Previous studies have proved that the piezoelectric L-shaped beam-mass structure is a good candidate to harvest energy from ambient mechanical vibration. However, most researches merely focused on bending mode of the structure, which only can capture energy from in-plane base excitation. To fully exert the advantages of L-shaped harvesters, this paper will explore their energy harvesting performance on torsional mode with out-of-plane base excitation. The electromechanical coupling governing equation of the L-shaped harvester in torsional mode is derived by applying Gauss's law and the Euler–Bernoulli beam theory with linear assumption, and the analytical results are also validated with experimental results. In addition, the influences of key geometric parameters on the resonance frequency and output voltage of the harvester are also presented. This work demonstrates the feasibility of utilizing torsional mode of the L-shaped unimorph structure to harvest energy from out-of-plane mechanical vibration, which shows the potential of designing multi-directional and multi-frequency L-shaped harvesters.

The thermoelastotransient response in a hollow sphere under different thermal shocks is analyzed. Coupled thermal stress and non-Fourier heat conduction are considered in the mathematic model. The systems of heat and motion equations are successfully uncoupled before Laplace transformation, and an analytic solution is given. By means of numerical Laplace inversion, the temperature and stress distributions are presented. From the numerical results from different thermal shocks, the influence of the impact speed to the coupled thermal stress problems can be observed. A comparison of temperature and stress distribution is given between the coupled thermal stress problems and static thermoelastic problems.