Keywords: piezoelectric material, active control, flexible multibody systems, elastic coupling, mode component synthesis.

In this paper the flexible multibody dynamics formulations of complex models including elastic components made of composite materials, which may be laminated and anisotropic, are extended to include piezoelectric transducers for sensing and actuation purposes. The only limitation on the deformation of a structural member is that its deformations must be elastic and linear when described in a coordinate frame fixed to a material point or region of its domain. The flexible finite element model for each flexible body is obtained such that the flexible body nodal coordinates are described with respect to the body fixed frame and the inertia terms involved in the mass matrix and in the gyroscopic force vector use a diagonalised mass description of the inertia terms.

The modal superposition technique is used to reduce the number of generalised coordinates to a reasonable dimension for complex shaped structural models of flexible bodies. The motion in the rigid and flexible body reference frames is described using Cartesian coordinates. The kinematic constraints between the different system components are introduced and the equations of motion of the flexible multibody system are solved using an augmented Lagrangean formulation, the accelerations and velocities being integrated in time using a multi-step multi-order integration algorithm based on Gear's method.

The active vibration control of the flexible multibody components is performed with collocated piezoelectric sensor or actuator pairs. Electromechanical coupling models of the surface-bonded piezoelectric transducers with the flexible multibody components are taken into account with the spatial models. These electromechanical effects are introduced in the flexible multibody equations of motion by the use of advanced finite plate or shell element, which is specially developed to this purpose [1]. A comparison between classical, constant gain and constant amplitude velocity feedback, and optimal, linear quadratic regulator, control strategies is performed in order to investigate their effectiveness to suppress vibrations in piezoelastic smart structures undergoing rigid body motion.

1

M.A. Neto, R.P. Leal, W. Yu, "A triangular finite element with drilling degrees of freedom for static and dynamic analysis of smart laminated structures", Computers and Structures, 2012. doi:10.1016/j.compstruc.2012.02.014

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