Marek Pietrzakowski

Active damping of beams by piezoelectric system: effects of bonding layer properties

Abstract The paper is aimed at the active damping of structural vibration of a simply supported beam by using a piezoelectric, collocated sensor/actuator pair. The control concept is based on the velocity feedback. The bending-extensional dynamic model of the beam with glued piezoelements is proposed. The shear bonding layers both for the actuator and the sensor are assumed visco-elastic described by the Kelvin–Voigt material. The steady-state response of the beam loaded by a harmonic concentrated force is obtained from the solution of the boundary value problem. The boundary problem is formulated by the governing equations for the sections with and without piezoelectric patches, boundary conditions at the ends of the beam, continuity conditions between sections and the free stress conditions at the actuator and sensor edges. The influence of bonding layer parameters on the dynamic response of the controlled beam is analysed. The results in terms of frequency response of the beam transverse displacements show that the stiffness of bonding layers affects significantly the active damping efficiency. The beam vibrations can be reduced considerably for relatively stiff glue layers. The range of material damping parameter of the bonding layer, which causes an increase in the resonant amplitudes, is also indicated. A growth of stiffness as well as passive damping of the bonding layer results in a slight increase of resonance frequencies. The effect of variations in the bonding layer parameters on the shear stress distribution along the sensor and actuator is also presented and discussed.

Natural frequency modification of thermally activated composite plates

Abstract The modification of dynamic properties of rectangular laminated plates and sandwich plates containing layers reinforced with shape memory alloy (SMA) fibers is analysed in this work. The concept of semi-active control is based on the ability of SMA material to change significantly its stiffness during a temperature-activated, reversible martensite transition. It is assumed that the laminate is midplane symmetric and symmetrically activated. Due to the quasi-steady one-dimensional model of conduction the temperature, martensite fraction and natural frequency time relations for the phase transition of SMA have been obtained. The influence of parameters of “heating” and “cooling” processes on the system response has been analysed. The numerical results show that the range of natural frequency changes depends on the SMA fiber volume fraction in activated layers and can be reduced by activation of only a part of the SMA fibers. The effect of the boundary conditions of laminated plates and the core thickness, in the case of sandwich plate analysis, on the efficiency of activation has also been discussed.

Pseudoelastic effect in autoparametric non-ideal vibrating system with SMA spring

Abstract In this paper a three degrees of freedom autoparametric system with limited power supply is investigated numerically. The system consists of the body, which is hung on a spring and a damper, and two pendulums connected by shape memory alloy (SMA) spring. Shape memory alloys have ability to change their material properties with temperature. A polynomial constitutive model is assumed to describe the behavior of the SMA spring. The non-ideal source of power adds one degree of freedom, so the system has four degrees of freedom. The equations of motion have been solved numerically and pseudoelastic effects associated with the martensitic phase transformation are studied. It is shown that in this type system one mode of vibrations might excite or damp another mode, and that except different kinds of periodic vibrations there may also appear chaotic vibrations. For the identification of the responses of the systems various techniques, including chaos techniques such as bifurcation diagrams and time histories, power spectral densities, Poincare maps and exponents of Lyapunov may be used.

Vibration Reduction of Laminated Plates With Various Piezoelectric Functionally Graded Actuators

The aim of the present study is to develop models of active laminated plates containing monolithic piezopolymer sensor layers and a new type of actuator layers made of Piezoelectric Functionally Graded (PFG) material, which is a mixture of piezoceramics and polymer or epoxy matrix. The electromechanical properties of the PFG layers can be tailored varying continuously the piezoceramic volume fraction across the thickness during the manufacturing process. The analysis and numerical simulations are focused on the relationship between the material compositional gradient and electromechanical properties and also dynamic responses of the structure obtained. Three types of functions, which describe the volume fraction distribution of constituents, are considered: exponential, parabolic and sigmoid. The effective properties of the PFG material, i.e. the Young’s modulus and piezoelectric coefficient gradations, are determined using to the rule of mixtures. A constant velocity feedback algorithm is used for the active damping of transverse plate vibration. The dynamic analysis concerns steady-state behavior of rectangular symmetrically laminated plates and is based on hypothesis of the classical plate theory. The numerical simulations are performed to recognize the influence of the applied pattern of the piezoceramic fraction distribution and its parameters on the gradient of elastic and piezoelectric properties within the PFG actuators and, as the final result, the active plate structural response presented in terms of amplitude-frequency characteristics. The changes in both the natural frequencies and resonant amplitudes are compared and the influence of the piezoceramic gradation on the control system operational effectiveness is also indicated and discussed.Copyright

Modelling of Piezoactuator Edge Delamination in Active Beam Systems

The objective of the study is to develop the modelling of piezoactuator edge delamination and the analysis of effects of the progressive damage process on the active beam dynamic behaviour. Delamination is described as a significant reduction of the bonding interlayer shear stiffness. It is assumed that the damaged region extends uniformly across the actuator from its ends to the centre. The beam is divided into sections for which the governing equations are formulated separately. The steady-state solution is obtained taking into account boundary and continuity conditions at the borders of the beam and actuator sections. The influence of the length and equivalent coupling stiffness of the damaged region on the dynamic characteristics and the control effectiveness is numerically investigated.

