Dajun Wang

Vibration Control of Plates Using Discretely Distributed Piezoelectric Quasi-Modal Actuators/Sensors

A novel approach is presented for vibration control of smart plates using discretely distributed piezoelectric actuators and sensors. The new method consists of techniques for designing quasi-modal sensors and quasi-modal actuators. The modal coordinates and the modal velocities are obtained approximately from the outputs of the discretely distributed piezoelectric sensor elements, whereas the modal actuators are implemented by applying proper voltages on each actuator element. The observation error of the modal sensor is analyzed, and an upper bound for the observation error is determined. The control spillover of the modal actuator is also estimated, and an upper bound of the control spillover is also found. The criteria are developed for finding the optimal locations and sizes of both piezoelectric sensor and actuator elements. In the optimality criteria the optimal locations and sizes of the sensor elements can be found by minimizing the observation error of the modal sensor, and those of the actuator elements can be obtained by minimizing both the control energy and the control spillover. The results obtained using the present optimal criteria show that they do not depend on the initial condition of vibration of the structures, nor do they depend on the control gains.

Free and forced vibration of repetitive structures

In this paper, the vibration problems of some repetitive structures, including symmetric, cyclic periodic, linear periodic, chain, and axi-symmetric structures is investigated. Eigen-value problems derived from the vibration equations of these structures are established based on their continuous models. The special properties of the structural modes of these structures are deduced. Applying these properties can provide effective reduction approach to solving the natural and forced vibration problems of these structures by either numerical or experimental methods. Furthermore, these properties can be applied in other aspects such as evaluating the reasonableness of the discrete models of these repetitive structures.

New method for deriving eigenvalue rate with respect to support location

The authors present a new method to derive the formulas of eigenvalue rate with respect to in-span support location using the generalized variational principle of the Rayleigh quotient. Following the ideas of this note, the eigenvalue rate, with respect to such variables as location of discrete or continuous in-span supports, the location of concentrated mass, location of elastic support, and location of a substructure, can be derived without any conceptual difficulties

Static shape control employing displacement–stress dual criteria

An approach employing displacement-stress dual criteria for static shape control is presented. This approach is based on normal displacement control, and stress modification is considered in the whole optimization process to control high stress in the local domain. Analysis results show that not only is the stress reduced but al so that the controlled surface becomes smoother than before.

Issues of control of structures using piezoelectric actuators

In this paper, some modeling topics on static deflection and vibration control of beam-like structures by using of piezoelectric actuators are discussed. This research is useful in modeling of structures with piezoelectric actuators, and is the basis of the design of static and dynamic control of structures. Furthermore, this research provides the theoretical tools for the design of locations of actuators and other related topics in the field of smart material and structures.

A note on wave control in lumped parameter system

The behavior of wave propagation in discrete system and that in a continuous system are different. In this paper the problem of distortion of a wave in discrete system being dependent on the step length used in discretization of continuous system is summarized and discussed, and the problem of the effect of wave control designed according to a discrete system being dependent on this step length is investigated by numeric computation.

REDUCTION APPROACHES FOR VIBRATION CONTROL OF REPETITIVE STRUCTURES

The reduction approaches are presented for vibration control of symmetric, cyclic periodic and linking structures. The condensation of generalized coordinates, the locations of sensors and actuators, and the relation between system inputs and control forces are assumed to be set in a symmetric way so that the control system posses the same repetition as the structure considered. By employing proper transformations of condensed generalized coordinates and the system inputs, the vibration control of an entire system can be implemented by carrying out the control of a number of sub-structures, and thus the dimension of the control problem can be significantly reduced.

Static shape control of repetitive structures integrated with piezoelectric actuators

In this paper, several simplification methods are presented for shape control of repetitive structures such as symmetrical, rotational periodic, linear periodic, chain and axisymmetrical structures. Some special features in the differential equations governing these repetitive structures are examined by considering the whole structures. Based on the special properties of the governing equations, several methods are presented for simplifying their solution process. Finally, the static shape control of a cantilever symmetrical plate with piezoelectric actuator patches is demonstrated using the present simplification method. The result shows that present methods can effectively be used to find the optimal control voltage for shape control.

Unified proof to oscillation property of discrete beam

The oscillation property (OP) is a fundamental and important qualitative property for the vibrations of single span one-dimensional continuums such as strings, bars, torsion bars, and Euler beams. Any properly discretized continuum model should keep the OP. In literatures, the OP of discrete beam models is discussed essentially by means of matrix factorization. The discussion is model-specific and boundary-conditionspecific. Besides, matrix factorization is difficult in handling finite element (FE) models of beams. In this paper, according to a sufficient condition for the OP, a new approach to discuss the property is proposed. The local criteria on discrete displacements rather than global matrix factorizations are given to verify the OP. Based on the proposed approach, known results such as the OP for the 2-node FE beams via the Heilinger-Reissener principle (HR-FE beams) as well as the 5-point finite difference (FD) beams are verified. New results on the OP for the 2-node PE-FE beams and the FE Timoshenko beams with small slenderness are given. Through a simple manipulation, the qualitative property of discrete multibearing beams can also be discussed by the proposed approach.