Distributed vibration control and identification of coupled elastic/piezoelectric systems: Finite element formulation and applications

Tzou, H. S.; Tseng, Chao-Wen

doi:10.1016/0888-3270(91)90044-6

Cited by 81 publications

(45 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The cantilever consists of two piezoelectric PVDF layers poled in opposite direction and was introduced by Tzou and Tseng [58]. Since then, the test has been numerously used, e.g.…”

Section: Piezoelectric Bimorphmentioning

confidence: 99%

“…The results are given in Figure 7(a) and are compared with other piezoelectric finite element formulations from the literature. Whereas [59] also shows a staircase function for a layered plate element and a shallow shell element, [60] and [58] give a linear distribution for a beam element and for a plate/shell element respectively. The linear distribution here results from the disregard of the electrodes and just represents the continuous material curve.…”

Section: Piezoelectric Bimorphmentioning

confidence: 99%

“…We incorporate the interpolations of the strains, the electric fields, the stress resultants, and the dielectric displacements in equation (58) and formulate the approximation of the variational formulation on element level as…”

Section: Approximation Of the Weak Form And Linearizationmentioning

confidence: 99%

See 2 more Smart Citations

A finite element formulation for piezoelectric shell structures considering geometrical and material non‐linearities

Schulz

Klinkel

Wagner

2011

Numerical Meth Engineering

View full text Add to dashboard Cite

In this paper we present a nonlinear finite element formulation for piezoelectric shell structures. Based on a mixed multi field variational formulation, an electro-mechanical coupled shell element is developed considering geometrically and materially nonlinear behavior of ferroelectric ceramics. The mixed formulation includes the independent fields of displacements, electric potential, strains, electric field, stresses, and dielectric displacements. Besides the mechanical degrees of freedom, the shell counts only one electrical degree of freedom. This is the difference of the electric potential in thickness direction of the shell. Incorporating nonlinear kinematic assumptions, structures with large deformations and stability problems can be analyzed. According to a Reissner-Mindlin theory, the shell element accounts for constant transversal shear strains. The formulation incorporates a three-dimensional transversal isotropic material law, thus the kinematic in thickness direction of the shell is considered. The normal zero stress condition and the normal zero dielectric displacement condition of shells are enforced by the independent resultant stress and resultant dielectric displacement fields. Accounting for material nonlinearities, the ferroelectric hysteresis phenomena are considered using the Preisach model. As a special aspect, the formulation includes temperaturedependent effects and thus the change of the piezoelectric material parameters due to the temperature. This enables the element to describe temperature dependent hysteresis curves.

show abstract

“…The cantilever consists of two piezoelectric PVDF layers poled in opposite direction and was introduced by Tzou and Tseng [58]. Since then, the test has been numerously used, e.g.…”

Section: Piezoelectric Bimorphmentioning

confidence: 99%

Section: Piezoelectric Bimorphmentioning

confidence: 99%

See 1 more Smart Citation

A finite element formulation for piezoelectric shell structures considering geometrical and material non‐linearities

Schulz

Klinkel

Wagner

2011

Numerical Meth Engineering

View full text Add to dashboard Cite

show abstract

“…A vast literature is already available based on geometrically linear (small deflection) theories for structures with piezoelectric layers or patches and associated numerical methods, see, for example, the pioneering works by Robbins and Reddy [1], see also Krommer [2], Maurini et al [3,4], dell'Isola and Rosa [5], for beams, by Mindlin [6], Lee [7], Yang et al [8], Ghosh and Batra [9], Carrera [10], Carrera and Boscolo [11], Maurini et al [12], Alessandroni et al [13], Rosi et al [14] for plates, by Rogacheva [15,16], Lammering [20], Tzou and Tseng [21], Tzou [22], Tzou and Ye [23], Le [17], Vetyukov et al [18], Kulikov and Plotnikova [19] for shells, among others. Nevertheless, one can observe still a lot of ongoing research activity to derive refined linear theories of adaptive beams, plates, and shells by using advanced kinematical hypotheses, for example, higherorder shear deformation or zigzag models with piecewise linear or cubic through-the-thickness distribution of the in-plane displacements, see, for example, Carrera [24], Carrera et al [25,26], Naumenko and Eremeyev [27,28], and the reference therein.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear finite element modeling of vibration control of plane rod-type structural members with integrated piezoelectric patches

Chróścielewski

Schmidt

Eremeyev

2018

Continuum Mech. Thermodyn.

