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.

研究了垂直于水平面的悬臂L形梁的振动特性。利用欧拉-伯努利梁理论建立了L形多梁结构的动力学模型，其中包括了每个子结构的振动方程，连接的匹配条件和边界条件。基于模态正交性，获得具有有限自由度的离散动力学模型。然后提出了分布式压电能量收集器，以收集L形梁的振动能量。与最传统的压电材料覆盖结构表面的能量收集器不同，分布式能量收集器放置在选定的点上。采用遗传算法获得可以提供最大输出功率的最佳位置。通过与有限元模型比较，验证了本模型的有效性和准确性。数值结果表明，离散模型仅用两种模式就能很好地表现结构的动力特性。通过比较不同的配置，可以得出分布式压电式能量收集器的最佳位置接近整个悬臂结构的固定端。