Free Vibration of Sandwich Beams with Different Boundary Conditions using Higher OrderSandwich Panel Theory

In the present paper, an analytical method is developedto analyze the vibrational response of sandwich beamswith different boundary conditions using the higherorder sandwich panel theory. The modal forms are givenin terms of Fourier series and the derivatives of them arelegitimized using Stock’s transformation. Then, equationsdivides into two types based on the manner ofunknowns. In addition to these two types of equations,there is a third type of ones, which describes theboundary conditions. By some algebraic manipulations,a system of equations appears which the number ofequations inside that depends on the boundary conditions.Furthermore, a pattern is recognized so that it canform the effect of boundary conditions on obtaining thesystem of equations of the problem. Thereby, straightconstitution of final system of equations becomes possiblevery fast and accurate. The procedure and numericalresults are verified using the results of those inliterature in which finite differences and experimentalmethods are applied. Then, the effect of sandwichparameters is studied on the natural frequencies.

کلیدواژه ها:

Free vibration ، Higher order sandwich paneltheory ، Different boundary conditions ، Fourier series ، Stock’s transformation.