EFFECTS OF ACTIVE DAMPING ON PARAMETRIC INSTABILITY OF COMPOSITE CYLINDRICAL SHELLS USING PIEZO FIBER COMPOSITES (original) (raw)
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Acta Mechanica, 2011
This paper reports the nonlinear dynamic stability characteristics of laminated composite cylindrical (CYL) and spherical (SPH) shells integrated with piezoelectric layers using the finite element method. The shells are subjected to a thermal environment in addition to the in-plane periodic load and the electric load. The theoretical formulation considers Sanders' approximation for doubly curved shells, and von Kármán type nonlinear strains are incorporated into the first-order shear deformation theory (FSDT). The formulation includes the effects of transverse shear, in-plane and rotatory inertia. The in-plane periodic load is taken as the parametric excitation in the governing equation. The nonlinear matrix amplitude equation is obtained by employing Galerkin's method. The correctness of the formulation is established by comparing the authors' results with those available in the published literature. Detailed parametric studies are carried out to investigate the effects of different parameters on the dynamic stability characteristics of laminated composite shells.
Modeling Of Piezolaminated Composite Shells For Vibration Control
1998
This paper develops the theory of piezolaminated shells. The fundamental equations governing the equivalent piezoelectric loads and sensor output are derived. The reciprocity between piezoactuation and piezosensing is pointed out. Piezoelectric shell finite elements are developed based on Mindlin elements. Di#erent electrical boundary conditions are examined. Key words: vibration control; piezoelectricity. 1. INTRODUCTION The use of piezoelectric materials as actuators and sensors for noise and vibration control has been demonstrated extensively over the past few years (a review can be found in (Preumont, 1997)). The design of control systems involving piezoelectric actuators and sensors requires an accurate knowledge of the transfer functions between the inputs and the outputs of the system. These are not easy to determine numerically, particularly for shell structures with embedded distributed actuators and sensors. The situation where they are nearly collocated is particularly cr...
This paper deals with the analysis of active control of vibration of thin laminated composite truncated circular conical shells using vertically and obliquely reinforced 1-3 piezoelectric composite (PZC) materials as the constraining layer of the active constrained layer damping (ACLD) treatment. A finite element model of smart truncated conical laminated shells integrated with the patches of such ACLD treatment has been developed to demonstrate the performance of these patches on enhancing the damping characteristics of thin symmetric and antisymmetric cross-ply and antisymmetric angle-ply laminated truncated conical shells. Velocity feedback control loop has been implemented to activate the patches. The effect of variation of semi-cone angle on the performance of the patches for controlling first few modes of the truncated conical laminated shells has been demonstrated. Emphasis has also been placed on exploring the effect of variation of piezoelectric fiber orientation angle in the constraining layer on the control authority of the ACLD patches.
Active flutter control of composite plate with embedded and surface bonded piezoelectric composites
2011
A novel idea of combining two kinds of electro-mechanical couplings to build Active Flutter Suppression (AFS) strategy for composite structures is presented. The commercially available MFC and a newly proposed shear actuated fiber composite (SAFC) are considered. MFC induces normal strains and SAFC can be made to couple the transverse shear strains. A four noded plate element is employed to build the clamped-free active laminated plate with four MFC and SAFC each. The stiffness, mass, actuator and sensor matrices are obtained from the electro-mechanical coupling analysis. The open loop flutter velocity is computed using the linear aerodynamic panel theory (DLM). Further, the structural and unsteady aerodynamic matrices are represented in state-space form to build the aero-servo-elastic plant. Presently, the unsteady aerodynamics is approximated using a rational polynomial approach. A Linear Quadratic Gaussian control is designed to perform the closed loop flutter calculations. The actuation authority is maintained same through applied control voltage, while evaluating the performance of MFC and SAFC. The results have significantly encouraged the concept of simultaneously targeting the normal and shear strains of aeroelastically excited modes through electromechanical couplings to build an efficient active flutter suppression system.
A nonlinear piezoelectric shell model capable of accurately expressing the direct and the converse piezoelectric effect is presented. The developed theory is meant to encompass large strains, displacements and rotations that can occur in the shell as a consequence of a complete coupling between the mechanical and the electrical fields. Based on results present in the literature according to which a linear dependence of the electric potential on the shell thickness is not adequate to represent its electrical behavior, a specific structure of the field of admissible displacements is taken into account. Warping functions characterized by an ad-hoc polynomial expansion aimed at expressing their dependence on the shell through-the-thickness coordinate are here considered to describe the shear and the extensional deformability of the shell transverse fibers. Linear constitutive relations for a transversely isotropic continuum are considered. Finally, the governing equations of motion of the shell are obtained via enforcement of the virtual work theorem.