Experimental and Simulation Investigations of the Cantilever Beam Energy Harvester

Machines, cars suspensions, buildings steel constructions etc. usually generate vibrations, which can be the excitement signal for piezoelectric energy harvesters. The piezoelectric patches attached to the vibrating construction have ability to convert mechanical energy of harmful vibrations into electrical energy.The goal of the study was to verify a finite element model of the piezoelectric beam energy harvester by comparing results of numerical simulations with those obtained experimentally. The stand used in the experiment consists of the cantilever beam with piezoelectric elements attached, which is excited by the base harmonic movement. The transverse displacements of the selected beam’s point and the base, and also the frequency of vibrations were observed and measured using an accelerometer and a B&K Pulse platform. A portable data acquisition module was used to quantify the voltage generated by the piezoelectric layers.The finite element model was built in ANSYS software. The beam and piezoelectric layers were modeled by twenty node elements with an additional electric degree of freedom for piezoelectric elements. A full piezoelectric matrix was used in the finite element analysis instead of a one-dimensional piezoelectric effect, which dominates in many analytical approaches. It allowed building a more accurate model of the system. The experimental tests and finite element method simulations were performed and acquired results were compared. The characteristics of voltage amplitude in the time and frequency domain were shown and discussed.

Vibration Control of Autoparametric System Using SMA Spring and MR Dampers in the Pendula Joins

This work is concerned with the problem of nonlinear dynamical motion of a non-ideal autoparametric system with two active elements — shape memory alloys (SMA) spring and the magnetorheological (MR) pin joint dampers in the neighbourhood internal and external resonance. A polynomial constitutive model was assumed to describe the behaviour of SMA’s spring and there was observed the pseudoelastic effects associated with martensitic phase transformations. The simplified resistance moment generated by the MR pin joint can be approximated using the hyperbolic tangent function. The influence of damping forces in MR dampers on the phenomenon of energy transfer and pseudoelastic effects associated with the martensitic phase transformation was studied. It was shown that in this type system one mode of vibrations might excite or damp another mode, and that except different kinds of periodic vibrations there may also appear chaotic vibrations. For the identification of the responses of the system various techniques, including chaos techniques such as bifurcation diagrams and time histories, power spectral densities (FFT), Poincare maps and exponents of Lyapunov may be used. The SMA spring and MR damper can be used to change the dynamic behaviour of the autoparametric system giving reliable semiactive control possibilities.Copyright

Effects of Piezoactuator Failure on Active Control of Beam Vibration

Relatively large, alternating in time, operational deformations of distributed piezoelectric actuators used in active vibration control may create a hazard of material degradation and damage of the actuator/host structure coupling. In the presented study a beam-like system with a surface mounted piezoelectric sensor/actuator pair operating in a closed loop with velocity feedback is analysed. The applied actuator is a piezoelectric fiber composite (PFC) with PZT (lead-zirconate-titanate) fibers aligned and polarized longitudinally. The uniform field method based on the rule of mixtures is used to determine the effective properties of the piezocomposite. Two types of the actuator failure are taken into account. The first relates to the edge delamination modelled as a significant reduction of the adhesive interlayer shear stiffness. The second relates to the PFC material degradation, which is regarded as a softening of the matrix material surrounding PZT fibers. It is assumed that the damaged adhesive region of the constant shear stiffness extends uniformly across the actuator from its ends to the centre. In analysis the beam is divided into sections due to its geometry, external loading and the damaged regions supposed. The governing equations of the activated beam sections are coupled equations related to the electrically induced tension/compression of the actuator and bending of the beam, respectively. The obtained steady-state solution satisfies boundary conditions and continuity conditions at the borders of the beam and the actuator sections. Results of calculations show the effects of stiffness degradation of both the bonding interlayer and the piezocomposite matrix material on the beam deflection and transmitted shear stresses. Besides, dynamic responses of the active system regarding changes of the control effectiveness are numerically investigated and discussed.Copyright

Monitoring of Roof Truss Girder Vibration Using Piezoelectric Sensors – FEM Simulation

In this paper modelling and numerical simulations of the roof truss girder with the surface mounted piezoelectric sensors applied to monitoring purposes are presented. In the first stage, a simply supported beam with piezoelectric sensors, excited by time varying vertical displacements of the supports, is examined using the finite element method (FEM) and an analytical approach. The aim of calculations is to validate the applied finite element (FE) model of the system. The compared results are in a good agreement and confirm the applied FE model correctness. In the second stage, a simplified FE model of the roof truss girder is investigated. Dynamic responses of the roof truss girder with two piezoelectric sensors are achieved using FEM simulations. As previously, the roof truss girder is excited by the time varying vertical movement of the supports. The influence of a local failure of the structure on its dynamic behaviour is tested as well. A defect is modelled by decreasing stiffness of a selected joint of the bars in the truss girder. The amplitude-frequency characteristics are calculated and compared with those obtained for the healthy structure.