Multi thermal waves in a thermo diffusive piezo electric functionally graded rod via refined multi-dual phase-lag model

Abstract

Abstract In the present work, a novel analytical model is provided for wave dispersion in a piezo-thermoelastic diffusive functionally graded rod through the multi-phase lag model and thermal activation. The plain strain model for thermo piezoelectric functionally graded rod is considered. The complex characteristic equations are obtained by using normal mode method which satisfies the nonlinear boundary conditions of piezo-thermoelastic functionally graded rod. The numerical calculations are carried out for copper material. The results of the variants stress, mechanical displacement, temperature and electric distribution, frequency are explored against the geometric parameters and some special parameters graded index, concentration constants are shown graphically. The observed results will be discuss elaborate. The results can be build reasonable attention in piezo-thermoelastic materials and smart materials industry.