Forced and free vibration of magnetostrictive laminated sandwich beams on Kerr?s foundations

The supporting system's influence on the dynamic behavior of the frequencies and deflection of the smart laminated composite sandwich beam with functionally graded faces is investigated according to a higher-order shear deformation theory. The graphite fiber constituent and the matrix material are distributed through the cross-section of the beam faces based on power law gradation. Kerr's foundation is proposed to use as a variable support system for the studied structure. The proposed structure is subjected to a magnetic field and an external force in x direction. For controlling the system, a simple feedback gain control with constant distribution is applied to the embedded Terfenol-D actuators. To obtain and solve the associated dynamic equations of the studied system, Hamilton's principle and Navier's approach are utilized. Several numerical examples are carried out to show the forced/ free vibration response of the system with detailed illustrations of the different geometrical parameters variation.