A Note on Free Vibration of a Double-beam System with Nonlinear Elastic Ier Layer

In this note, small amplitude free vibration of a double-beam system in presence of ier layer nonlinearity is investigated. The nonlinearity is due to ier layer material and is not related to large amplitude vibration. At first, frequencies of a double-beam system with linear ier layer are studied and categorized as synchronous and asynchronous frequencies. It is revealed that the ier layer does not affect higher modes significantly and mainly affects the first frequency. Then, equation of motion in the presence of cubic nonlinearity in the ier layer is derived and transformed to the form of Duffing equation. Using an analytical solution, the effect of nonlinearity on the frequency for simply-supported and clamped boundary conditions is analyzed. Results show that the nonlinearity effect is not significant and, in small amplitude free vibration analysis of a double-beam system, the material nonlinearity of the ier layer could be neglected.