Free and forced random vibration analysis of sandwich plates with thick viscoelastic cores

Free vibrations and the transverse response of sandwich plates with viscoelastic cores under wide-band random excitation is studied with special attention to the so-called pumping, thickness-shear and stretching modes. The quadratic displacement field is adopted for all displacement components of the core to accurately capture the higher modes excited by the wide-band excitation. The Love-Kirchhoff plate theory is used for the face layers. The viscoelastic behavior of the core is modeled by the Golla–Hughes–McTavish method. An analytical solution using the normal mode method is provided for the simply supported boundary conditions by including a different family of modes. The effects of some geometric and material properties on the frequencies, damping ratios and also root mean square responses are explored. The participation of the through-the-thickness deformation in the bending mode vibration of the top layer is also investigated, which is found to be mostly resulting from the second order term of the transverse displacement expansion in symmetric configurations. Moreover, the alteration of the response with the exclusion of a different family of modes from the solution is investigated.