State-space approach to nonlocal thermo-viscoelastic piezoelectric materials with fractional dual-phase lag heat transfer

Abstract

Purpose The purpose of this study is to develop a comprehensive size-dependent piezoelectric thermo-viscoelastic coupling model that accounts for two fundamentally distinct size-dependent models that govern fractional dual-phase lag heat transfer and viscoelastic deformation, respectively. Design/methodology/approach The fractional calculus has recently been shown to capture precisely the experimental effects of viscoelastic materials. The governing equations are combined into a unified system, from which certain theorems results on linear coupled and generalized theories of thermo-viscoelasticity may be easily established. Laplace transforms and state–space approach will be used to determine the generic solution when any set of boundary conditions exists. The derived formulation is used to two concrete different problems for a piezoelectric rod. The numerical technique for inverting the transfer functions is used to generate observable numerical results. Findings Some analogies of impacts of nonlocal thermal conduction, nonlocal elasticity and DPL parameters as well as fractional order on thermal spreads and thermo-viscoelastic response are illustrated in the figures. Originality/value The results in all figures indicate that the nonlocal thermal and viscoelastic parameters have a considerable influence on all field values. This discovery might help with the design and analysis of thermal-mechanical aspects of nanoscale devices.

Response of frequency domain in generalized thermoelastic medium under modified Green‐Lindsay with non‐local and two temperature

“…In Figures (13)(14)(15)(16)(17)(18)(19)(20)(21)(22)(23)(24), F I G U R E 1 1 Variation of t zr versus r (Thermal point source over circular region).…”

“…For piezoelectric materials, Ezzat and Muhiameed [14] investigated a problem having the impact of non‐local in the context of visco‐thermoelastic solids. Authors have given their contribution to thermo‐viscoelasticity theory for piezoelectric materials, notable of them are [15 – 17]. Based on the modified couple stress theory, Abouelregal [18] investigated the thermo‐viscoelastic interactions of rotating micro‐beams to examine the size‐dependent effect.…”

Elasto‐thermodiffusive interaction under void due to nonlocal stress theory

“…Nonlocal elasticity theories have been applied to the problems of harmonic plane wave propagation in classical and nonclassical elastic materials. To name a few such works are by Ezzat et al [22][23][24]. Recently, based on the nonlocal stress theory Sur has reported the problem of thermoelastic interaction in a slim strip characterized by hereditary features in the context of MGT theory [25] and another problem for an infinite body with a cylindrical hole was also analyzed [26].…”

Analysis of nonlocal effects on plane waves in a transversely isotropic visco-thermoelastic medium with variable thermal conductivity

“…The plane wave propagation in a nonlocal visco-thermoelastic half-space considering temperature-dependent characteristics was studied by Jain et al (2021). The thermo-viscoelastic behaviour of a nonlocal piezoelectric material with fractional dual-phase lag heat transfer was investigated by Ezzat et al (2022).…”