View full text Add to dashboard Cite

This paper addresses modeling and finite element analysis of the transient large-amplitude vibration response of thin rod-type structures (e.g., plane curved beams, arches, ring shells) and its control by integrated piezoelectric layers. A geometrically nonlinear finite beam element for the analysis of piezolaminated structures is developed that is based on the Bernoulli hypothesis and the assumptions of small strains and finite rotations of the normal. The finite element model can be applied to static, stability, and transient analysis of smart structures consisting of a master structure and integrated piezoelectric actuator layers or patches attached to the upper and lower surfaces. Two problems are studied extensively: (i) FE analyses of a clamped semicircular ring shell that has been used as a benchmark problem for linear vibration control in several recent papers are critically reviewed and extended to account for the effects of structural nonlinearity and (ii) a smart circular arch subjected to a hydrostatic pressure load is investigated statically and dynamically in order to study the shift of bifurcation and limit points, eigenfrequencies, and eigenvectors, as well as vibration control for loading conditions which may lead to dynamic loss of stability.

show abstract

“…However, these SBT based models are insignificant for thick and short piezoelectric smart beams with thick piezoelectric face layers as SBT neglects shear effect in faces. Tzou and Tseng (1991) proposed a non-conforming hexahedron piezoelectric finite element by adding internal degrees of freedom to the original eight node hexahedron solid element (Tzou and Tseng, 1988), to give improved performance in thin structural analysis. Tzou and Ye (1996) developed a new laminated quadratic C 0 piezoelastic triangular shell finite element using layerwise constant shear angle theory.…”

Section: Introductionmentioning

confidence: 99%

An accurate novel coupled field Timoshenko piezoelectric beam finite element with induced potential effects

Sulbhewar

Raveendranath

2014

Lat. Am. j. solids struct.

View full text Add to dashboard Cite

An accurate coupled field piezoelectric beam finite element formulation is presented. The formulation is based on First-order Shear Deformation Theory (FSDT) with layerwise electric potential. An appropriate through-thickness electric potential distribution is derived using electrostatic equilibrium equations, unlike conventional FSDT based formulations which use assumed independent layerwise linear potential distribution. The derived quadratic potential consists of a coupled term which takes care of induced potential and the associated change in stiffness, without bringing in any additional electrical degrees of freedom. It is shown that the effects of induced potential are significant when piezoelectric material dominates the structure configuration. The accurate results as predicted by a refined 2D simulation are achieved with only single layer modeling of piezolayer by present formulation. It is shown that the conventional formulations require sublayers in modeling, to reproduce the results of similar accuracy. Sublayers add additional degrees of freedom in the conventional formulations and hence increase computational cost. The accuracy of the present formulation has been verified by comparing results obtained from numerical simulation of test problems with those obtained by conventional formulations with sublayers and ANSYS 2D simulations.

show abstract

Distributed vibration control and identification of coupled elastic/piezoelectric systems: Finite element formulation and applications

Cited by 81 publications

References 12 publications

A finite element formulation for piezoelectric shell structures considering geometrical and material non‐linearities

A finite element formulation for piezoelectric shell structures considering geometrical and material non‐linearities

Nonlinear finite element modeling of vibration control of plane rod-type structural members with integrated piezoelectric patches

An accurate novel coupled field Timoshenko piezoelectric beam finite element with induced potential effects

Contact Info

Product

Resources

About