S Raja

Active vibration control of smart plates with partially debonded multilayered PZT actuators

The influence of actuator damage on the performance of closed loop vibration control is numerically evaluated. Debonding is considered a damage mode and finite element procedures are subsequently developed to introduce its effect on system matrices, namely elastic and electro-elastic stiffness. A simple modelling scheme for multiple debonding is proposed, which can also idealize multiple delamination in the host laminate. Debonding in actuators in general has reduced their load carrying appreciably as well as vibration control characteristics. Therefore, incorporating such a damage mode in the control design as an uncertainty parameter would help to realize a damage-tolerant active vibration control system. It is interesting to note that debonding in actuators has influenced both active damping and active stiffening effects.

Bending behavior of hybrid-actuated piezoelectric sandwich beams

The finite element analysis is presented for hybrid-actuated piezoelectric sandwich beam structures. The hybrid actuation is modelled by incorporating a transversely polarized, d31-based extension actuation lamina and an axially polarized, d15-based shear actuation lamina. Further the bending behavior of sandwich beams are evaluated for various boundary conditions with segmented actuators. The active stiffening effect is assessed through bending deflection behavior. The extension and shear actuators are collocated as well as noncollocated along the length of beam to see the combined actuation effort. It is observed that for the clamped-free case, the actuation effect is augmented with collocated actuators; however this trend is not followed in the other cases. Interestingly, the non-collocated actuators show better cumulative actuation effort for different boundary conditions except in the hinged-hinged case, where shear actuation appears to be predominant. As extension and shear actuations have distinctive features, both can be employed in a non-collocated fashion for better control action.

Constitutive modeling of SMA SMP multifunctional high performance smart adaptive shape memory composite

Materials design involving the thermomechanical constitutive modeling of shape memory alloy (SMA) and shape memory polymer (SMP) composites is a key topic in the development of smart adaptive shape memory composites (SASMC). In this work, a constitutive model for SASMC is developed. First, a one-dimensional SMA model, which can simulate the pseudoelastic (PE) and shape memory effects (SME) is presented. Subsequently, a one-dimensional SMP model able to reproduce the SME is addressed. Both SMA and SMP models are based on a single internal state variable, namely the martensite fraction and the frozen fraction, which can be expressed as a function of temperature. A consistent form of the analytical solution for the SMP model is obtained using the fourth-order Runge–Kutta method. Finally, the SASMC constitutive model is proposed, following two analytical homogenization approaches. One approach is based on an equivalent inclusion method and the other approach is the rule of mixtures. The SMA and SMP constitutive models are validated independently with experimental results. However, the validation of the composite model is performed using the two homogenization approaches and a close agreement in results is observed. Results regarding the isothermal and thermomechanical stress–strain responses are analyzed as a function of SMA volume fraction. Further, it is concluded that the proposed composite model is able to reproduce consistently the overall composite response by taking into consideration not only the phase transformations, variable modulus and transformation stresses in SMA but also the variable modulus, the evolution of stored strain and thermal strain in the SMP.

Deflection and Vibration Control of Laminated Plates Using Extension and Shear Actuated Fiber Composites

The use of surface bonded and embedded piezoelectric composite actuators is examined through a numerical study. Modelling schemes are therefore developed by applying the isoparametric finite element approach to idealise extension-bending and shear-bending couplings due to piezoelectric actuations. A modal control based linear quadratic regulator is employed to perform the active vibration control studies. Influence of shear actuation direction and its width has been examined and interesting deflection patterns are noticed. The through width SAFC develops a constant deflection beyond its length along the laminated plate length. In contrast, segmented SAFC produces a moderate to linearly varying deflection pattern. MFC actuators have shown promising features in vibration control performances. Nevertheless, closed loop damping presents the efficiency of SAFC in the vibration control application. It is therefore envisaged that optimally actuated smart laminates can be designed using MFC and SAFC to efficiently counteract the disturbance forces.

Deformation of a Beam with Partially Debonded Piezoelectric Actuators

A linear and a non-linear mathematical models for analyzing the deformation behavior of a beam with a pair of partially debonded piezoelectric actuators are developed on the basis of the Timoshenko beam theory. Effect of buckling is considered in the linear model, where the debonded actuator region is assumed to generate the Euler buckling load when the axial force in the region is larger than the load. The static behavior of the beam is investigated for extension and bending deformation. When the actuator debonds from its edge, the performance deteriorates; in contrast, the debonding in the middle of the actuator does not show any performance degradation until the debonded region buckles. The deformation behavior obtained from the linear model has been found to have good agreement with that from the non-linear model. The non-linear analysis shows that after the buckling the debonded actuator region maintains an axial force of the order of the Euler buckling load of a fix—fix column for the extending actuation, although for the bending actuation, it retains nearly 75% of the Euler buckling load. Further, the strain distribution in the debonded region shows that the buckling may occur before cracks begin in the actuator.

