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This study uses the piezoelectric technology to collect vibration energy from the fixed-fixed nonlinear elastic beams attached with the piezo-patch between the two ends. Both single elastic steel sheet (SESS) and double elastic steel sheet (DESS) systems are investigated and correlated. To simulate the power generation of the vibration energy harvester (VEH) of both the SESS and the DESS in different engineering elements, the simple harmonic external force generated by a shaker at the location of the piezo-patch is used as the source. With this, more vibration converted electric energy is derived from the transverse deformation and flapping from the DESS than the SESS beam. The equation of a nonlinear Euler–Bernoulli beam is coupled with the electric energy equation of the piezo-patch to simulate the SESS VEH system. The flapping force from the DESS VEH system can be considered the concentrated external load applied on the SESS beam model. The method of multiple scales (MOMS) is employed to analyze this nonlinear problem. The fixed points plots and the numerical results confirm this theory presented for the two beam systems, which can be used for evaluating similar engineering systems. Experiments are also performed in this study. The Taguchi method is used to analyze the optimum locations of the shaker and piezo-patch, as well as the confidence level of the factors. The method of nonlinear analysis presented in this study demonstrates its accuracy compared with the linear case. The transverse DESS VEH model proposed is proved to be feasible and more effective than the SESS system.

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This technical note investigates a hinged-hinged nonlinear Euler-Bernoulli beam resting on an elastic foundation subjects to moving loads. The method of multiple scales (MOMS) is employed to analyze this nonlinear beam model. The fixed points plots are made to identify the system’s internal resonance. The frequency ratio plot is proposed to predict the system internal resonance conditions. This study improved the author’s earlier work for a wider range of prediction on internal resonance conditions. The continuous concentrated moving loads are applied to this nonlinear beam model. The dynamic vibration absorber (DVA) is attached on the beam to reduce vibration and prevent internal resonance. The mass, spring constant and location of the DVA are studied to obtain the best damping effect on the nonlinear beam with moving loads. The results are verified by numerical results and ANSYS simulations.