Smart Active Vibration Control System of a Rotary Structure Using Piezoelectric Materials

A smart active vibration control (AVC) system containing piezoelectric (PZT) actuators, jointly with a linear quadratic regulator (LQR) controller, is proposed in this article to control transverse deflections of a wind turbine (WT) blade. In order to apply controlling rules to the WT blade, a state-of-the-art semi-analytical solution is developed to obtain WT blade lateral displacement under external loadings. The proposed method maps the WT blade to a Euler–Bernoulli beam under the same conditions to find the blade’s vibration and dynamic responses by solving analytical vibration solutions of the Euler–Bernoulli beam. The governing equations of the beam with PZT patches are derived by integrating the PZT transducer vibration equations into the vibration equations of the Euler–Bernoulli beam structure. A finite element model of the WT blade with PZT patches is developed. Next, a unique transfer function matrix is derived by exciting the structures and achieving responses. The beam structure is projected to the blade using the transfer function matrix. The results obtained from the mapping method are compared with the counter of the blade’s finite element model. A satisfying agreement is observed between the results. The results showed that the method’s accuracy decreased as the sensors’ distance from the base of the wind turbine increased. In the designing process of the LQR controller, various weighting factors are used to tune control actions of the AVC system. LQR optimal control gain is obtained by using the state-feedback control law. The PZT actuators are located at the same distance from each other an this effort to prevent neutralizing their actuating effects. The LQR shows significant performance by diminishing the weights on the control input in the cost function. The obtained results indicate that the proposed smart control system efficiently suppresses the vibration peaks along the WT blade and the maximum flap-wise displacement belonging to the tip of the structure is successfully controlled

Effect of a Bonded Patch on Aeroelastic Behavior of Cantilevered Plates

In recent years, many researchers have studied vibration suppression of fluttering plates using piezoelectric actuators. Lots of these researchers have focused on optimal placement of piezoelectric patches to obtain maximum controllability. Although mass and stiffness characteristics of bonded patches can alter aeroelastic behavior of fluttering plates, few of them considered the effect of the mentioned parameters in optimization process. This paper investigates effect of a bonded patch on aeroelastic behavior of cantilevered plates in supersonic flow. For this purpose, critical dynamic pressure and limit-cycle oscillations of the system are studied. Von Karman plate theory along with first order piston theory is employed for mathematical simulation of the system. Obtained results reveal that a bonded patch with a small mass ratio can change the system critical dynamic pressure significantly, where the main part of the variations is resulted from the added mass of the bonded patch. The maximum raise of dynamic pressure is acquired when the patch is placed on the plate’s leading edge. The results show that mass and stiffness characteristics of bonded piezoelectric patches can have a great impact on aeroelastic performance of fluttering plates. Therefore, these parameters must be considered as effective factors for optimal placement of piezo-actuators

Dynamic response of multiple nanobeam system under a moving nanoparticle

In this article, nonlocal continuum based model of multiple nanobeam system (MNBS) under a moving nanoparticle is investigated using Eringen’s nonlocal theory. Beam layers are assumed to be coupled by winkler elastic medium and the nonlocal Euler-Bernoulli beam theory is used to model each layer of beam. The Hamilton’s principle, Eigen function technique and the Laplace transform method are employed to solve the governing equations. Analytical solutions of the transverse displacements for MNBs with simply supported boundary condition are presented for double layered and three layered MNBSs. For higher number of layers, the governing set of equations is solved numerically and the results are presented. This study shows that small-scale parameter has a significant effect on dynamic response of MNBS under a moving nanoparticle. Sensitivity of dynamical deflection to variation of nonlocal parameter, stiffness of Winkler elastic medium and number of nanobeams are presented in nondimensional form for each layer. Keywords: Dynamic response, Analytical solution, Moving particle, Nanobeam, Multi-layered nanobea

On the exact in-plane and out-of-plane free vibration analysis of thick functionally graded rectangular plates: explicit 3_D elastic solutions

In this paper exact closed-form solutions of 3-D elasticity theory are presented to study both in-plane and out-of-plane free vibrations for thick functionally graded simply supported rectangular plates. The solution procedure of the transverse vibration utilizes Levinson\u2019s representation form to describe the displacement; in this way, the 3-D elasto-dynamic equations are written in terms of some suitable independent functions satisfying ordinary differential equations. A similar procedure is presented for in-plane vibration by introducing an appropriate displacement field. In each case, the obtained ordinary differential equations are analytically solved and boundary conditions are satisfied. The proposed solutions are validated by comparing some of the present results with corresponding results known in the literature as well as with 3-D Finite Element Method. Finally, the influence of inhomogeneity on the natural frequencies for a thick functionally graded rectangular plate is discussed