A four-node quadrilateral element for vibration and damping analysis of sandwich plates with viscoelastic core

Abstract

Constrained layer damping treatments have been widely used as an effective way for vibration control and noise reduction of thin-walled plates and shells. Despite extensive application in vibration and damping analysis of sandwich plates with viscoelastic core, the rectangular element is challenged by irregular structural forms in practical engineering. In this paper, a three-layer four-node quadrilateral element with seven degrees of freedom at each node is presented. Compared with classical rectangular element, the four-node quadrilateral element has stronger adaptability in complex structural forms and boundary conditions. Based on the layer-wise theory where the constrained layer and the base layer meet Kirchhoff theory and the viscoelastic layer satisfies first-order shear deformation theory, the finite element formulation of the sandwich plate with viscoelastic core is derived by the Hamilton principle in variational form and based on the generalization of the discrete Kirchhoff Quadrilateral plate element. The complex modulus model is employed to describe the viscoelastic core of sandwich plates, allowing for the material’s frequency dependent characteristics. The natural frequencies and associated modal loss factors are computed based on the complex eigenvalue problems. The frequency dependent characteristic of the viscoelastic core is considered and an iterative procedure is introduced to solve the nonlinear eigenvalue problem. At last, six verification numerical examples that include three sandwich beam-plates and three sandwich plates are provided to compare present method with experiment, analytical method, Galerkin method, finite element methods and commercial software (NASTRAN). The results show that the proposed finite element can accurately and efficiently simulate the sandwich plates treated with constrained layer damping with a variety of structural forms and boundary conditions.

Analysis and Optimization of Damping Properties of Constrained Layer Damping Structures with Multilayers

“…In general, the VEMs are frequency-and temperaturedependent. However, if the modulus of VEM does not change too much in the whole frequency domain or changes slightly in a special frequency band, the modulus can be deemed as a constant to describe the VEM approximately or in this special frequency band [30]. In the following studies, the complex constant modulus of the VEM is used.…”

“…where M and K are the mass and complex stiffness matrices, respectively; U i and λ * i are the complex eigenvector and associated complex eigenvalue, respectively; the natural frequency f i and the corresponding loss factor η i of the ith mode can be calculated as follows [30]:…”

“…To evaluate the accuracy of the formulated COMSOL model of the CLD structure, the natural frequencies and the associated loss factors for the first six modes of an example are calculated using COMSOL. e material and geometrical properties of the example CLD structure are used as the same as those in the literature [1,30] (as shown in Table 1).…”

Topology optimization of partial constrained layer damping treatment on plate for maximizing modal loss factors

“…Yang et al 26 used the finite element method to establish the dynamic model of the sandwich beam and used state-space method to solve the inherent vibration characteristics of the structure. Ren and Zhao 27 proposed a three-layer four-node quadrilateral finite element for CLD structures with complex structural forms and boundary conditions. Li et al 28 presented a reduced passive CLD finite element model based on the first shear deformation theory and improved reduced system condensation method, and the frequency dependence of the viscoelastic materials is also considered.…”

Natural frequency, damping and forced responses of sandwich plates with viscoelastic core and graphene nanoplatelets reinforced face sheets

“…Rani and Lal (2019) considered the shear deformation and inertial rotation on the core, and the Chebyshev collocation technique has been used to obtain the frequencies of the sandwich plate. Ren and Zhao (2019) presented a three-layer four-node quadrilateral element with seven degrees of freedom at each node to study the vibration of the viscoelastic sandwich layer. Safaei et al (2019) investigated the effects of loading frequency on the dynamic behavior of nanocomposite sandwich plates under periodic thermo-mechanical loadings.…”