Active control of nonlinear vibration of sandwich piezoelectric beams: A simplified approach

Belouettar, Salim; Azrar, L.; Daya, El Mostafa; Laptev, V L; Potier‐Ferry, Michel

doi:10.1016/j.compstruc.2007.02.009

Cited by 56 publications

(40 citation statements)

References 15 publications

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“…Nonlinear free and forced oscillations of piezoelectric clamped-clamped microresonators have been studied in [20] and in [21] when lying in an electrostatic environment. The influence of imperfections on the nonlinear vibratory behavior of doubly supported sandwich piezoelectric beam has been treated in [22,23]. Analytical models of piezoelectrically actuated microcantilevers may be found in [24][25][26].…”

Section: Introductionmentioning

confidence: 99%

Finite element reduced order models for nonlinear vibrations of piezoelectric layered beams with applications to NEMS

Lazarus

Thomas

Deü

2012

Finite Elements in Analysis and Design

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a b s t r a c tThis article presents a finite element reduced order model for the nonlinear vibrations of piezoelectric layered beams with application to NEMS. In this model, the geometrical nonlinearities are taken into account through a von Ká rmá n nonlinear strain-displacement relationship. The originality of the finite element electromechanical formulation is that the system electrical state is fully described by only a couple of variables per piezoelectric patches, namely the electric charge contained in the electrodes and the voltage between the electrodes. Due to the geometrical nonlinearity, the piezoelectric actuation introduces an original parametric excitation term in the equilibrium equation. The reduced-order formulation of the discretized problem is obtained by expanding the mechanical displacement unknown vector onto the short-circuit eigenmode basis. A particular attention is paid to the computation of the unknown nonlinear stiffness coefficients of the reduced-order model. Due to the particular form of the von Ká rmá n nonlinearities, these coefficients are computed exactly, once for a given geometry, by prescribing relevant nodal displacements in nonlinear static solutions settings. Finally, the low-order model is computed with an original purely harmonic-based continuation method. Our numerical tool is then validated by computing the nonlinear vibrations of a mechanically excited homogeneous beam supported at both ends referenced in the literature. The more difficult case of the nonlinear oscillations of a layered nanobridge piezoelectrically actuated is also studied. Interesting vibratory phenomena such as parametric amplification or patch length dependence of the frequency output response are highlighted in order to help in the design of these nanodevices.

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Section: Introductionmentioning

confidence: 99%

Finite element reduced order models for nonlinear vibrations of piezoelectric layered beams with applications to NEMS

Lazarus

Thomas

Deü

2012

Finite Elements in Analysis and Design

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“…In the coupled problem of forced vibrations and self-heating of a compound shell of revolution with temperature-dependent viscoelastic properties, the nonlinear system of equations (7)- (19) is solved by a time-marching integration method [6,13]. To this end, we transform the system of electroelastic equations to a form that describes the widest possible class of shells of revolution, including circular plates and cylindrical shells.…”

Section: Problem Solvingmentioning

confidence: 99%

“…At the first step, the problem is solved considring isothermal electromechanical characteristics of materials. After the dissipation function (18) is found, the heat-conduction problem (17), (19) is solved by the explicit finite-difference method. Then, the stiffness characteristics (4), (15) = .…”

Section: Problem Solvingmentioning

confidence: 99%

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Control of axisymmetric resonant vibrations and self-heating of shells of revolution with piezoelectric sensors and actuators

Киричок

2011

Int Appl Mech

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The coupled problem of forced vibrations and self-heating of thermoviscoelectroelastic shells of revolution with piezoceramic sensor and actuator under monoharmonic loading is solved. The temperature dependence of the complex characteristics of the passive and piezoactive materials is taken into account. The coupled nonlinear problem of thermoelectroelasticity is solved by time-marching integration, using discrete orhogonalization to integrate the equations of elasticity and explicit finite differencing to solve the heat conduction equation. The effect of the dimensions of the sensor and actuator and self-heating on the sensor voltage and on the active damping of forced vibrations of a circular plate under uniform monoharmonic transverse pressure is studied Introduction. Study of the forced vibrations of layered plates and shells is an important division of dynamics because they model the mechanical behavior of the majority of thin-walled structural members in modern engineering. These elements sustain intensive stationary and nonstationary, including harmonic loads, which can cause large stresses and high-amplitude displacements. Passive damping is used to decrease the amplitude of forced vibrations of thin-walled elements with highly elastic coatings with high hysteresis losses [3, 15, 16, etc.]. Recent trends are toward intensive development of methods for active control and damping of stationary and nonstationary vibrations of thin-walled elements with piezoelectric inclusions [13, 20, 27, 28, etc.]. Such inclusions play the role of either sensors, which indicate the mechanical state of the thin-walled element, or actuators, to which voltage of appropriate amplitude and phase is applied to damp the mechanical vibrations of the element. The forced vibrations of thin-walled elements are usually controlled using both actuators and sensors. The sensor-actuator relationship is described by feedback equations [9,13,27,28]. The state of the art in active damping of the vibrations of thin-walled elements in the isothermal case is discussed in the monographs [13, 27, 28, etc.].The effectiveness of active damping is strongly dependent on the electromechanical properties of materials, the dimensions and arrangement of the sensors and actuators, and the boundary conditions [10,12,14]. A significant factor influencing the effectiveness of active damping is thermal effects due to hysteresis losses in the material or heat transfer to the environment. The influence of temperature on the effectiveness of actuators and sensors in damping the forced vibrations of circular and rectangular plates was first studied in [3-11, etc.]. Electromechanical models of layered shells with distributed piezoelectric sensors and actuators for controlling forced stationary and nonstationary vibrations were constructed in [7,8].A separate group of structural elements includes sandwich structures with one passive layer bonded to two piezoactive layers of which one is an actuator and the other is a sensor. Numerical results were mainly obtained f...

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“…Ову теорију су за анализу нелинеарних вибрација паметне композитне греде користили су истраживачи у радовима [20,21].…”

Section: моделовање танкозидних композитних структураunclassified

Dynamic behavior of smart thin-walled composite structures

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Active control of nonlinear vibration of sandwich piezoelectric beams: A simplified approach

Cited by 56 publications

References 15 publications

Finite element reduced order models for nonlinear vibrations of piezoelectric layered beams with applications to NEMS

Finite element reduced order models for nonlinear vibrations of piezoelectric layered beams with applications to NEMS

Control of axisymmetric resonant vibrations and self-heating of shells of revolution with piezoelectric sensors and actuators

Dynamic behavior of smart thin-walled composite structures

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