Non-linear losses study in strongly coupled piezoelectric device for broadband energy harvesting

Abstract

Piezoelectric vibration harvesters with strong electromechanical coupling coefficients have recently been combined with nonlinear electrical techniques capable of tuning their resonant frequency as a solution to provide energy to wireless sensor nodes from wideband vibrations. To be fully competitive, this approach requires piezoelectric generators with strong global electromechanical coupling coefficients k². However, the presence of non-linear dielectric and piezoelectric losses in piezoelectric materials significantly reduces the power harvested when strongly coupled materials are used. This paper presents a non-linear model that allows for a better consideration of losses for such piezoelectric harvesters. An experimental validation is performed with a strongly coupled cantilever based on a PMN-PT material (k²=16 %). The results reveal the importance of considering non-linear dielectric losses. Indeed, we show thanks to the model that neglecting these losses can induce an 18 % overestimation of the harvested power for the presented prototype driven at 0.5 m/s 2 amplitude ambient acceleration. Nomenclature Mass of the proof massVibration pulsation Rotary inertia of the proof mass according to its center of gravity Vibration frequency Distance between the free end of the beam and the center of gravity of the proof mass ( ) Vibration mode shape Ratio between the rotation inertia and the mass 31 2 Material coupling coefficient of the piezoelectric material Beam length 2 Global electromechanical coupling coefficient of the piezoelectric harvester Proof mass length Equivalent linear stiffness Proof mass height Forcing term Beam and mass width Equivalent mass Substrate volume Θ Linear coupling term Volume of piezoelectric material Equivalent clamped capacitance Mass per unit length of the bimorph Linear coupling term per unit length ℎ Piezoelectric patches thickness 2 Second order coupling term per unit length ℎ Substrate thickness 2 Second order bending stiffness per unit length 31 Linear piezoelectric equivalent coefficient 2 Nonlinear stiffness 31 Coefficient of the piezoelectric constant matrix Θ 2 Nonlinear coupling term 11 Coefficient of the compliance matrix of the piezoelectric material Resistive load 33 Coefficient of the free dielectric matrix of the piezoelectric material 1 Linear mechanical structural loss coefficient 33 Linear dielectric permittivity equivalent coefficient 2 Second order structural loss coefficient 11 Linear elastic equivalent coefficient 1 Linear dielectric loss coefficient 111 Nonlinear elastic constant 2 second order dielectric loss coefficient 311 Nonlinear piezoelectric equivalent constant , Coefficients that define the beam mode shape expression Young modulus of the substrate Beam end relative velocity displacement Linear bending stiffness Base displacement of the beam Longitudinal spatial coordinate Acceleration amplitude of the beam base Lateral spatial coordinate ( ) Transverse deflection of the beam Transversal spatial coordinate Nonlinear electric enthalpy density of the piez...

A strong electromechanically coupled and low-damped harvester for resonant frequency tuning

“…7. As the prototype exhibits a softening behavior and nonlinear losses with the variation of the acceleration level, the measurements have been fitted with the one mechanical degree of freedom nonlinear model presented in [6]. We notice that the results deduced from the model are close to the measurements despite the wide frequency range of measurements.…”

“…For given substrate and piezoelectric materials, RT is maximized for an optimal thickness ratio (hp/hs) opt . This optimal ratio is determined by calculating the zero of the derivative of the RT expression and is given in (6). (hp/hs ) opt depends only on a rigidity ratio κ that is defined in (7).…”

“…The maximum achievable value of RT for given piezoelectric and substrate materials, noted RT max , is determined by replacing hp/hs in ( 2) by (6). Fig.…”

“…We notice that the results deduced from the model are close to the measurements despite the wide frequency range of measurements. As explained in [6], [7], the power can be maximized with optimal capacitor and resistor pairs or some electrical techniques (e.g. SC-SECE [2]) in the frequency range between the power peaks given by resistors.…”

“…Although this value does not exactly equal the simulation results due to large uncertainties in spacing and glue thickness, the present harvester is one of the most coupled harvesters in the state of the art. As explained in[6],[7], the power can be maximized with optimal capacitor and resistor pairs or some electrical techniques (e.g. SC-SECE[2]) in the frequency range between the power peaks given by resistors.…”