Energy analysis of a piezoelectric patch laminated on cylindrical panels subjected to harmonic line loadings

In order to transform the vibration energy into electric energy, piezoelectric materials are often used due to their properties. This paper proposes an energy analysis model of cylindrical panels laminated with piezoelectric patch. With simply supported boundary condition at four sides, panels are excited by harmonic line loadings in transverse direction. Love & Kirchhoff thin shell theory and electromechanical equations are used to derive the voltage across the surface area of the piezoelectric patch. Considering the thin thickness of piezoelectric patch, its capacitance can be estimated by utilizing the formula of plate capacitor. Consequently, the energies can be presented with the equations only containing variables of capacitance and voltage. In case study, effect of the line loading location is firstly studied. The results show that the optimal position of longitudinal line loading is related to circumferential mode number, while it's only related to longitudinal mode number for circumferential line loading. The effect of the cylindrical panel curvature is also discussed afterward.