Magneto-electro-mechanical responses of smart sensor/actuator for detection the information in football’s ball

A small-scale formulation is developed based on modified couple stress theory (MCST) for shear deformation analysis of piezomagnetic nano-panels. This theory employs the couple stress and symmetric curvature tensors to include the length scale parameter in the micro scale to capture size-dependency. The micro-panel is fabricated from an elastic core integrated with two piezoelectric/piezomagnetic face sheets subjected to initial electromagnetic loads. Using the principle of virtual work, the static governing equations are derived in terms of radial, axial, and circumferential displacements, axial and circumferential rotations, and electromagnetic potentials. An analytical method is employed to solve the governing equations. The structure is used for detection of the information in the football's ball with changes of the position of the equipment in the sport. The results are estimated using the proposed model. Effect of important material and geometric parameters such as micro length scale parameter, initial electromagnetic potentials, and some geometric parameters such as length and span angle are also investigated on the bending features such as deformation and rotations components as well as maximum electromagnetic potentials.