Modeling and analysis of laminate composite plates with embedded active-passive piezoelectric networks

The objective of this work is to present the finite element modeling of laminate composite plates with embedded piezoelectric patches or layers that are then connected to active-passive resonant shunt circuits, composed of resistance, inductance and voltage source. Applications to passive vibration control and active control authority enhancement are also presented and discussed. The finite element model is based on an equivalent single layer theory combined with a third-order shear deformation theory. A stress-voltage electromechanical model is considered for the piezoelectric materials fully coupled to the electrical circuits. To this end, the electrical circuit equations are also included in the variational formulation. Hence, conservation of charge and full electromechanical coupling are guaranteed. The formulation results in a coupled finite element model with mechanical (displacements) and electrical (charges at electrodes) degrees of freedom. For a Graphite-Epoxy (Carbon-Fibre Reinforced) laminate composite plate, a parametric analysis is performed to evaluate optimal locations along the plate plane (xy) and thickness (z) that maximize the effective modal electromechanical coupling coefficient. Then, the passive vibration control performance is evaluated for a network of optimally located shunted piezoelectric patches embedded in the plate, through the design of resistance and inductance values of each circuit, to reduce the vibration amplitude of the first four vibration modes. A vibration amplitude reduction of at least 10 dB for all vibration modes was observed. Then, an analysis of the control authority enhancement due to the resonant shunt circuit, when the piezoelectric patches are used as actuators, is performed. It is shown that the control authority can indeed be improved near a selected resonance even with multiple pairs of piezoelectric patches and active-passive circuits acting simultaneously. (C) 2010 Elsevier Ltd. All rights reserved.

Integrating structural and input design of a 2-DOF high-speed parallel manipulator: A flexible model-based approach

This paper discusses the integrated design of parallel manipulators, which exhibit varying dynamics. This characteristic affects the machine stability and performance. The design methodology consists of four main steps: (i) the system modeling using flexible multibody technique, (ii) the synthesis of reduced-order models suitable for control design, (iii) the systematic flexible model-based input signal design, and (iv) the evaluation of some possible machine designs. The novelty in this methodology is to take structural flexibilities into consideration during the input signal design; therefore, enhancing the standard design process which mainly considers rigid bodies dynamics. The potential of the proposed strategy is exploited for the design evaluation of a two degree-of-freedom high-speed parallel manipulator. The results are experimentally validated. (C) 2010 Elsevier Ltd. All rights reserved.

Refined sandwich model for the vibration of beams with embedded shear piezoelectric actuators and sensors

This work extends a previously presented refined sandwich beam finite element (FE) model to vibration analysis, including dynamic piezoelectric actuation and sensing. The mechanical model is a refinement of the classical sandwich theory (CST), for which the core is modelled with a third-order shear deformation theory (TSDT). The FE model is developed considering, through the beam length, electrically: constant voltage for piezoelectric layers and quadratic third-order variable of the electric potential in the core, while meclianically: linear axial displacement, quadratic bending rotation of the core and cubic transverse displacement of the sandwich beam. Despite the refinement of mechanical and electric behaviours of the piezoelectric core, the model leads to the same number of degrees of freedom as the previous CST one due to a two-step static condensation of the internal dof (bending rotation and core electric potential third-order variable). The results obtained with the proposed FE model are compared to available numerical, analytical and experimental ones. Results confirm that the TSDT and the induced cubic electric potential yield an extra stiffness to the sandwich beam. (C) 2007 Elsevier Ltd. All rights reserved.

Financial distress, financial constraint and investment decision: Evidence from Brazil

This paper analyses the presence of financial constraint in the investment decisions of 367 Brazilian firms from 1997 to 2004, using a Bayesian econometric model with group-varying parameters. The motivation for this paper is the use of clustering techniques to group firms in a totally endogenous form. In order to classify the firms we used a hybrid clustering method, that is, hierarchical and non-hierarchical clustering techniques jointly. To estimate the parameters a Bayesian approach was considered. Prior distributions were assumed for the parameters, classifying the model in random or fixed effects. Ordinate predictive density criterion was used to select the model providing a better prediction. We tested thirty models and the better prediction considers the presence of 2 groups in the sample, assuming the fixed effect model with a Student t distribution with 20 degrees of freedom for the error. The results indicate robustness in the identification of financial constraint when the firms are classified by the clustering techniques. (C) 2010 Elsevier B.V. All rights reserved.

