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Journal ArticleDOI

Linear and Nonlinear Analysis of a Smart Beam Using General Electrothermoelastic Formulation

01 Apr 2004-AIAA Journal (American Institute of Aeronautics and Astronautics)-Vol. 42, Iss: 4, pp 840-849
TL;DR: In this article, coupled electrothermoelastic equations applicable to the analysis of smart structures have been derived from first principles, and applying a layer-by-layer finite element model, the induced potential and mechanical deformations in the piezo and non-piezo core material have been obtained for various cases of actuation and sensing of a smart beam under external mechanical load and actuation potential.
Abstract: Coupled electrothermoelastic equations applicable to the analysis of smart structures have been derived from first principles. Using the equations and applying a layer-by-layer finite element model, the induced potential and mechanical deformations in the piezo and nonpiezo core material have been obtained for various cases of actuation and sensing of a smart beam under external mechanical load and actuation potential. The present study clearly brings out the essential difference between sensing and actuation. It is also brought out that the interaction between polarization and electric field in the piezo continuum leads to nonlinear distributed body force and nonsymmetric stress tensor. These nonlinear effects are found to have significant influence on the deformation of a smart beam under actuation. Shape control studies of multipatch smart beams have also been investigated.
Citations
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Journal ArticleDOI
TL;DR: In this article, a general formulation for the reduction of the three-dimensional problem of electrothermoelasticity in slender solids to an arbitrarily defined reference line is presented, which is based on a variationalasymptotic formulation, using the slenderness ratio as small parameter.
Abstract: A general formulation for the reduction of the three-dimensional problem of electrothermoelasticity in slender solids to an arbitrarily defined reference line is presented The dimensional reduction is based on a variationalasymptotic formulation, using the slenderness ratio as small parameter In the proposed scheme, the coupled linear electroelastic equations are solved at the cross-sectional level using the finite element method Furthermore, modal components of the displacement field are added to introduce arbitrary deformation shapes into the onedimensional analysis, and arbitrary electric modes are used to define applied electric fields at the cross section This results in a general definition of a coupled electroelastic stiffness, which can be used in virtually all composite and active beam formulations, as well as in the development of new low-order high-accuracy reduced models for active structures Finally, the formulation also yields recovery relations for the elastic and electric fields in the original three-dimensional solid, once the one-dimensional problem is solved The method has been implemented in a computer program (UM/VABS) and numerical results are presented for active anisotropic beam cross sections of simple geometries, which are shown to compare very well with three-dimensional finite element analysis

107 citations

Journal ArticleDOI
TL;DR: In this article, coupled electro-thermo-elastic equations applicable for the analysis of smart structures with piezoelectric patches/layers have been derived from the fundamental principles of mass, linear momentum, angular momentum, energy and charge conservation.
Abstract: Coupled electro-thermo-elastic equations applicable for the analysis of smart structures with piezoelectric patches/layers have been derived from the fundamental principles of mass, linear momentum, angular momentum, energy and charge conservation. The relevant constitutive equations have been obtained by using the second law of thermodynamics. The interaction of the electric field and polarization introduces distributed non-linear body force in the piezo material, and in addition renders the stress tensor non-symmetric due to distributed couple. Using the linear equations, and applying a layer-by-layer finite element model, the induced electric potential and mechanical deformations in the piezo and non-piezo core material have been obtained for various cases of actuation and sensing of a smart beam under external mechanical, electrical and thermal loadings. The mathematical formulation and the solution technique have been validated by comparing the results of the present study with those available in the literature. It is also shown that piezo patches can be effectively used for shape control.

32 citations

Journal ArticleDOI
TL;DR: In this paper, Cimento revisited some variational principles for the fundamental equations of a regular region of piezoelectric, thermopiez-olectric and hygrothermopiezoellectric materials in the elastic range.
Abstract: In this paper some variational principles are revisited for the fundamental equations of a regular region of piezoelectric, thermopiezoelectric, and hygrothermopiezoelectric (but non-stochastic, non-local, and non-relativistic) materials in the elastic range. Certain oversights, and especially, those involving the so-called Hu-Washizu variational principle of piezoelectricity that was first formulated in a paper (“Variational Principles in Piezoelectricity,” Lettere Al Nuovo Cimento, vol. 7, 449–454, 1973) are clarified within the “ISI-Web of Science” publications in the open literature. Similar variational principles of piezoelectricity are cited.

32 citations

Journal ArticleDOI
TL;DR: In this paper, a multi-field layer-wise finite element is proposed to assure high accuracy and nonlinearity of displacement, electric and thermal fields for active piezolaminated plates considering thermopiezoelastic behaviors.
Abstract: Nonlinear dynamics of active piezolaminated plates are investigated considering snap-through thermopiezoelastic behaviors. For highly deformed structures with small strain, the incremental total Lagrangian formulation is presented based on Hamilton's variational principles. A multi-field layer-wise finite element is proposed to assure high accuracy and nonlinearity of displacement, electric and thermal fields. For dynamic consideration of thermopiezoelastic snap-through phenomena, the implicit Newmark-beta scheme with the Newton–Raphson iteration is implemented for the transient response of various piezolaminated models with symmetric or eccentric active layers. To validate the new finite element formulation and code, dynamic analyses of nonlinear elastic plates are compared with published data, resulting in good agreements and better solutions. The bifurcate buckling and sling-shot buckling of the symmetric and eccentric structural models are first investigated and the characteristics of piezoelectric active responses are studied to find snap-through piezoelectric potentials and the load-path tracking map. The thermoelastic stable and unstable postbuckling, thermopiezoelastic snap-through phenomena with several attractors are proved using the nonlinear time responses for initial conditions and damping loss factors. Present results show that the snap-through phenomena should be investigated with respect to nonlinear dynamics for shape control of piezolaminated buckled plates by using piezoelectric materials.

