Vibrations of Phase-Lags on Electro-Magneto Nonlocal Elastic Solid with Voids in Generalized Thermoelastic Cylinder/Disk

Abstract

The stress-strain-temperature relations, strain-displacement relations and governing equations have been addressed for electro-magneto transversely isotropic nonlocal elastic hollow cylinder with voids in the reference of 3-phase-lag effect of heat conduction. The strength of the magnetic field proceeds in the direction of the z-axis of the hollow cylinder/disk. The simultaneous differential equations have been eliminated by applying elimination technique to obtain unknown field functions such as dilatation, equilibrated voids volume fraction, temperature, displacement and stresses. Free vibration analysis has been explored by applying stress free and thermally insulated/isothermal boundaries. Analytical results are verified by employing numerically analyzed results for unknown field functions and presented graphically for the vibrations of stress free field functions such as thermoelastric damping, frequencies and frequency-shift. The results have been authenticated by analyzing analytical and numerical results with existing literature with earlier published work. The study of present paper based on 3-phase-lag model of generalized thermoelasticity may receive better approach to allow voids and relaxation time parameters, which have many applications in the field of science, technology and engineering. The study may also be useful in the area of seismology for mining and drilling in the earth’s crust.
 HIGHLIGHTS
 
 The analysis for electro-magneto transversely isotropic nonlocal thermoelastic hollow cylinder with voids in the reference of 3-phase-lag effect of heat conduction
 The strength of the magnetic field proceeds in the direction of the z-axis of the nonlocal thermoelastic hollow cylinder/disk
 Free vibration analysis has been explored by applying stress free and thermally insulated/isothermal boundaries
 Analytical results are verified by employing numerically analyzed results for unknown field functions and presented graphically for the vibrations of stress free field functions such as damping, frequencies and frequency-shift
 
 GRAPHICAL ABSTRACT