Nonlinear damping and forced vibration investigation of three-layered viscoelastic sandwich beams on nonlinear elastic foundation with interlaminar continuous shear stress Zig–Zag theories

The objective of this research is to investigate nonlinear elastic foundation effects on the damping characteristics and forced vibrations of sandwich beam, in which a viscoelastic layer is positioned between two identical elastic layers. The analytical formulation takes into account both normal and shear deformations in the core by employing the interlaminar continuous shear stress Zig–Zag Theories (IC-ZZT). The coupling of geometric nonlinearity results in a nonlinear frequency–amplitude equation, which is influenced by several complex coefficients. The paper's first section focuses on determining the linear and nonlinear damping parameters for laminated composite beams. In the second part, a nonlinear forced vibration analysis is conducted, considering both small and large vibration amplitudes. Results show that the nonlinear elastic foundation coefficients have a significant effect on the damping and nonlinear vibration response of sandwich beams.