Analytical modeling of self-powered electromechanical piezoelectric bimorph beams with multidirectional excitation

Unused mechanical energies can be found in numerous ambient vibration sources in industry including rotating equipment, vehicles, aircraft, piping systems, fluid flow, and even external movement of the human body. A portion of the vibration energy can be recovered using piezoelectric transduction and stored for subsequent smart system utilization for applications including powering wireless sensor devices for health condition monitoring of rotating machines and defence communication technology. The vibration environment in the considered application areas is varied and often changes over time and can have components in three perpendicular directions, simultaneously or singularly. This paper presents the development of analytical methods for modelling of self-powered cantilevered piezoelectric bimorph beams with tip mass under simultaneous longitudinal and transverse input base motions utilizing the weak and strong forms of Hamiltonian’s principle and space- and time-dependent eigenfunction series which were further formulated using orthonormalization. The reduced constitutive electromechanical equations of the cantilevered piezoelectric bimorph were subsequently analysed using Laplace transforms and frequency analysis to give multi-mode frequency response functions (FRFs). The validation between theoretical and experimental results at the single mode of eigenfunction solutions reduced from multi-mode FRFs is also given.