In vibration analysis of sandwich beam/plates, it is often assumed that there is shear deformation only, without extension or compression in the viscoelastic layer. Certainly, this assumption may have limitations, for example, with increase of the core thickness or frequency range of vibration. The purpose of this paper is to consider the normal, as well as shear strain of the core material for modal parameter estimation of the sandwich plates and to investigate how much error will be caused by neglecting the extension or compression in the core material.
Natural frequencies and modal loss factors are estimated for simply supported(S-S-S-S) and clamped(C-C-C-C)square sandwich plates by taking the normal as well as shear deformation into account for dynamic modeling. Nondimensional characteristic equations are formulated and solved numerically for various ratios of the base layer thickness to plate length, core layer thickness to base layer, constraining layer thickness to base layer, and shear modulus of core material to elastic modulus of base layer.
Since material properties of the viscoelastic cores are mostly frequency dependent, it is difficult to obtain modal parameters of a sandwich plates by solving eigenvalue problems. Therefore, in this study, it is evaluated error due to using finite difference method to get the response for an excitation at each frequency and introduced proper mesh size to satisfy the accuracy of ordinary finite difference expressions.
The effects of the various parameters on the modal properties are shown to be intercorrelated to each other and hence difficult to summarize in one phrase. Normal deformation of the core material plays an important role when the thickness ratio of constraining layer to base layer is 0.5 and its Poisson's ratio is smaller than 0.49, and hence need to be included in the dynamic modeling especially for estimation of modal damping when one of the following conditions are met; 1) the ratio of base layer thickness to plate length is greater than 0.02, 2) the thickness ratio of core layer to base layer is greater than 0.01, 3) the wavelength of a mode is less than one third of the plate length, 4) the ratio of shear modulus of core material to elastic modulus of base material is less than $10^{-5}$.
In order to verify the proposed modeling method the experimental study of a sandwich plates was also performed. The experimental results present that proposed modeling shows good prediction of natural frequency and modal loss factor.
