This study considers a slender fixed-free nonlinear beam to simulate the main body of a vibration elastic steel sheet (ESS). We added another elastic steel sheet (ESS) to the main ESS to instruct a double elastic steel sheet (DESS) vibration system. The piezoelectric patch (Piezo-Patch) was installed on the proper position of the DESS system. The objective of this study is to find if there is any internal resonance in this system and convert the vibration energy into electric energy. We applied Newton's second law of motion, and referred to the Bernoulli-Euler Beam theoretical model, the equation of motion was derived and coupled with the current equation derived from the electric energy theory. We employed the method of multiple scales (MOMS) to analyze this nonlinear problem. The Fixed point plots (steady state frequency response) were obtained. In addition, in order to analyze the electric energy efficiency, we analyze the coupled system by the fourth-order Runge-Kutta method, and compare it with the experimental results to prove that the theoretical model can accurately predict the experimental results.
