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Kessentini S.,University of Sfax | Choura S.,Micro Electro Thermal Systems Research Unit | Najar F.,Applied Mechanics Research Laboratory | Franchek M.A.,University of Houston
JVC/Journal of Vibration and Control | Year: 2010

In this paper, we develop a mathematical model of a horizontal axis wind turbine (HAWT) with flexible tower and blades. The model describes the flapping flexures of the tower and blades, and takes into account the nacelle pitch angle and structural damping. The eigenvalue problem is solved both analytically and numerically using the differential quadrature method (DQM). The closed-form and numerical solutions are compared, and the precision of the DQM-estimated solution with a low number of grid points is concluded. Next, we examine the effects of pitch angle and blade orientation on the natural frequencies and mode shapes of the wind turbine. We find that these parameters do not incur apparent alteration of the natural frequencies. Then, we examine the linear dynamics of the wind turbine subjected to persistent excitations applied to the tower. We investigate the effects of the pitch angle and blade orientation on the linear vibrations of the wind turbine. We demonstrate that the time response of the coupled system remain nearly unaffected. We show that small vibrations of the tower induce important blade deflections, and thus, the dynamic tower- blade coupling cannot be considered insignificant. © 2010 SAGE Publications Los Angeles, London, New Delhi, Singapore. Source


Ouled Chtiba M.,Applied Mechanics Research Laboratory | Choura S.,Applied Mechanics Research Laboratory | Nayfeh A.H.,Virginia Polytechnic Institute and State University | El-Borgi S.,Applied Mechanics Research Laboratory
Journal of Sound and Vibration | Year: 2010

We propose an optimal design for supplementing flexible structures with a set of absorbers and piezoelectric devices for vibration confinement and energy harvesting. We assume that the original structure is sensitive to vibrations and that the absorbers are the elements where the vibration energy is confined and then harvested by means of piezoelectric devices. The design of the additional mechanical and electrical components is formulated as a dynamic optimization problem in which the objective function is the total energy of the uncontrolled structure. The locations, masses, stiffnesses, and damping coefficients of these absorbers and capacitances, load resistances, and electromechanical coupling coefficients are optimized to minimize the total energy of the structure. We use the Galerkin procedure to discretize the equations of motion that describe the coupled dynamics of the flexible structure and the added absorbers and harvesting devices. We develop a numerical code that determines the unknown parameters of a pre-specified set of absorbers and harvesting components. We input a set of initial values for these parameters, and the code updates them while minimizing the total energy in the uncontrolled structure. To illustrate the proposed design, we consider a simply supported beam with harmonic external excitations. Here, we consider two possible configurations for each of the additional piezoelectric devices, either embedded between the structure and the absorbers or between the ground and absorbers. We present simulations of the harvested power and associated voltage for each pair of collocated absorber and piezoelectric device. The simulated responses of the beam show that its energy is confined and harvested simultaneously. © 2009 Elsevier Ltd. All rights reserved. Source


Ouled Chtiba M.,Applied Mechanics Research Laboratory | Choura S.,Applied Mechanics Research Laboratory | El-Borgi S.,Applied Mechanics Research Laboratory | Nayfeh A.H.,Virginia Polytechnic Institute and State University
JVC/Journal of Vibration and Control | Year: 2010

We propose a novel strategy for the optimal design of supplementary absorbers that warrant confinement with and without suppression of vibrations in flexible structures. We assume that the uncontrolled structure is sensitive to vibrations and that the absorbers are the elements where the vibrational energy is to be transferred. The design of these absorbers is formulated as a dynamic optimization problem in which the objective function is the total energy of the uncontrolled structure. The locations, masses, stiffnesses, and damping coefficients of these absorbers are optimized to minimize the total energy of the structure. We use the Galerkin method to discretize the equations of motion that describe the coupled dynamics of the flexible structure and the added absorbers. We develop a numerical code that computes the unknown parameters for a prespecified set of absorbers. We input a set of initial values for these parameters, and the code updates them while minimizing the total energy in the uncontrolled structure. To show the viability of the proposed design, we consider a simply supported beam with and without external excitations. In the absence of structural damping, we demonstrate that the beam, subjected to either an initial distributed energy or a harmonic excitation, periodically exchanges the vibration energy with the added absorbers. For damped beams, we show that the vibrational energy can be confined to the absorbers for suppression or harnessing purposes. © 2010 SAGE Publications Los Angeles, London, New Delhi, Singapore. Source

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