Mathematical dynamics of electromechanical piezoelectric energy harvesters

Abstract

This research investigates vibration energy harvesting by modelling several piezoelectric-based structures. The usage of piezoelectric transduction under input vibration environments can be profitable for obtaining electrical energy for powering smart wireless sensor devices for health condition monitoring of rotating machines, structures and defence communication technology. The piezoelectric transduction shows strong prospect in the application of power harvesting because it can be applied at the microelectromechanical system design level in compact configuration with high sensitivity with respect to low input mechanical vibration. In this research work, the important aspects of the continuum thermopiezoelectric system associated with the laws of thermodynamics, Maxwell relations and Legendre transformations have been developed to explore the macroscopic thermopiezoelectric potential equations, the thermopiezoelectric equations of state and energy function forms. The application of the continuum thermopiezoelectric behaviour can be used to further formulate novel analytical methods of the electromechanical cantilevered piezoelectric bimorph beams with the tip mass using the weak and strong forms resulting from Hamiltonian’s principle.The constitutive electromechanical dynamic equations of the piezoelectric bimorph beam under one or two input base excitations can be used to derive the equations of the coupled electromechanical dynamic response of transverse-longitudinal form (CEDRTL), the coupled electromechanical dynamic response of longitudinal form (CEDRL) and the coupled electromechanical dynamic response of transverse form (CEDRT). The derivation of the constitutive electromechanical dynamic equations using the weak form of Hamiltonian’s principle can be further derived using the Ritz method associated with orthonomality whereas the closed form or distributed parameter reduced from strong form of Hamiltonian’s principle, can be further formulated using the convergent eigenfunction series with orthonormality. Laplace transformation can be used to give the solution in terms of the multi-mode transfer functions and multi-mode frequency response functions of dynamic displacement, velocity, electric voltage, current, power and optimal power. Moreover, the broadband multi-electromechanical bimorph beam with multi-resonance can also be explored showing the single- and multi-mode transfer functions and frequency response functions. A parametric case study of the piezoelectric bimorph beam with the tip mass and transverse input excitation is discussed to validate the weak and closed forms of the CEDRTL, under series and parallel connections, using the multi-mode frequency response functions with variable load resistance.A further case study of a broadband multi-electromechanical piezoelectric bimorph beam is also discussed using the weak form of the CEDRT to give the frequency response functions under variable load resistance. Finally, the piezoelectric bimorph beams with and without tip masses under transverse base input excitation are also comprehensively discussed using the weak forms of the CEDRTL and CEDRT models and compared with experimental results for variable load resistance. A piezoelectric bimorph beam with tip mass is investigated to show the close agreement between the CEDRTL model and experimental results using the polar amplitudes from the combined action of simultaneous longitudinal and transverse base input excitation.