Theoretical analysis of dynamic property for piezoelectric cantilever triple-layer benders with large piezoelectric and electromechanical coupling coefficients

Gong, Liang; Pan, Chun; Pan, Qianqian; Feng, Zhi Hua

doi:10.1142/s2010135x1650017x

Cited by 6 publications

(4 citation statements)

References 21 publications

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“…The bending stiffness and the moment for a symmetric bimorph in short circuit condition are obtained from (27) and given in (36) and (37) [40]. By integrating equation 37twice and considering the boundary conditions at the clamped end ( (0, ) = 0 and ′(0, ) = 0), we obtain the expression of the stiffness matrix 2 given in (38).…”

Section: Mode Shapes Determinationmentioning

confidence: 99%

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Strongly coupled piezoelectric cantilevers for broadband vibration energy harvesting

et al. 2020

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Vibration energy harvesters based on piezoelectric resonators are promising for powering Wireless Sensors Nodes (WSNs). Yet, any mismatch between the resonant frequency of traditional harvesters and the vibration frequency can drastically decrease the scavenged power and make them ineffective. Electrical techniques able to tune the resonant frequency of piezoelectric harvesters has been proposed as a solution and opens up new perspectives. To be fully competitive, this approach requires energy harvesters with very strong global electromechanical coupling coefficients k² (>10%), whose design remains a challenge today. This work reports on a method to design strongly coupled piezoelectric cantilevers thanks to an analytical approach based on the Rayleigh-Ritz method and a two degrees-of-freedom model, which considers the proof mass inertia effects. Through an expression of the coupling coefficient, we provide design guidelines, which are experimentally validated. We show that a long proof mass is a very effective configuration to maximize the global electromechanical coupling coefficient and consequently the frequency bandwidth of the system. Three proposed prototypes exhibit some of the strongest squared global electromechanical coupling coefficients k² of the state-of-the-art of piezoelectric harvesters (16.6% for the PMN-PT cantilever, 11.3% and 16.4% for the narrow and wide PZT-5A cantilevers respectively) and demonstrate a wide bandwidth behavior (10.1%, 7.8% and 11.3% of the central frequency respectively). Using a strongly coupled prototype based on PZT-5A leveraged by a dedicated integrated circuit, we experimentally show that it can harvest enough power (more than 100µW) to supply a WSN over a frequency bandwidth as large as 21%.

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Section: Mode Shapes Determinationmentioning

confidence: 99%

“…Finally, equations (38) to (40) and the force and moment equilibrium analysis at the end of the beam lead to the 2-DOF coupled equation system (41) when no external excitation is considered.…”

Section: Mode Shapes Determinationmentioning

confidence: 99%

Strongly coupled piezoelectric cantilevers for broadband vibration energy harvesting

et al. 2020

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“…The apostrophes represent the spatial derivative according to coordinate. As discussed in [25], the electric field must be considered variable across the patches thicknesses for strongly coupled piezoelectric materials. Then the expression of the transverse electric field is given by (16) where is the flux leakage as introduced in [26] and expressed in (17).…”

Section: Hamilton Principlementioning

confidence: 99%

“…The total kinetic energy considered in the Hamilton principle consists of the kinetic energies of the beam and of the proof mass including its rotary inertia is expressed in (24). represents the mass per unit length of the bimorph expressed in (25) where and are the densities of the piezoelectric material and of the substrate respectively. ̇ is the base (clamped end) velocity, ̇ is the beam end relative velocity, ̇′ is the beam end speed of rotation.…”

Section: Hamilton Principlementioning

confidence: 99%

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

Gibus

Gasnier

Morel

et al. 2022

Mechanical Systems and Signal Processing

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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...

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Dynamic modeling of a piezoelectric micro-lens actuator with experimental validation

Rasid

Michael

Pota

2023

Sensors and Actuators A: Physical

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Theoretical analysis of dynamic property for piezoelectric cantilever triple-layer benders with large piezoelectric and electromechanical coupling coefficients

Cited by 6 publications

References 21 publications

Strongly coupled piezoelectric cantilevers for broadband vibration energy harvesting

Strongly coupled piezoelectric cantilevers for broadband vibration energy harvesting

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

Dynamic modeling of a piezoelectric micro-lens actuator with experimental validation

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