Non-Linear Analysis of Composite Structures with Integrated Piezoelectric Sensors and Actuators
2002
This paper deals with the geometrically non-linear analysis of thin plate/shell laminated structures with embedded integrated piezoelectric actuators or sensors layers and/or patches. The model is based on the Kirchhoff classical laminated theory and can be applied to plate and shell adaptive structures with arbitrary shape, general mechanical and electrical loadings. The finite element model is a nonconforming single layer triangular plate/shell element with 18 degrees of freedom for the generalized displacements and one electrical potential degree of freedom for each piezoelectric layer or patch. An updated Lagrangian formulation associated to Newton-Raphson technique is used to solve incrementally and iteratively the equilibrium equations.The model is applied in the solution of four illustrative cases, and the results are compared and discussed with alternative solutions when available.
Journal of Sound and Vibration, 2005
An exact three-dimensional solution is obtained for the cylindrical bending vibration of simply supported laminated composite plates with an embedded piezoelectric shear actuator. The piezoelectric actuator, which is poled in the longitudinal direction, will induce a transverse shear strain in the hybrid laminate when it is subjected to an electric field in the thickness direction. Suitable displacement and electric potential functions that identically satisfy the boundary conditions at the simply supported edges are used to reduce the equations that govern the steady-state vibrations of the hybrid laminate to a set of coupled ordinary differential equations, which are solved by employing the power series method. Natural frequencies, mode shapes, displacements, electric potential and stresses are presented for three-layer hybrid laminates consisting of a piezoelectric shear actuator sandwiched between fiber-reinforced composite layers. Active vibration damping is implemented using either a position feedback controller or velocity feedback controller. Frequency response curves for different controller frequencies, controller damping ratio and feedback gain demonstrate that the embedded shear actuator can be used for active damping of the fundamental flexural mode. In addition, it is shown that vibration suppression of thickness modes is also feasible using a shear actuator.
2021
In this paper, the nonlinear vibration control of the piezoelectric laminated cylindrical shell with point supported elastic boundary condition is analyzed, in which the geometric nonlinearity is considered by the first-order shear nonlinear shell theory. In the model, different boundary conditions are simulated by introducing a series of artificial springs. The elastic-electrically coupled differential equations of piezoelectric laminated cylindrical shells are obtained based on the Chebyshev polynomials and Lagrange equation, and decoupled by using the negative velocity feedback adjustment. Later, the Incremental Harmonic Balance Method (IHBM) is deduced, and the frequency-amplitude response of the piezoelectric laminated cylindrical shell is obtained by IHBM. Finally, the influence of the constant gain, size and position of the piezoelectric layer on frequency-amplitude response are investigated. The results show that the position, size and constant gain of the piezoelectric laye...
Analytical and numerical modelling of laminated composites with piezoelectric layers
Journal de Physique IV (Proceedings), 2004
We propose an accurate and efficient approach to laminated piezoelectric plates based on a refinement of elastic displacement and electric potential through the plate thickness. More precisely, the model accounts for a shearing function and a layerwise approximation for the electric potential. The layerwise approach becomes a necessity in order to accommodate electric potential at the electrode interfaces. The equations of motion for the piezoelectric composite are deduced from a variational formulation incorporating the continuity conditions at the layer interfaces by using Lagrange multipliers. Different situations are investigated among them (i) bimorph and (ii) sandwich structures for two kinds of electromechanical loads applied (density of force and electric potential) and are compared to the finite element computations performed on the 3D model. The vibration problem is also presented and the frequencies for the axial and flexural modes are obtained. At last performance and effectiveness of the model are also discussed and applications to control of the structure shape and vibration are proposed.
Experimental studies of the vibrations and dynamic stability of laminated composite shells
International Applied Mechanics, 2009
The paper discusses the results of systematic experimental studies of vibrations and dynamic instability of thin shells of revolution made of laminated composite materials (glassfiber-reinforced plastics). The basic patterns in the dynamic deformation of shells during natural, forced, and parametric vibrations are considered. The damping parameters of natural vibrations are analyzed. The wave deformation modes of shells subject to periodic excitation are studied. The effect of long-term vibratory loading (torsion) on the dynamic characteristics of three-layer glassfiber-reinforced plastic shells is examined