Vibration analysis and distributed piezoelectric energy harvester design for the L-shaped beam

The vibration characteristics of a cantilever L-shaped beam perpendicular to the horizontal plane are investigated in this paper. The dynamical model of the L-shaped multi-beam structure is established by using the Euler-Bernoulli beam theory, where vibration equations of each substructure, matching conditions of the connection and boundary conditions are included. Based on the modal orthogonality, the discrete dynamical model with finite degrees of freedom is obtained. Then the distributed piezoelectric energy harvester is proposed to collect the vibration energy of the L-shaped beam. Different the most traditional energy harvester that the piezoelectric material covers the surface of the structure, the distributed energy harvester is placed on the selected points. The genetic algorithm is adopted to obtain the optimal position that can provide the maximum output power. The validation and accuracy of the present model is verified by comparison with the finite element model. Numerical results show the discrete model can perform the dynamic characteristics of the structure well with only two modes. By the comparison of different configurations, it concludes that the optimal position of the distributed piezoelectric energy harvester is close to the fixed end of the whole cantilever structure.