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 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 studied and categorized as synchronous and asynchronous frequencies, and it is revealed that ier layer does not affect higher modes significantly and mainly affects first frequency. Then, Equation of motion in presence of cubic nonlinearity in ier layer derived and transformed to the form of Duffing equation. By using analytical solution, the effect of nonlinearity is analyzed on frequency for simply-support and clamp boundary conditions. Results show the nonlinearity effect is not significant and in small amplitude free vibration analysis of a double-beam system, the material nonlinearity of ier layer could be neglected.