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Energy harvesting from nonlinear vibrations of an L-shaped beam using piezoelectric patches

S. Sharifi-Moghaddam, R. Tikani and S. Ziaei-Rad

Journal of the Brazilian Society of Mechanical Sciences and Engineering, Volume 43, Issue 3, February 2021, 158



In the present study, the energy harvesting from nonlinear vibrations of an L-shaped beam with the use of piezoelectric patches is evaluated. The beam was assumed to be a Euler–Bernoulli type in which the effects of rotational inertia and shear forces are neglected. Also, the effective mass of the beam is assumed to be at the end of the beam. The axial displacement of the beam is included with the assumption of small excitation amplitude. The effect of the piezoelectric patch on the equations of motion is also considered. First, the nonlinear motion equations of an L-shaped beam are extracted by the use of the Lagrange method, and then, the obtained equations of motion are solved by multiple scales technique. Also, the mode shapes of the system are calculated for the linear undamped system. The dimensions of the L-shaped beam are chosen in such a way that the ratio of the first-to-second natural frequency is 1 to 2, in order to increase the bandwidth of the energy harvesting. Finally, the results of the analytical solutions are compared and validated with the experimental results. Good agreement was observed between the theoretical values and the measured data.



A. Energy harvesting; B. L-shaped beam; C. Nonlinear vibrations; D. Piezoelectric patch


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