A simple method for non-linear analysis of steel fiber reinforced concrete

This paper proposes a physical non-linear formulation to deal with steel fiber reinforced concrete by the finite element method. The proposed formulation allows the consideration of short or long fibers placed arbitrarily inside a continuum domain (matrix). The most important feature of the formulation is that no additional degree of freedom is introduced in the pre-existent finite element numerical system to consider any distribution or quantity of fiber inclusions. In other words, the size of the system of equations used to solve a non-reinforced medium is the same as the one used to solve the reinforced counterpart. Another important characteristic of the formulation is the reduced work required by the user to introduce reinforcements, avoiding ""rebar"" elements, node by node geometrical definitions or even complex mesh generation. Bounded connection between long fibers and continuum is considered, for short fibers a simplified approach is proposed to consider splitting. Non-associative plasticity is adopted for the continuum and one dimensional plasticity is adopted to model fibers. Examples are presented in order to show the capabilities of the formulation.

Analyzing static three-dimensional elastic domains with a new infinite boundary element formulation

A new two-dimensionally mapped infinite boundary element (IBE) is presented. The formulation is based on a triangular boundary element (BE) with linear shape functions instead of the quadrilateral IBEs usually found in the literature. The infinite solids analyzed are assumed to be three-dimensional, linear-elastic and isotropic, and Kelvin fundamental solutions are employed. One advantage of the proposed formulation over quadratic or higher order elements is that no additional degrees of freedom are added to the original BE mesh by the presence of the IBEs. Thus, the IBEs allow the mesh to be reduced without compromising the accuracy of the result. Two examples are presented, in which the numerical results show good agreement with authors using quadrilateral IBEs and analytical solutions. (C) 2010 Elsevier Ltd. All rights reserved.

Improved finite element for 3D laminate frame analysis including warping for any cross-section

The most ordinary finite element formulations for 3D frame analysis do not consider the warping of cross-sections as part of their kinematics. So the stiffness, regarding torsion, should be directly introduced by the user into the computational software and the bar is treated as it is working under no warping hypothesis. This approach does not give good results for general structural elements applied in engineering. Both displacement and stress calculation reveal sensible deficiencies for both linear and non-linear applications. For linear analysis, displacements can be corrected by assuming a stiffness that results in acceptable global displacements of the analyzed structure. However, the stress calculation will be far from reality. For nonlinear analysis the deficiencies are even worse. In the past forty years, some special structural matrix analysis and finite element formulations have been proposed in literature to include warping and the bending-torsion effects for 3D general frame analysis considering both linear and non-linear situations. In this work, using a kinematics improvement technique, the degree of freedom ""warping intensity"" is introduced following a new approach for 3D frame elements. This degree of freedom is associated with the warping basic mode, a geometric characteristic of the cross-section, It does not have a direct relation with the rate of twist rotation along the longitudinal axis, as in existent formulations. Moreover, a linear strain variation mode is provided for the geometric non-linear approach, for which complete 3D constitutive relation (Saint-Venant Kirchhoff) is adopted. The proposed technique allows the consideration of inhomogeneous cross-sections with any geometry. Various examples are shown to demonstrate the accuracy and applicability of the proposed formulation. (C) 2009 Elsevier Inc. All rights reserved.

An extended BEM formulation for plates reinforced by rectangular beams

This article presents a BEM formulation developed particularly for analysis of plates reinforced by rectangular beams. This is an extended version of a Previous paper that only took into account bending effects. The problem is now re-formulated to consider bending and membrane force effects. The effects of the reinforcements are taken into account by using a simplified scheme that requires application of ail initial stress field to locally correct the bending and stretching stiffness of the reinforcement regions. The domain integrals due to the presence of the reinforcements are then transformed to the reinforcement/plate interface. To reduce the number of degrees of freedom related to the presence of the reinforcement, the proposed model was simplified to consider only bending and stretching rigidities in the direction of the beams. The complete model can be recovered by applying all six internal force correctors, corresponding to six degrees of freedom per node. Examples are presented to confirm the accuracy of the formulation and to illustrate the level of simplification introduced by this strong reduction in the number of degrees of freedom. (C) 2008 Elsevier Ltd. All rights reserved.

