Shell finite element for smart piezoelectric composite plate/shell structures and its application to the study of active vibration control

Balamurugan, V.; Narayanan, S.

doi:10.1016/s0168-874x(00)00070-6

Cited by 135 publications

(91 citation statements)

References 16 publications

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“…The lower surface is bordered by a piezoelectric PZT layer. The geometry and the material parameters for the graphite epoxy and PZT layers according to Balamurugan and Narayanan [64] are given in Table 2. The system is simply supported at the rectilinear edges and is modeled by 15 × 4 elements with 15 elements in circumference direction and 4 elements for the width b.…”

Section: • Cylindrical Shellmentioning

confidence: 99%

“…The results, normalized by the thickness h, are depicted in Figure 10 dependent on the normalized radius R between 0 • and 90 • of the cylinder segment. We compare the present shell formulation with data from Balamurugan and Narayanan [64] for a degenerated nine-node quadrilateral shell element with quadratic approach for the electric potential in thickness direction and with Saravanos [65] who provides a laminated eight-node shell element with lineare electric thickness potential. The good accordance of the results shows the reliable applicability of the present laminated four node formulation for layered piezo-mechanical structures.…”

Section: • Cylindrical Shellmentioning

confidence: 99%

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

Schulz

Klinkel

Wagner

2011

Numerical Meth Engineering

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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.

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Section: • Cylindrical Shellmentioning

confidence: 99%

Section: • Cylindrical Shellmentioning

confidence: 99%

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

Schulz

Klinkel

Wagner

2011

Numerical Meth Engineering

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“…Among them, negative velocity feedback control [3][4][5][6][7][8][9] and positive position feedback control [10][11][12][13][14] became the two most popular classical control strategies for easy implementation. As the most famous control method in industry, PID control was applied to vibration suppression in many papers [15][16][17][18][19].…”

Section: Introductionmentioning

confidence: 99%

Generalized‐Disturbance Rejection Control for Vibration Suppression of Piezoelectric Laminated Flexible Structures

Zhang

Wang

Zhang

et al. 2018

Shock and Vibration

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In the framework of disturbance rejection (DR) control, the paper proposes a generalized-disturbance rejection (GDR) control with proportional-integral (PI) observer for vibration suppression of smart structures under any unknown continuous disturbances. In the proposed GDR-PI control, a refined state space model is first constructed, and a generalized disturbance including the disturbance influence matrices, unknown physical disturbances, and state variables is defined. In the closed loop of GDR-PI control, physical disturbances can be counteracted indirectly by feeding back estimated generalized disturbances. By this means, the GDR-PI control remedies most of the defects in conventional DR control and has excellent performances especially in the following situations: (i) the disturbances are completely unknown; (ii) the number of sensor signals is less than the number of disturbances; (iii) the unknown disturbances vary fast. Finally, the GDR-PI control is validated and compared with ∞ state feedback control and conventional DR control available in the literature for vibration suppression of smart beams.

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“…The application of negative velocity feedback control, Lyapunov feedback control and LQR control can be found in many papers in literature, e.g. [3,4]. The aim of this paper is to construct a linear FE model for active control of a piezoelectric integrated smart beam based on the FOSD theory.…”

Section: Introductionmentioning

confidence: 99%

LQR Control for Vibration Suppression of Piezoelectric Integrated Smart Structures

Zhang

Schmidt

2012

Proc Appl Math and Mech

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In the present paper, the equations of motion for piezoelectric integrated smart beams are derived by applying Hamilton's principle and the Finite Element (FE) method, based on the First-Order Shear Deformation (FOSD) theory. Then, a state space model is constructed from the equations of motion for control design. A Linear Quadratic Regulator (LQR) control for vibration suppression is implemented on the mathematical model of the piezoelectric bonded beam. Finally, a numerical application is performed to testify the applicability and effectiveness of the present method.

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Shell finite element for smart piezoelectric composite plate/shell structures and its application to the study of active vibration control

Cited by 135 publications

References 16 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

Generalized‐Disturbance Rejection Control for Vibration Suppression of Piezoelectric Laminated Flexible Structures

LQR Control for Vibration Suppression of Piezoelectric Integrated Smart Structures

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