Vibration/bending analysis of waist twisting disc with three-layer circular magnetic porous micro-plate in sports equipments during exercise

In the present study, bending and free vibration analyses of a micro annular plate with piezomagnetic layers are investigated based on FSDT in the presence of magnetic field and resting on the elastic foundation. The multi-field constitutive relations are developed using modified strain gradient theory and the equilibrium governing equations of motion micro annular plate are derived using minimum of total potential energy and Hamilton's principles. One can arrive at numerical results using the semi analytical solution procedure. The Ritz method is used to obtain the results in the parametric state. The boundary conditions are applied to guess the primary functions and the minimization is used to obtain the unknown coefficients in the assumed solution. The effect of micro parameter, various geometric parameter and the foundation parameter is studied on the dynamic and static responses.