J. Dias Rodrigues

The application of genetic algorithms for shape control with piezoelectric patches—an experimental comparison

The problem of shape control and correction of small displacements in composite structures using piezoelectric actuators glued or embedded was addressed. A finite element model based on Mindlin plate theory was used to characterize the behaviour of the structure and the one of the actuators. Emphasis was put on the development of an efficient and general methodology, based on genetic algorithms, for the determination of the optimal actuation voltages needed to apply to the piezoelectric actuators in such a way that a pre-defined shape of the structure is achieved. The model was investigated numerically and verified experimentally. Measurements were carried out using electronic speckle pattern interferometry. Good agreement was found between simulation results and the optically measured values.

Experimental modal analysis of a synthetic composite femur

In this paper we describe the experimental characterization of the modal parameters of a synthetic composite femur model widely used in biomechanical research studies. The objective of the experimental procedure was to identify the natural frequencies and mode shapes of an unconstrained (free-free) femur. The experimental data were compared with the same obtained in an analog study performed with a fresh cadaveric femur bone. Other objective of the study was to investigate modal analysis as a technique to validate a finite element model of a composite femur with isotropic material properties.

PARTIAL CONSTRAINED VISCOELASTIC DAMPING TREATMENT OF STRUCTURES: A MODAL STRAIN ENERGY APPROACH

The constrained viscoelastic layer damping treatment is an effective means for the passive vibration control of plate and beam-kind structures. In order to reduce the treatment cost, while minimizing structural modifications, particularly the increase in mass, constrained viscoelastic treatments can be successfully applied in a partial and localized manner. The effectiveness of these treatments depends on their extension and relative location with respect to the target mode shape, which is not usually expeditiously established. In order to minimize the cost of the numerical optimization of the partial treatments, an efficient numerical methodology based on the ratio between the modal strain energy of the treated area and that of the structure is hereby proposed. This method is used in the analysis of the location and extension effects of partial constrained viscoelastic treatments on the modal damping of thin plates. The numerical results are verified through an experimental study on specimens with partial constrained viscoelastic layer damping treatments.

Active vibration control of a smart beam through piezoelectric actuation and laser vibrometer sensing: simulation, design and experimental implementation

A velocity feedback control system is evaluated in the active control of vibrations of a smart beam with a pair of surface mounted piezoelectric ceramic patches, and finite element (FE) model results are validated against measured ones. To this end, a three-layered smart beam FE model is utilized, where a partial layerwise theory and a fully coupled electro-mechanical theory are considered for the formulation of the displacement field and electric potential, respectively. Regarding the test rig, it consists of a cantilever smart aluminum beam with two piezoelectric patches mounted close to the clamped end. One of the piezoelectric patches is utilized to excite the beam while the other is utilized as an actuator in the feedback control loop. The control voltage applied to the actuator is proportional to the transverse velocity at the free end, which is measured by a laser vibrometer. First, the quasi-static actuation capacity of the piezoelectric patches is evaluated. Next, the free and forced velocity responses to an initial displacement field and harmonic excitation are analyzed. The capacity to predict instabilities and the accuracy of the FE model are demonstrated and the applicability and functionality of the velocity feedback vibration control system are discussed.

Application of Cork Compounds in Sandwich Structures for Vibration Damping

The remarkable damping over a broad temperature range and thermal insulation properties of cork make it a suitable material to be applied on integrated and surface damping treatments in sandwich structures, improving its dynamic behavior. Experimental analysis and numerical modeling of sandwich structures with cork compound layers is therefore essential for a better understanding of the cork compound influence on the dynamic properties of a layered structure. In this article, an evaluation study on the dynamic properties of a set of sandwich plates with cork compound cores inside two aluminium faces is performed. For this purpose, three test samples were assembled following the described configuration, using cork compounds with different properties (density, granulometry and thickness). To numerically simulate these layered plates, a partial layerwise plate finite element (FE), with a multilayer configuration, was developed and integrated in a MATLAB FE code. The constitutive relation of the cork compounds is included in the FE model by using the material complex modulus in a direct frequency analysis procedure. For the different cork compounds hereby considered, the extensional complex modulus was previously identified by using a specific experimental methodology which simulates a semidefinite two degrees of freedom system, where the cork compound test sample represents the complex stiffness. From the complex modulus data, both extensional storage modulus and loss factor of the cork compound were obtained. The experimental evaluation of the dynamic properties of the sandwich plates was performed carrying out an experimental modal analysis on each test specimen, being measured a set of frequency response functions (FRFs). Additionally, the developed layerwise plate element was validated through the comparison between the measured driving point FRFs and the FE method predicted ones.

