauss-Lobatto collocation points are adopted to obtain accurate numerical approximations in the spatial discretization while maintaining computational efficiency. The effects of the fractional-order parameter and thermal relaxation time on the displacement components, stress fields, temperature distribution, electric displacement, and electric potential are analysed in detail. The results reveal that the fractional-order parameter significantly modifies the propagation behaviour of thermal and mechanical waves, while the thermal relaxation time strongly influences the stress distribution and electric response within the plate. Moreover, the accuracy and convergence of the proposed formulation are discussed through percent relative error analysis under the successive mesh refinements. The proposed DQM-based computational framework provides an efficient and robust approach for analysing and optimizing advanced smart structures operating under transient thermo-electrical loading.