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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.

This paper presents a design, development and experimental verification of an active vibration control system of aluminum plate. The active structure consists of an aluminum rectangular plate as the host structure, strain gages as the sensor element and a piezoceramic patch as the actuation element. Based on characteristics of the integrated elements with use of the fuzzy optimization strategy based on the pseudogoal function the optimal orientation of piezoelectric actuator is found, and the whole active vibration control system is designed and developed. The active vibration control system is controlled by proportional-integral-derivative (PID) control strategy. Control algorithm was implemented on the PIC32MX440F256H microcontroller platform. In order to prevent it from negative occurrences from derivative and integral terms in a PID controller, the first-order low-pass filters are implemented in the derivative action and in the feedback of integral action. The experiment considers active damping control under periodic excitation. Experiments are conducted to verify the effectiveness of the vibration suppression and to compare the damping effect with different adjustment of PID gains. Experimental results corresponding to the developed active vibration control system are presented. The system suppresses more than 90% of vibration amplitude, which confirms the high level of effectiveness in vibration active damping at the proposed active structure. [ABSTRACT FROM AUTHOR]

This paper presents experimental verification of the active vibration control of a smart cantilever composite beam using a PID controller. In order to prevent negative occurrences in the derivative and integral terms in a PID controller, first-order low-pass filters are implemented in the derivative action and in the feedback of the integral action. The proposed application setup consists of a composite cantilever beam with a fiber-reinforced piezoelectric actuator and strain gage sensors. The beam is modeled using a finite element method based on third-order shear deformation theory. The experiment considers vibration control under periodic excitation and an initial static deflection. A control algorithm was implemented on a PIC32MX440F256H microcontroller. Experimental results corresponding to the proposed PID controller are compared with corresponding results using proportional (P) control, proportional–integral (PI) control and proportional–derivative (PD) control. Experimental results indicate that the proposed PID controller provides 8.93% more damping compared to a PD controller, 14.41% more damping compared to a PI controller and 19.04% more damping compared to a P controller in the case of vibration under periodic excitation. In the case of free vibration control, the proposed PID controller shows better performance (settling time 1.2 s) compared to the PD controller (settling time 1.5 s) and PI controller (settling time 2.5 s). [ABSTRACT FROM AUTHOR]

Control performances of smart structures depend on the size and location of the piezoelectric actuators and sensors as well as on the applied control algorithm. This article presents optimal vibration control of a thin-walled composite beam by using the fuzzy optimization strategy based on the particle swarm optimization algorithm. The optimization of the size and location of the conventionally collocated piezoelectric actuators and sensors, and optimization of the controller parameters are performed separately. The optimization criteria for optimal size and location of piezoelectric actuators and sensors are based on eigenvalues of the controllability Grammian matrix. The optimization procedure implies constraint of the original dynamic properties change and limitation of the beam mass increase. The particle swarm optimization-based linear quadratic regulator has been implemented for optimal vibration control in order to maximize the modal closed-loop damping ratios and minimize the control voltages required for actuation while keeping them below breakdown voltage for the used piezoelectric actuator. A pseudo-goal function, derived from the fuzzy set theory, gives an expression for global objective functions eliminating the use of weighting coefficients and penalty functions. The problem is formulated using the finite element method based on the third-order shear deformation theory. Several numerical examples are presented for the cantilever beam. [ABSTRACT FROM PUBLISHER]