Exact dynamic stiffness formulations and vibration response analysis of orthotropic viscoelastic plate built-up structures

The analytical damped dynamic stiffness formulation is developed for the dynamic response analysis of orthotropic viscoelastic plate built-up structures with a general frequency-dependent damping model. The governing differential equation in the frequency domain is established, which allows for the direct introduction of frequency-dependent damping models by considering internal (material) and external (environmental) damping. The adopted viscoelastic damping model is sufficiently general to describe various types of damping, including viscous or non-viscous, integer or fractional order models. Then, the exact damped dynamic stiffness formulations for both in-plane and out-of-plane vibrations of plate elements are developed. Arbitrarily distributed excitations can be applied to the plate nodal boundaries based on the analytical Fourier-type forward and inverse transforms. The dynamic response analysis of the viscoelastic plate is carried out, which verifies the accuracy and efficiency of this method within the broadband frequency range. The numerical results serve as a valuable reference and can be used as benchmark solutions. Accurate and profound comprehension of the dynamical behavior of viscoelastic plates is a key task in designing these structures, and also optimizing their vibrational behavior. This method offers a powerful tool for representing the broadband dynamics of viscoelastic plate structures, utilizing very few degrees of freedom.