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

2004 ◽  
Vol 126 (1) ◽  
pp. 63-70 ◽  
Author(s):  
D. W. Wang ◽  
H. S. Tzou ◽  
H.-J. Lee
Keyword(s):  
Finite Element ◽  
Elastic Beam ◽  
Shell Element ◽  
Finite Element Formulation ◽  
Element Formulation ◽  
Control Analysis ◽  
Finite Element Code ◽  
Vibration Sensing ◽  
And Control ◽  
Piezoelectric Shell

Adaptive structures involving large imposed deformation often go beyond the boundary of linear theory and they should be treated as “nonlinear” structures. A generic nonlinear finite element formulation for vibration sensing and control analysis of laminated electro/elastic nonlinear shell structures is derived based on the virtual work principle. A generic curved triangular piezoelectric shell element is proposed based on the layerwise constant shear angle theory. The dynamic system equations, equations of electric potential output and feedback control force defined in a matrix form are derived. The modified Newton-Raphson method is adopted for nonlinear dynamic analysis of large and complex piezoelectric/elastic/control structures. A finite element code for vibration sensing and control analysis of nonlinear active piezoelectric structronic systems is developed. The developed piezoelectric shell element and finite element code are validated and then applied to control analysis of flexible electro-elastic (piezoelectric/elastic) structural systems. Vibration control of constant-curvature electro/elastic beam and plate systems are studied. Time-history responses of free and controlled nonlinear electro/elastic beam and plate systems are presented and nonlinear effects discussed.

Control of Largely-Deformed Nonlinear Electro/Elastic Beam and Plate Systems: Finite Element Formulation and Analysis

2002 ◽  
Author(s):  
D. W. Wang ◽  
H. S. Tzou ◽  
H.-J. Lee
Keyword(s):  
Finite Element ◽  
Virtual Work ◽  
Nonlinear Dynamic Analysis ◽  
Elastic Beam ◽  
Shell Element ◽  
Finite Element Formulation ◽  
Element Formulation ◽  
Control Analysis ◽  
Control Force ◽  
Piezoelectric Shell

Adaptive structures involving large imposed deformation often go beyond the boundary of linear theory and they should be treated as “nonlinear” structures. A generalized nonlinear finite element formulation for vibration sensing and control analysis of laminated electro/elastic nonlinear shell structures is derived based on the virtual work principle. A generic curved triangular piezoelectric shell element is proposed based on the layerwise constant shear angle theory. The dynamic system equations, equations of electric potential output and feedback control force defined in a matrix form are derived. The modified Newton-Raphson method is adopted for nonlinear dynamic analysis of large and complex piezoelectric/elastic/control structures. The developed piezoelectric shell element and finite element code are validated and then applied to control analysis of flexible electro-elastic (piezoelectric/elastic) structural systems. Vibration control of constant-curvature electro/elastic beam and plate systems is studied. Time-history responses of free and controlled nonlinear electro/elastic beam and plate systems are presented and nonlinear effects discussed.

Dynamics and Control of Adaptive Nonlinear Piezothermoelastic Structures With Coupled Electric, Thermal and Mechanical Fields: A Finite Element Approach

2002 ◽  
Author(s):  
H. S. Tzou ◽  
D. W. Wang
Keyword(s):  
Finite Element ◽  
Electric Potential ◽  
Shell Element ◽  
Shell Structures ◽  
Control Analysis ◽  
Control Force ◽  
Vibration Sensing ◽  
Dynamics And Control ◽  
And Control ◽  
Piezoelectric Shell

Piezoelectric sensors and actuators are widely used in smart structures, mechatronic and structronic systems, etc. This paper is to investigate the dynamics and control of nonlinear laminated piezothermoelastic shell structures subjected to the combined mechanical, electrical, and thermal excitations by the finite element method. Governing relations of nonlinear strain-displacement, electric field-electric potential, and temperature gradient-temperature field for a piezothermoelastic shell are presented in a curvilinear coordinate system. Based on the layerwise constant shear angle theory, a generic curved triangular laminated piezothermoelastic shell element is developed. Generic nonlinear finite element formulations for vibration sensing and control analysis of laminated piezoelectric shell structures are derived based on the virtual work principle. Dynamic system equations, equations of electric potential output, and feedback control force are derived and discussed. The modified Newton-Raphson method is used for efficient nonlinear dynamic analysis of complex nonlinear piezoelectric/elastic/control structural systems. For vibration sensing and control, various control algorithms are implemented. The developed nonlinear piezothermoelastic shell element and finite element code are validated and applied to analysis of nonlinear flexible structronic systems. Vibration sensing and control of constant/non-constant curvature piezoelectric shell structures are studied. Thermal effect to static deflection, dynamic response, and control is investigated.

Dynamics and Active Control of Largely Deflected Active Structures Using the Finite Element Technique

2003 ◽  
Author(s):  
D. W. Wang ◽  
H. S. Tzou ◽  
S. M. Arnold ◽  
H.-J. Lee
Keyword(s):  
Finite Element ◽  
Elastic Plate ◽  
Geometrical Nonlinearity ◽  
Nonlinear Dynamic Analysis ◽  
Time History ◽  
Control Analysis ◽  
Control Force ◽  
Finite Element Code ◽  
Plate Structures ◽  
Vibration Sensing

This paper focuses on the vibration, sensing and distributed control of laminated electro/elastic nonlinear plate structures based on newly developed nonlinear shell piezoelastic finite elements. The generic governing electromechanical finite element equations for nonlinear piezoelastic shell structures are developed for the curved hexahedral and triangular piezoelectric shell elements based on the layerwise constant shear angle theory. The nonlinear system equations are linearized to enhance computational feasibility. Equations of electric potential output and feedback control force defined in a matrix from are derived. The modified Newton-Raphson method is adopted for nonlinear dynamic analysis of large and complex piezoelectric/elastic/control structures. A finite element code for vibration sensing and control analysis of nonlinear active piezoelectric structronic systems is developed. Standard structural problems involving geometrical nonlinearity are tested to validate the current finite element code and verify the accuracy of the proposed hexahedral and triangular elements. Vibration control of constant-curvature electro/elastic plate structures is studied. Time-history responses of free and controlled largely deflected nonlinear electro/elastic plate systems are presented and nonlinear effects discussed.

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