Dynamic Response Of A Thermopiezoelectric Rod With Fractional Order Strain Thermoelastic Theory

The classic Fourier equation of heat conduction reveals that heat travels at infinite speed.When extreme conditions occur,the accuracy of this description is challenged.To overcome this shortcoming,scholars have established a non-Fourier heat conduction law.With the continuous development of science and technology,on the basis of non-Fourier heat conduction,scholars have developed a generalized thermoelastic theory that considers coupled responses.At present,the widely used generalized thermoelastic theory mainly includes: L-S theory modified by the C-V heat wave equation;G-L theory established by introducing two thermal relaxation times;G-N theory without energy dissipation.The successful application of fractional calculus in various fields of natural sciences and engineering has become a research focus in current generalized thermoelastic theory.The introduction of fractional calculus in the heat conduction equation can more accurately describe the material’s thermoelastic behavior,and thus more truly describe the memory dependence and global correlation of materials.Therefore,a fractional-order generalized thermoelastic theory was developed.Two common types of Youssef-type and Sherief-type fractional-order integral-modified heat conduction models were developed.Youssef derived a new thermoelastic theory based on fractional strain,which is considered to be a new modification of the Duhamel-Neumann stress-strain relationship.Based on the Youssef-type fractional strain generalized thermoelastic theory,this paper studies the multi-field coupling response of piezoelectric rods.The specific research contents include:(1)Based on Youssef-type fractional strain generalized thermoelastic theory and non-local theory,with the help of Laplace transform and its inverse transform method,the non-local thermoelastic problem of piezoelectric rods under the action of a moving heat source is analyzed.The distribution law of dimensionless physical quantities(displacement,temperature,electric potential,and stress)is obtained when the three influencing factors of fractional strain parameters,heat source speed,and non-local parameters change.(2)Based on Youssef-type fractional strain generalized thermoelasticity theory and temperature-dependent material property thermoelasticity theory,with the help of Laplace transform and its inverse transform method,the dynamic response of piezoelectric rods whose material properties change with temperature is analyzed.The distribution law of dimensionless physical quantities(displacement,temperature,electric potential,and stress)is obtained when the three influencing factors of fractional strain parameters,heat source speed,and material property parameters change.