Nonlinearities in Langevin transducers

Guyomar, Daniel; Aurelle, N.; Richard, Claude; Gonnard, P.; Eyraud, L.

doi:10.1109/ultsym.1994.401694

Cited by 32 publications

(13 citation statements)

References 3 publications

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“…Substituting (22) and (29)(30)(31)(32)(33) into (28), and eliminating the terms that lead to secular terms, we obtain the complex-valued modulation equation…”

Section: Discussionmentioning

confidence: 99%

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Effects of nonlinear piezoelectric coupling on energy harvesters under direct excitation

2011

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A nonlinear analysis of an energy harvester consisting of a multilayered cantilever beam with a tip mass is performed. The model takes into account geometric, inertia, and piezoelectric nonlinearities. A combination of the Galerkin technique, the extended Hamilton principle, and the Gauss law is used to derive a reduced-order model of the harvester. The method of multiple scales is used to determine analytical expressions for the tip deflection, output voltage, and harvested power near the first global natural frequency. The results show that one-or two-mode approximations are not sufficient to produce accurate estimates of the voltage and harvested power. A parametric study is performed to investigate the effects of the nonlinear piezoelectric coefficients and the excitation amplitude on the system response. The effective nonlinearity may be of the hardening or softening type, depending on the relative magnitudes of the different nonlinearities.

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“…Substituting (22) and (29)(30)(31)(32)(33) into (28), and eliminating the terms that lead to secular terms, we obtain the complex-valued modulation equation…”

Section: Discussionmentioning

confidence: 99%

“…Based on the electric Gibbs function, Joshi [30], Guyomar et al [31], and Arafa and Baz [32] developed the piezoelectric consti- (1)…”

Section: Introductionmentioning

confidence: 99%

Effects of nonlinear piezoelectric coupling on energy harvesters under direct excitation

2011

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“…Including the nonlinear piezoelectric contribution, one finds that D 2 is given by the following relation [28,29]:…”

Section: Problem Formulationmentioning

confidence: 99%

Global nonlinear distributed-parameter model of parametrically excited piezoelectric energy harvesters

2011

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A global nonlinear distributed-parameter model for a piezoelectric energy harvester under parametric excitation is developed. The harvester consists of a unimorph piezoelectric cantilever beam with a tip mass. The derived model accounts for geometric, inertia, piezoelectric, and fluid drag nonlinearities. A reduced-order model is derived by using the EulerLagrange principle and Gauss law and implementing a Galerkin discretization. The method of multiple scales is used to obtain analytical expressions for the tip deflection, output voltage, and harvested power near the first principal parametric resonance. The effects of the nonlinear piezoelectric coefficients, the quadratic damping, and the excitation amplitude on the output voltage and harvested electrical power are quantified. The results show that a one-mode approximation in the Galerkin approach is not sufficient to evaluate the performance of the harvester. Furthermore, the nonlinear piezoelectric coefficients have an important influence on the harvester's behavior in terms of softening or hardening. Depending on the excitation frequency, it is determined that, for small values of the quadratic damping, there is an overhang associated with a subcritical pitchfork bifurcation.A. Abdelkefi · A.H. Nayfeh · M.R. Hajj ( ) Virginia Tech,

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“…Se analiz-en todo caso, la presencia de modos resonantes en las muestras (15,16), y fundamentalmente las posibles desviaciones de las frecuencias de los mismos al someterles a campos oscilantes, siempre menores que el de polarizaci-n. En la figura 2 puede verse el resultado para una resonancia. Tanto en esta figura como en el resto de resultados observados, se comprueba que existe una ligera variaci-n en la respuesta de las muestras pero que en todo momento es poco significativa.…”

Section: Dependencia Con La Amplitud Del Campo Oscilante Aplicadounclassified

No linealidad en muestras cerámicas de PZT muy delgadas

Frutos¹,

González²,

Duro³

et al. 1999

Bol. Soc. Esp. Ceram. Vidr.

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El desarrollo de sensores piezoelŽctricos de alta frecuencia, exige trabajar con muestras de material muy delgadas, del orden de micras. En estos espesores, las tensiones de trabajo causan fuertes perturbaciones en los materiales, provocando respuestas no lineales, sumamente dependientes de las condiciones de trabajo. Con el objetivo de avanzar en el conocimiento de este fen-meno, y haciendo uso de la tŽcnica de Espectroscopia de Impedancia Compleja, hemos analizado la respuesta de muestras de PZT cer ‡mico adelgazadas a espesores de micras, en funci-n del campo aplicado y de la amplitud de la se-al de an ‡lisis. El estudio de estos resultados, puede permitir sentar las bases para el desarrollo de sensores ultras-nicos de alta frecuencia sintonizables. Palabras clave: Piezoelectricidad, resonancia, sensores, no linealidad. No lineal response in thin samples OF PZT ceramics.The development of piezoelectric sensors for high frequency requires to work with very thin samples of material. At this thick nesses, the stress concentration produces strong perturbations in the materials, and the origin oF a non linear response, which depends field on working conditions. With the goal to advance in the knowledgement of this phenomenon, and by using Complex Impedance Spectroscopy, we have analysed the response of PZT ceramics with thickness of microns as a function of the applied and the amplitude of the analysis signal. These results allow to establish the base to the development of ultrasonic tunable sensors for high frequency.

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Nonlinearities in Langevin transducers

Cited by 32 publications

References 3 publications

Effects of nonlinear piezoelectric coupling on energy harvesters under direct excitation

Effects of nonlinear piezoelectric coupling on energy harvesters under direct excitation

Global nonlinear distributed-parameter model of parametrically excited piezoelectric energy harvesters

No linealidad en muestras cerámicas de PZT muy delgadas

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