The nonlocal elasticity together with electro‐magneto thermal dual‐phase‐lag (DPL) model to a transversely isotropic generalized thermoelastic hollow sphere with voids is addressed in radial direction. The governing equations and stress–strain‐displacement relations have been resolved by applying time harmonics technique. The elimination technique is employed to resolve the homogeneous equations to find the unknowns. The unknowns such as dilatation, displacement, voids volume fraction, temperature change, and radial/de‐hoop stresses have been calculated analytically. In order to discover the vibration analysis, the numerical Iteration method has been applied to thermally insulated/isothermal boundary conditions. For computation purpose the software like MATLAB tool has been used. The real parts of generated data obtained from the frequency equations have also been shown graphically to frequency shift and natural frequencies. The effects of DPL model of the theory of generalized transversely isotropic thermoelasticity with voids have been represented with and without the effects of magnetic field for nonlocal/local elastic materials and validated with existing literature.
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
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