Hygrothermal vibration of a laminated sandwich plate with magnetostrictive faces and a homogeneous core

Abstract Hygrothermal forced vibration and damping analyses of a simply supported symmetric laminated composite plate with homogeneous core and magnetostrictive layers are examined using the exponential displacement model in this article. Three hygrothermal environment distribution types are investigated: uniform, linear and nonlinear rises in the present analysis. The equations of motion for laminated rectangular plates subjected to hygrothermal loads and in‐plane forces in x and y directions are developed through Hamilton's principle. The closed‐form solution is arrived at based on Navier's technique to analyze the hygrothermal effect on the vibrational behavior of the structure. Some parametric examples are presented to discuss the effects of the smart layer location, lamination schemes, mode number, aspect ratio, thickness ratio, feedback gain control value, in‐plane forces, core thickness‐to‐fiber reinforced layer thickness ratio, magnetostrictive layer thickness to fiber‐reinforced layer thickness ratio, temperature and moisture changes on vibration response of the proposed model. The study results illustrate that the high hygro ratio weakens the plate stiffness, and accordingly, the amplitude of the deflection increases with raising the moisture and/or temperature. The numerical results emphasize the strong role of the feedback control gain values and the smart layer position in controlling the system vibration. The largest deflections and highest damping time interval happen in the uniform temperature distribution and moisture concentration case. Moreover, the vibration frequencies of the thin smart plates are smaller than the thick ones.