BEM formulation for reinforced plates

This article presents a BEM formulation developed to analyse reinforced plate bending. The reinforcements are formulated using a simplified scheme based on applying an initial moment field adopted to locally correct the stiffness of the reinforcement regions. The domain integrals due to the presence of the reinforcements are then transformed to the reinforcement/plate interface. The increase in system stiffness due to the reinforcements can be taken into account independently for each coefficient. Thus, one can conveniently reduce the number of degrees of freedom required in considering the reinforcement. Only one degree-of-freedom is required at each internal node when taking into account only the flexural stiffness of beams. Examples are presented to confirm the accuracy of the formulation. (C) 2009 Elsevier Ltd. All rights reserved.

A simple way to introduce fibers into FEM models

This communication proposes a simple way to introduce fibers into finite element modelling. This is a promising formulation to deal with fiber-reinforced composites by the finite element method (FEM), as it allows the consideration of short or long fibers placed arbitrarily inside a continuum domain (matrix). The most important feature of the formulation is that no additional degree of freedom is introduced into the pre-existent finite element numerical system to consider any distribution of fiber inclusions. In other words, the size of the system of equations used to solve a non-reinforced medium is the same as the one used to solve the reinforced counterpart. Another important characteristic is the reduced work required by the user to introduce fibers, avoiding `rebar` elements, node-by-node geometrical definitions or even complex mesh generation. An additional characteristic of the technique is the possibility of representing unbounded stresses at the end of fibers using a finite number of degrees of freedom. Further studies are required for non-linear applications in which localization may occur. Along the text the linear formulation is presented and the bounded connection between fibers and continuum is considered. Four examples are presented, including non-linear analysis, to validate and show the capabilities of the formulation. Copyright (c) 2007 John Wiley & Sons, Ltd.

Robust Control of Flight Simulator Motion Base

The purpose of this study is to apply robust inverse dynamics control for a six-degree-of-freedom flight simulator motion system. From an implementation viewpoint, simplification of the inverse dynamics control law is introduced by assuming control law matrices as constants. The robust control strategy is applied in the outer loop of the inverse dynamic control to counteract the effects of imperfect compensation due this simplification. The control strategy is designed using the Lyapunov stability theory. Forward and inverse kinematics and a full dynamic model of a six-degree-of-freedom motion base driven by electromechanical actuators are briefly presented. A describing function, acceleration step response and some maneuvers computed from the washout filter were used to evaluate the performance of the controllers.

Enhanced aeroelastic energy harvesting by exploiting combined nonlinearities: theory and experiment

Converting aeroelastic vibrations into electricity for low power generation has received growing attention over the past few years. In addition to potential applications for aerospace structures, the goal is to develop alternative and scalable configurations for wind energy harvesting to use in wireless electronic systems. This paper presents modeling and experiments of aeroelastic energy harvesting using piezoelectric transduction with a focus on exploiting combined nonlinearities. An airfoil with plunge and pitch degrees of freedom (DOF) is investigated. Piezoelectric coupling is introduced to the plunge DOF while nonlinearities are introduced through the pitch DOF. A state-space model is presented and employed for the simulations of the piezoaeroelastic generator. A two-state approximation to Theodorsen aerodynamics is used in order to determine the unsteady aerodynamic loads. Three case studies are presented. First the interaction between piezoelectric power generation and linear aeroelastic behavior of a typical section is investigated for a set of resistive loads. Model predictions are compared to experimental data obtained from the wind tunnel tests at the flutter boundary. In the second case study, free play nonlinearity is added to the pitch DOF and it is shown that nonlinear limit-cycle oscillations can be obtained not only above but also below the linear flutter speed. The experimental results are successfully predicted by the model simulations. Finally, the combination of cubic hardening stiffness and free play nonlinearities is considered in the pitch DOF. The nonlinear piezoaeroelastic response is investigated for different values of the nonlinear-to-linear stiffness ratio. The free play nonlinearity reduces the cut-in speed while the hardening stiffness helps in obtaining persistent oscillations of acceptable amplitude over a wider range of airflow speeds. Such nonlinearities can be introduced to aeroelastic energy harvesters (exploiting piezoelectric or other transduction mechanisms) for performance enhancement.