The dynamic analysis of piping systems using pseudo-dynamic techniques

This paper describes an application of pseudo-dynamic techniques to the dynamic analysis of piping structures. Essentially it consists in coupling a direct time integration algorithm, such as the Newmark method, to an experimental step. At each time step the integration algorithm generates a displacement vector of the structure, which is prescribed for the test specimen. This is mounted in a rigid test rig fitted with a set of displacement actuators and load cells at the level of the structure degrees of freedom. The load cells allow the reading of the internal restoring force vector, which is fed back to the direct time integration algorithm in an actual time step. Further calculations for the velocity and acceleration vectors will define a new structure configuration by evaluating a new displacement vector referred to the next time step. This procedure makes it possible to assess experimentally a realistic stress distribution at sections of complex shape piping parts. The method is a precise tool in dynamic analysis and, on being carried out in a quasi-static procedure, it operates with less expensive equipment than is necessary in real dynamic test.

Multilayer Damping Treatments: Modeling and Experimental Assessment

The sandwich panels with viscoelastic cores, which represent the physical application of the viscoelastic integrated damping treatment concept, associate different materials, each one having a specific structural contribution, where the outside faces, usually made from a stiff material, guarantee the stiffness of the composite structure whereas the viscoelastic and soft core provides the damping capability. The application of soft cores, specially the thick ones, into sandwich plates produces an important decoupling effect, leading to a significant flexural stiffness reduction of the sandwich plate, as experimental and numerical results evidence. From this observation and pursuing a solution to minimize such effect, the partitioning of the core layer into multiple layers separated by thin constraining layers is hereby considered. Taking advantage of the application of the multiple viscoelastic layers in the sandwich core, it is also analyzed the potential use of different viscoelastic materials in order to spread out the efficient temperature range of the damping treatment. To verify and evaluate the effects of the multilayer and multi-material viscoelastic cores in sandwich panels, an experimental and a numerical study were conducted on specimens representative of these design concepts. The results achieved from this study demonstrate the applicability of the two multiple layer configurations, evidencing the effect of the partitioning procedure of the core onto the reduction of the bending stiffness decay and the efficient temperature range enlargement when adopting viscoelastic materials with different transition temperatures.

Experimental Identification of GHM and ADF Parameters for Viscoelastic Damping Modeling

Viscoelastic materials can be used as an effective means of controlling the dynamics of structures, reducing and controlling the structural vibrations and noise radiation. They can be used as surface mounted or embedded damping treatments, utilizing passive viscoelastic materials alone, the so-called passive treatments, or in an unified way with active materials such as piezoelectrics, the so-called hybrid treatments. The use of these materials in damping treatments provides high damping capability over wide temperature and frequency ranges. The extensive use of passive or hybrid treatments using viscoelastic materials has motivated the development of damping models to be used and integrated into commercial or home-made finite element (FE) codes. The implementation of the Golla-Hughes- McTavish (GHM) and anelastic displacement fields (ADF) models in a general FE model with viscoelastic damping is presented and discussed in this paper. Additionally, a direct frequency analysis (DFA) is also described and employed.

Shells with Hybrid Active-Passive Damping Treatments: Modeling and Vibration Control

This paper concerns the mathematical modeling and finite element (FE) solution of general anisotropic shells with hybrid active-passive damping treatments. A fully-coupled piezo-visco-elastic mathematical model of the shell (host structure) and segmented arbitrarily stacked layers of damping treatments is considered. A discrete layer approach is employed in this work, and the weak form of the governing equations is derived for a single generic layer of the multilayer shell using Hamilton’s principle and a mixed (displacement/stresses) definition of the displacement field. First, a fully refined deformation theory of the generic layer, based on postulated out-of-plane shear stress definitions and in the in-plane stresses obtained with a Reissner-Mindlin type shell theory, is outlined. A semi-inverse procedure is used to derive the layer mixed non-linear displacement field, in terms of a blend of the generalized displacements of the Love-Kirchhoff and ReissnerMindlin theories and of the stress components at the generic layer interfaces. No assumptions regarding the thinness of the shell are considered. Regarding the definition of the electric potential, the direct piezoelectric effects are condensed into the model through effective stiffness and strains definitions, and the converse counterpart is considered by the action of prescribed electric potential differences in each piezoelectric layer. Then, the weak forms of a partially refined theory, where only the zero-order term of the non-linear fully refined transverse displacement is retained, are derived for an orthotropic doublycurved piezo-elastic generic shell layer. Based on the weak forms a FE solution is initially developed for the single layer. The degrees of freedom (DoFs) of the resultant four-noded generic piezo-elastic single layer FE are then ”regenerated” into an equivalent eight-node 3-D formulation in order to allow through-the-thickness assemblage of displacements and stresses, yielding a partially refined multilayer FE assuring displacement and shear stress interlayer continuity and homogeneous shear stress conditions at the outer surfaces. The shear stresses DoFs are dynamically condensed and the FE is reduced to a displacementbased form. The viscoelastic damping behavior is considered at the global FE model level by means of a Laplace transformed ADF model. The active control of vibration is shortly discussed and a set of indices to quantify the damping performance and the individual contributions of the different mechanisms are proposed.