Nonlocal elasticity and thermal dual‐phase‐lag effect on the vibration analysis of transversely isotropic electro‐magneto generalized thermoelastic sphere with voids
Sita Ram Sharma, Jai Chand Mehalwal, Nantu Sarkar, Dinesh Kumar Sharma
Abstract
Abstract 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.