Fast experimental identification of suspension models for control design

This paper presents both the theoretical and the experimental approaches of the development of a mathematical model to be used in multi-variable control system designs of an active suspension for a sport utility vehicle (SUV), in this case a light pickup truck. A complete seven-degree-of-freedom model is successfully quickly identified, with very satisfactory results in simulations and in real experiments conducted with the pickup truth. The novelty of the proposed methodology is the use of commercial software in the early stages of the identification to speed up the process and to minimize the need for a large number of costly experiments. The paper also presents major contributions to the identification of uncertainties in vehicle suspension models and in the development of identification methods using the sequential quadratic programming, where an innovation regarding the calculation of the objective function is proposed and implemented. Results from simulations of and practical experiments with the real SUV are presented, analysed, and compared, showing the potential of the method.

Experimental investigation of flow-induced vibration on isolated and tandem circular cylinders fitted with strakes

The effect of varying the geometric parameters of helical strakes on vortex-induced vibration (VIV) is investigated in this paper. The degree of oscillation attenuation or even suppression is analysed for isolated circular cylinder cases. How a cylinder fitted with strakes behaves when immersed in the wake of another cylinder in tandem arrangement is also investigated and these results are compared to those with a single straked cylinder. The experimental tests are conducted at a circulating water channel facility and the cylindrical models are mounted on a low-damping air bearing elastic base with one degree-of-freedom, restricted to oscillate in the transverse direction to the channel flow. Three strake pitches (p) and heights (h) are tested: p = 5, 10, 15d, and h = 0.1, 0.2, 0.25d. The mass ratio is 1.8 for all models. The Reynolds number range is from 1000 to 10000, and the reduced velocity varies up to 21. The cases with h = 0.1d strakes reduce the amplitude response when compared to the isolated plain cylinder, however the oscillation still persists. On the other hand, the cases with h = 0.2, 0.25d strakes almost completely suppress VIV. Spanwise vorticity fields, obtained through stereoscopic digital particle image velocimetry (SDPIV), show an alternating vortex wake for the p = 10d and h = 0.1d straked cylinder. The p = 10d and h = 0.2d cylinder wake has separated shear layers with constant width and no roll-up close to the body. The strakes do not increase the magnitude of the out-of-plane velocity compared to the isolated plain cylinder. However, they deflect the flow in the out-of-plane direction in a controlled way, which can prevent the vortex shedding correlation along the span. In order to investigate the wake interference effect on the strake efficiency, an experimental arrangement with two cylinders in tandem is employed. The centre-to-centre distance for the tandem arrangement varies from 2 to 6. When the downstream p = 10d and h = 0.2d cylinder is immersed in the wake of an upstream fixed plain cylinder, it loses its effectiveness compared with the isolated case. Although the oscillations have significant amplitude, they are limited, which is a different behaviour from that of a tandem configuration with two plain cylinders. For this particular case, the amplitude response monotonically increases for all gaps, except one, a trait usually found in galloping-like oscillations. SDPIV results for the tandem arrangements show alternating vortex shedding and oscillatory wake. (C) 2010 Elsevier Ltd. All rights reserved.

Recycling Krylov subspaces for efficient large-scale electrical impedance tomography

Electrical impedance tomography (EIT) captures images of internal features of a body. Electrodes are attached to the boundary of the body, low intensity alternating currents are applied, and the resulting electric potentials are measured. Then, based on the measurements, an estimation algorithm obtains the three-dimensional internal admittivity distribution that corresponds to the image. One of the main goals of medical EIT is to achieve high resolution and an accurate result at low computational cost. However, when the finite element method (FEM) is employed and the corresponding mesh is refined to increase resolution and accuracy, the computational cost increases substantially, especially in the estimation of absolute admittivity distributions. Therefore, we consider in this work a fast iterative solver for the forward problem, which was previously reported in the context of structural optimization. We propose several improvements to this solver to increase its performance in the EIT context. The solver is based on the recycling of approximate invariant subspaces, and it is applied to reduce the EIT computation time for a constant and high resolution finite element mesh. In addition, we consider a powerful preconditioner and provide a detailed pseudocode for the improved iterative solver. The numerical results show the effectiveness of our approach: the proposed algorithm is faster than the preconditioned conjugate gradient (CG) algorithm. The results also show that even on a standard PC without parallelization, a high mesh resolution (more than 150,000 degrees of freedom) can be used for image estimation at a relatively low computational cost. (C) 2010 Elsevier B.V. All rights reserved.