A general vibration theory for constrained layer damping-treated thick sandwich structures

Abstract

The vibration equations of a thick sandwich structure with a viscoelastic material core were derived. The host layer was assumed thick and the top layer could be thin or thick. This type of structures may apply to various cases and the particular application for which it fit is that of constrained layer damping treatment for vibration attenuating. The governing differential equations contained nine displacements for thick–thick surface layers. For cases of thin–thick, the number of displacement was significantly reduced to only five, which were one transverse displacement, two in-plane displacements, and two layer rotation angles, all associated with the host layer. The derived theory was general, and it could be not only specialized for many commonly seen structures such as beams, plates, and cylindrical shells but also degenerated into one- or two-layer structures. Specialization for a sandwich cylindrical shell was extensively illustrated, and numerical results of natural frequencies and damping were compared to those of thin shell theory. How each layer's thickness influenced the frequency and damping of the sandwich shell were particularly discussed.

Stability of solution for Rao-Nakra sandwich beam model with Kelvin-Voigt damping and time delay

“…When 𝑠(𝑥, 𝑡) = 0, system (1.10)-(1.12) reduces to the Timoshenko system. For more sandwich beam models found in the literature see for instance [7,8] with references therein.…”

Active vibration control of thin constrained composite damping plates with double piezoelectric layers

“…The experiments of active vibration control for the composite plates and shells with arrays of piezoelectric patches were performed and the features of active control were demonstrated [19,44,45]. Firstorder and third-order shear deformation theories were employed to establish the governing equations of the constrained sandwich damping plates and shells [46][47][48][49][50]. These shear deformable models [46,49,50] could be utilized in a broad frequency range and normal deformation of the viscoelastic core in the thickness direction needed to be taken into account in the medium and high frequency range.…”

“…Firstorder and third-order shear deformation theories were employed to establish the governing equations of the constrained sandwich damping plates and shells [46][47][48][49][50]. These shear deformable models [46,49,50] could be utilized in a broad frequency range and normal deformation of the viscoelastic core in the thickness direction needed to be taken into account in the medium and high frequency range. Vibrations of the composite plates with a periodic perforated viscoelastic damping layer were explored by asymptotic analysis and the finite element method [51][52][53].…”

General Homogenised Formulation for Thick Viscoelastic Layered Structures for Finite Element Applications

“…This method defines an equivalent flexural stiffness that links the shear strain in the damping layer to the bending motion of the plate. The analytical procedure has been followed in subsequent works such as [12], in which the work by Ross, Kerwin and Ungar was extended or, after, in [13] in which a model for thick layered structures that considers nine degrees of freedom (DOF) is presented. This last work is stated as a general case and can degenerate into one-or two-layered structures so it can also be applied to FLD structures.…”