Effects of Internal Connecting Layer Properties on the Vibrations of Double Beams at Different Boundary Conditions

Double beams are important engineering and practical applications that are used in the construction of structures, aircraft, and construction. The properties of the inner layer between the two beams affect the frequencies of these double beams. In this work, the effect of linear elasticity and non-linear elasticity on frequencies of double beams has been calculated at different boundary conditions like simply-supported to simply-supported, clamped to clamped, free to free, clamped to free, clamped to simply supported, and simply-supported to free. The energy balance method based on Galerkin-Petrov (EGP) and Homotopy Perturbation Method (HPM) are used to compute the effect of the non-linearity stiffness of the inner layer on those frequencies. There is no significant difference in the frequencies computed by both methods with very little difference between them. Increasing the linear elasticity values of the inner layer causes an increase in frequencies and increasing the values of the non-linear elasticity of the inner layer causes a very slight increase in the values of the frequencies of the double beams. The increase in the maximum amplitude values affected the increase in the first frequency of the double beams, its effect increases by increasing the values of the non-linear elasticity of the inner layer, and its effect is limited on the second frequency and upwards.