25 citations

Journal ArticleDOI
TL;DR: In this paper, the second-order nonlinear constitutive equations are used in the variational principle approach to develop a nonlinear finite element (FE) model for piezoelectric laminated composite plates and shells.
Abstract: In this article, we focus on static finite element (FE) simulation of piezoelectric laminated composite plates and shells, considering the nonlinear constitutive behavior of piezoelectric materials under large applied electric fields. Under the assumptions of small strains and large electric fields, the second-order nonlinear constitutive equations are used in the variational principle approach, to develop a nonlinear FE model. Numerical simulations are performed to study the effect of material nonlinearity for piezoelectric bimorph and laminated composite plates as well as cylindrical shells. In comparison to the experimental investigations existing in the literature, the results predicted by the present model agree very well. The importance of the present nonlinear model is highlighted especially in large applied electric fields, and it is shown that the difference between the results simulated by linear and nonlinear constitutive FE models cannot be omitted.

23 citations

References
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Journal ArticleDOI
TL;DR: In this article, a bibliography is given containing 2067 references published during 2002 and 2003 on piezoelectric and pyroelectric properties of materials and their applications, which contains listings of journal articles with complete bibliographic citations.
Abstract: A bibliography is given containing 2067 references published during 2002 and 2003 on piezoelectric and pyroelectric properties of materials and their applications. It contains listings of journal articles with complete bibliographic citations. This bibliography is the continuation of a series published semi-annually.

47 citations

Journal ArticleDOI
TL;DR: In this paper, a multi-field layer-wise finite element is proposed to assure high accuracy and nonlinearity of displacement, electric and thermal fields for active piezolaminated plates considering thermopiezoelastic behaviors.
Abstract: Nonlinear dynamics of active piezolaminated plates are investigated considering snap-through thermopiezoelastic behaviors. For highly deformed structures with small strain, the incremental total Lagrangian formulation is presented based on Hamilton's variational principles. A multi-field layer-wise finite element is proposed to assure high accuracy and nonlinearity of displacement, electric and thermal fields. For dynamic consideration of thermopiezoelastic snap-through phenomena, the implicit Newmark-beta scheme with the Newton–Raphson iteration is implemented for the transient response of various piezolaminated models with symmetric or eccentric active layers. To validate the new finite element formulation and code, dynamic analyses of nonlinear elastic plates are compared with published data, resulting in good agreements and better solutions. The bifurcate buckling and sling-shot buckling of the symmetric and eccentric structural models are first investigated and the characteristics of piezoelectric active responses are studied to find snap-through piezoelectric potentials and the load-path tracking map. The thermoelastic stable and unstable postbuckling, thermopiezoelastic snap-through phenomena with several attractors are proved using the nonlinear time responses for initial conditions and damping loss factors. Present results show that the snap-through phenomena should be investigated with respect to nonlinear dynamics for shape control of piezolaminated buckled plates by using piezoelectric materials.

25 citations

Journal ArticleDOI
TL;DR: In this article, the authors studied the distributed vibration sensing and control of a piezoelectric laminated curved beam with a distributed sensor and actuator, and evaluated the effectiveness of active damping controls with respect to different beam thickness, and sensor/actuator thickness.
Abstract: The distributed vibration sensing and control of a piezoelectric laminated curved beam are studied. The mathematical model of a curved beam with a distributed piezoelectric sensor and actuator is formulated first, followed by vibration analysis. This model provides estimates of the sensor signal, actuator-induced membrane force, and actuator-induced bending moment, as well as predicting the controlled damping ratio and dynamic response. The sensor sensitivity with various sensor thicknesses is studied and compared. The effectiveness of active damping controls is evaluated with respect to different beam thickness, and sensor/actuator thickness. Numerical examples are provided and simulation results are discussed.

24 citations

Journal ArticleDOI
TL;DR: An analytical solution of composite beams with piezoelectric laminae is presented in this article, where the governing equation of smart laminated composite beams, which is based on first-order deformation theory (Mindlin plate theory), is derived.
Abstract: An analytical solution of composite beams with piezoelectric laminae is presented. The governing equation of smart laminated composite beams, which is based on first-order deformation theory (Mindlin plate theory), is derived. The main feature of this work is that it introduces the displacement potential function to simplify the governing equation. A new assumption of harmonic vibration and the transformation method of complex numbers are introduced. The behavior of feedback control gain and its control effects are studied. Graphical outputs are also generated, to study the effectiveness of piezoelectric sensors and actuators in actively controlling the transverse of smart laminated beams.

22 citations

Journal ArticleDOI
TL;DR: Using laws of conservation, a general electrothermoelastic formulation has been developed for the analysis of smart structures based on this formulation a layer-by-layer finite element model was developed using variational principle as mentioned in this paper, which effectively captured the continuity of shear stress across the interface between piezolayers and the metallic host material.
Abstract: Using laws of conservation, a general electrothermoelastic formulation has been developed for the analysis of smart structures Based on this formulation a layer-by-layer finite element model has been developed using variational principle It is shown that the layer-by-layer finite element modeling effectively captures the continuity of shear stress across the interface between piezolayers and the metallic host material Several studies of actuation and sensing of single and multipatch smart beams have been carried out The key difference between actuation and sensing has been brought out with regard to the variation of shear stress along the span at interfaces between piezopatch and the core In addition, the influence of electric field along the span of a piezo cantilever beam has been studied, and it is shown that this electric field produces a large transverse shear stress resulting in a steplike deformation of the piezobeam It is envisaged that this concept can be used to develop a switch in a microelectromechanical-system device

7 citations