Control of Nonlinear Electro/Elastic Beam and Plate Systems (Finite Element Formulation and Analysis)

Wang, D. W.; Tzou, H. S.; Lee, H.-J.

doi:10.1115/1.1640357

Cited by 16 publications

(9 citation statements)

References 25 publications

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“…Secondly, the strain-stress relationship of PVDF and PPy films becomes nonlinear as the strain increases [22,23,29,30]. Thirdly, under large swelling, the symmetrical trilayer arrangement generates a neutral line that is no longer at the center line due to the geometric nonlinearity.…”

Section: Nonlinear Mechanical Model Based On a Swelling Frameworkmentioning

confidence: 99%

Nonlinear elastic modeling of differential expansion in trilayer conjugated polymer actuators

Yang¹,

Pence²,

Tan³

2008

Smart Mater. Struct.

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Conjugated polymers are promising actuation materials for biomimetic robots and biomedical devices. Large bending is involved in some of these applications. This poses significant challenges in electromechanical modeling, because the linear elasticity theory is only valid when the strain is small. In this paper an effective strategy based on the nonlinear elasticity theory is proposed to model the mechanical output of a trilayer conjugated polymer beam under actuation. Instead of using the elastic modulus as in the linear elasticity theory, we use a nonlinear strain energy function to capture the stored elastic energy under actuation-induced swelling, which further allows us to compute the induced stress. The deformation variables are obtained by numerically solving the force and bending moment balance equations simultaneously. Experimental results have demonstrated that the proposed model shows superiority over the linear model, and is able to capture the actuation behavior well under large actuation voltages. The proposed framework can also be applied to the analysis of large deformations in some other electroactive polymers.

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Section: Nonlinear Mechanical Model Based On a Swelling Frameworkmentioning

confidence: 99%

Nonlinear elastic modeling of differential expansion in trilayer conjugated polymer actuators

Yang¹,

Pence²,

Tan³

2008

Smart Mater. Struct.

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“…T HE active control of flexible structures has been an active field of research for several decades, and has played an important role in the incorporation of lightweight, lightly damped and inherently flexible designs for manipulator links, rotor blades, and aerospace structures (Narayanan and Balamurugan, 2003;Oliveira et al, 2004;Wang et al, 2004a;Hu and Ma, 2005;Wang and Mills, 2005;Vasques and Rodrigues, 2006). Lightweight designs have several advantages, such as high payload/weight ratio for power efficiency and fast maneuvering, in comparison to more massive, yet rigid, predecessors.…”

Section: Introductionmentioning

confidence: 99%

Finite Element Modeling of a Slewing Non-linear Flexible Beam for Active Vibration Control with Arrays of Sensors and Actuators

Gilardi

Buckham

Park

2009

Journal of Intelligent Material Systems and Structures

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In this article, a new finite element model (FEM) of an EulerBernoulli beam, developed through an absolute nodal coordinate formulation (ANCF), is presented for simulation and analysis of the performance of surface-bonded piezoelectric actuators in suppressing non-linear transverse vibrations that are induced by very fast slewing. The elastic deformations experienced are an order of magnitude larger than cases considered to date, and the model employs a unique cubic spline approximation to the beam's deformed elastic line that is in terms of node positions and curvatures. To ensure relevant commentary on the vibration suppression properties of the distributed piezoelectric actuators, a material damping model was introduced in the continuum equations to capture the non-linear damping of the very slender beam that is observed in experiments. Following the ANCF methodology, the constitutive damping moment is formulated in terms of the absolute nodal coordinates with care taken to ensure the calculation is singularity free. Galerkin's method of weighted residuals is applied to discretize the revised equations of motion derived for the beam continuum. The FE beam model exploits a synergy between the twisted spline geometry and the lumped mass approximation to halve the size of the matrix equations that must be solved on each time step. However, this condensation of the matrix equations requires the use of interelement boundaries at the edges of the surface-bonded piezos. Using a single-link flexible manipulator as an example, a number of static and dynamic simulation examples that illustrate the validity of our FEM are presented, including comparisons to theoretical and other existing numerical solutions in literature. In addition, active vibration control examples are presented using proportional-and derivative-based hub motion and piezoelectric actuator controls in suppressing dramatic vibrations induced by fast slewing.

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“…Oh et al [8] numerically proved the thermopiezoelastic snapping phenomena of active piezolaminated plates based on multifield layerwise theories. Wang et al [9] reported adaptive structures involving large imposed deformation based on total Lagrangian formulation. Ahmad et al [10] formulated linear and nonlinear models of a smart beam using general electrothermoelastic relations.…”

Section: Introductionmentioning

confidence: 99%

Thermopiezoelastic nonlinear dynamics of active piezolaminated plates

Oh¹

2005

Smart Mater. Struct.

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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.

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Control of Nonlinear Electro/Elastic Beam and Plate Systems (Finite Element Formulation and Analysis)

Cited by 16 publications

References 25 publications

Nonlinear elastic modeling of differential expansion in trilayer conjugated polymer actuators

Nonlinear elastic modeling of differential expansion in trilayer conjugated polymer actuators

Finite Element Modeling of a Slewing Non-linear Flexible Beam for Active Vibration Control with Arrays of Sensors and Actuators

Thermopiezoelastic nonlinear dynamics of active piezolaminated plates

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