magneto-dependent vibrational responses of multi-directional functionally graded materials smart sandwich shallow shell panels

The vibrational frequency characteristics of a shallow shell with an integrated magnetostrictive face sheet and a core made of three-phase multi-directional functionally graded materials (fgm) are discussed in the present study. properties of the materials are varied along axes of the structure gradually in 3d gradation based on a power-law variation and using three constituents. for analyzing this issue, a high-order exponential shear deformation model is employed. the conditions of zero stress at the free surfaces are satisfied in the used theory without needing factor of the correction. the governing system of the proposed model is obtained by employing hamilton's technique and solved to determine the deflections and eigenfrequencies. the dynamical motion system is damped and the deflections are reduced by using terfenol-d actuating layers and based on the control of velocity feedback system. some factors, including the curvature, power-law indexes, velocity feedback gain value, and thickness ratio are used to examine the vibration characteristics of shallow shells. the major results of study indicate an increment in the eigenfrequency of vibration for the studied structure as a result of the gradation indexes increase. additionally, an increase in the velocity feedback gain leads to a decrease of deflections result of transient (time-varying) behavior for the system due to an increase in the damping value of vibration regardless of all other factors.