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This article presents free vibration analysis of structures composed of rigid bodies connected with elastic beam segments. It is assumed that the mass centers of rigid bodies are not located on the neutral axes of undeformed elastic beam segments as well as rigid bodies perform planar motion in the same plane and their mass centers are located in that plane. For determination of natural frequencies of the system, modification of the conventional continuous-mass transfer matrix method has been performed. The elastic beam segments are treated as Euler-Bernoulli beams. Numerical example is presented.

Piezoelectric actuators are widely used in structural systems for active vibration control with the aim to enhance the performance of systems. The developed system of active vibration control consists of active structure, controller and high voltage amplifier. In this paper, the composite beam is host structure for sensor platform (strain gages) and actuator platform (dual layer PZT piezoelectric actuator). In order to improve the dynamic characteristics of active system, the coefficients of PID controller are changed. The effectiveness of active vibration control system at mode of interest can be improved with change of PID coefficients, but the stability of system can be reduced. The instability of the active structure is often perturbed by spillover effect. In this paper the importance of considering spillover effects in closed loop of piezoelectric active structures is demonstrated and shown the importance of change the PID coefficients in stability of active vibration control system. Experimental results which correspond to the developed active vibration control system are presented and affirmed stability on proposed active structure.

This paper presents the multi-objective fuzzy optimization of sizing and location of piezoelectric actuators and sensors on the thin-walled composite beam for active vibration control, using the degree of controllability (DC) for controlled modes as optimization criteria. The optimization process is performed constraining the original dynamics properties change including the limitation of increase of the mass, using or neglecting the limitation in degrees of controllability for residual modes for reduction spillover effect. Pseudogoal functions derived on the fuzzy set theory gives a unique expression for global objective functions eliminating the use of penalty functions. The problem is formulated using the finite element method based on the third-order shear deformation theory. The particle swarm optimization technique is used to find optimal configuration. Several numerical examples are presented for the cantilever beam.

This paper suggests a quaternion approach for the modeling kinematics and dynamics of rigid multi-body systems. Instead of the regular 'Newton-Euler' and Lagrange method used in the traditional way, Lagrange's equations of second kind in the covariant form are used by applying Rodriguez approach and quaternion algebra. A model of multi-body system of n rigid bodies in terms of quaternions is obtained, which is useful for studying kinematics, dynamics as well as for research of control system designs.