Effect of Electromagnetic Field on Vibrations of Nonlocal Elastic Cylinders with Double Porosity

The vibration characteristics of an isotropic and homogeneous elastic hollow cylinder with double porosity, emphasizing the influence of the magnetic field in the context of nonlocal elasticity, are investigated. The constitutive relations and governing equations are described in the radial direction.

A technique of time-harmonic vibration is implemented to derive a set of ordinary differential equations from the governing equations. The frequency equation for the vibration continuation is established under the conditions of traction-free boundary conditions. MATLAB software is employed with a numerical iteration method to explore free vibration analysis.

Analytical results have been authenticated with Computer-simulated numerical results and are presented through graphical representations illustrating the frequency shift for both the nonlocal and local elastic cylinders with double porous structures under the influence of a magnetic field.

Numerically simulated data are tabulated to depict natural frequencies as a function of the mode numbers. The distinct behaviors associated with specific modes and the tendency towards linearity as the mode numbers increase highlight the intricate interaction between the magnetic field and the dynamic attributes of the system.