Bending Behavior of Piezo-Hygrothermo-Elastic Smart Laminated Composite Flat and Curved Plates with Active Control

The actuation and sensing behavior of piezo-hygrothermo-elastic flat and curved plates with active control is presented. A finite element procedure involving coupled piezoelectric field with hygrothermal strain is derived using first order shear deformation theory and is implemented in a nine-noded Lagrangian plate element. The accuracy of the element to model the piezoelectric, pyroelectric, hygroelastic, and thermoelastic behaviors of flat and doubly curved plates is validated with standard benchmark problems. The directional actuation that represents the piezoelectric anisotropy is introduced in the analysis and a comparison is made with isotropic actuation to control the thermal and moisture induced deformation in the laminated plates. Numerical studies are carried out with different fiber orientations to capture the influence of piezoelectric anisotropy on the actuation and sensing characteristics of the active lamina. The directionally actuated piezoelectric lamina that has a reduced piezoelectric capability in transverse direction is efficient, if properly tailored along the fiber directions. However, it is observed that the isotropic actuation has the potential to control the thermal and moisture developed deflection in angle-ply and cross-ply laminates. The actuator lamina is efficient if placed on the top of curved laminates in controlling the deflection.

Active Stiffening and Active Damping Effects on Closed Loop Vibration Control of Composite Beams and Plates

The influences of active stiffening (displacement control) and active damping (velocity control) effects introduced by collocated piezoelectric actuators and sensors on vibration control of composite structures are studied in this paper. A nine-node piezoelectric plate finite element is derived using the first order shear deformation theory to model the distributed actuation and sensing numerically. An output feedback control strategy is developed with the linear quadratic regulator theory in modal domain to estimate the optimal gains for different control efforts off line. Further, the developed control procedure is realised experimentally in an active control system. As an illustration, the effects of both displacement and velocity controls are shown on a CFRP beam. A periodic excitation is applied as disturbance and the amplitude response control is achieved by controlling the displacement and velocity of the vibrating system. It is observed that the active stiffening effect through displacement control is more effective for modes that have the amplitude of vibration relatively high. However, the active damping effect introduced by velocity control is efficient in the third mode control, which shows that a small amount of active damping is sufficient to stabilise a mode having comparatively less amplitude of vibration. Influence of active stiffening on the closed loop system frequency is observed to be more than that of active damping effect.

Formulation of 36-noded piezoelectric spectral finite element scheme with active/passive layers coupled by Lagrange multipliers

A novel spectral finite element formulation scheme is presented for modeling a plate structure with surface-mounted piezoelectric transducers. Surface-mounted piezoelectric transducers may asymmetrically distribute the mass in the thickness direction of the plate/panel structure, resulting in a coupled mass matrix in spectral element formulation. A new procedure is developed by equating the layer-wise kinematics of the element using undetermined Lagrange multipliers to achieve the diagonal mass matrix. To demonstrate the effectiveness of the element formulation scheme, a two-dimensional piezoelectric spectral element is constructed with 36 nodes and five active/passive layers (layers: transducer/bond/plate/bond/transducer). The performance of the developed element is illustrated by (a) simulation of Lamb wave propagation and estimation of its velocity, and (b) simulation of the effect of transducer size, its dynamics and shear lag on sensors response. The results presented highlight the importance of modeling the dynamics of transducers and understanding the effects on sensor response. The presented technique has relevance in the field of structural health monitoring, wherein it can be used to model and simulate aircraft panels with surface-mounted piezoelectric transducers.

Active flutter control of composite plate with embedded and surface bonded piezoelectric composites

A novel idea of combining two kinds of electro-mechanical couplings to build Active Flutter Suppression (AFS) strategy for composite structures is presented. The commercially available MFC and a newly proposed shear actuated fiber composite (SAFC) are considered. MFC induces normal strains and SAFC can be made to couple the transverse shear strains. A four noded plate element is employed to build the clamped-free active laminated plate with four MFC and SAFC each. The stiffness, mass, actuator and sensor matrices are obtained from the electro-mechanical coupling analysis. The open loop flutter velocity is computed using the linear aerodynamic panel theory (DLM). Further, the structural and unsteady aerodynamic matrices are represented in state-space form to build the aero-servo-elastic plant. Presently, the unsteady aerodynamics is approximated using a rational polynomial approach. A Linear Quadratic Gaussian control is designed to perform the closed loop flutter calculations. The actuation authority is maintained same through applied control voltage, while evaluating the performance of MFC and SAFC. The results have significantly encouraged the concept of simultaneously targeting the normal and shear strains of aeroelastically excited modes through electromechanical couplings to build an efficient active flutter suppression system.

Design and Development of a Smart Composite T-Tail for Transport Aircraft

The experience gained in developing a smart T-Tail concept for low speed transport aircraft is presented. Multi-layered PZT stack actuators are employed to demonstrate the active vibration control of three aeroelastically critical modes. The limitations of stack actuation in terms of its output parameters, namely induced force and deflection are overcome by adopting a mechanical amplification system. Flexural hinges are employed to protect the stacks from shear failures. Two stack actuating mechanisms are optimally placed in the horizontal stabilizer and two are integrated onto the vertical stabilizer. A Linear Quadratic Gaussian control scheme is implemented in dSPACE 1104Ⓡ to conduct the hardware in loop experiments. Independent modal control and multi-modes control concepts are experimentally demonstrated under an aircraft power simulated environment.