Search

Acoustic radiation from vibrating structures is simulated by a Galerkin boundary element method based on the Burton–Miller approach. The boundary element operators are evaluated by the fast multipole method that allows large-scale computations in the medium frequency range. Two iterative solvers are considered: the generalized minimal residual method and a multigrid solver. Both approaches can be accelerated greatly by the presented approximate inverse preconditioner.

Pump suctuation and valve action in piping systems can lead to undesired excitation of structural components by propagating sound waves in the suid path. This vibro–acoustic problem is addressed by studying the dynamics as well as excitation mechanism. It is found that internal suid sow does neither alter operational desections nor vibrational modes considerably for low Mach numbers as encountered in most piping systems conveying heavy suids. Therefore, the suid is modelled at rest to solve the vibro–acoustic problem. On the other hand suid–structure interaction has a significant insuence and cannot be neglected. Pipe models are generated in three dimensions by using Finite Elements. The acoustic wave equation in the suid is hereby fully coupled to the structural domain at the suid-structure interface. These models are used for simulating mode excitation by transient simulation and modal analysis. Reduced component models allow for efficient simulations. The model reduction is hereby based on a modal truncation. Afterwards, dominant modes are selected based on controllability and observability considerations. Modal controllabilities are furthermore used to quantify the excitation of vibrational modes by white noise at the pipe inlet. (© 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

This work considers active vibration control of a fluid-loaded structure by means of a modal concept. The resulting ‘adaptive structure’ comprises actuators and sensors, thus, they become an integral part of the structure. A real-time controller is designed to reduce structural vibrations in the adaptive structure. The controller is based on a modal state-space formulation of the equation of motion for the test panel, where the effect of fluid-structure interaction has been considered in the mathematical model. The modal parameters for the fluid-loaded test structure are identified from experimental modal analysis. In order to fulfill the observability and controllability conditions, a design methodology for sensor and actuator placement is presented. Finally, experiments are conducted to verify the proposed concept.

A coupling algorithm based on Lagrange multipliers is proposed for the simulation of structure-acoustic field interaction. Finite plate elements are coupled to a Galerkin boundary element formulation of the acoustic domain. The interface pressure is interpolated as a Lagrange multiplier, thus, allowing the coupling of non-matching grids. The resulting saddle-point problem is solved by an approximate Uzawa-type scheme in which the matrix-vector products of the boundary element operators are evaluated efficiently by the fast multipole boundary element method. The algorithm is demonstrated on the example of a cavity-backed elastic panel.

This brief note describes a method for calculating the eigenfrequencies of a rotating acoustic air column inside labyrinth seals in turbomachinery. The method is applied to nonrotating air columns as well as to rotating air columns considering a body fixed and a spatial fixed coordinate system.

This paper presents a new symmetric formulation for structural acoustics in the frequency domain. Usually, the structural domain is discretized with the Finite-Element Method (FEM), whereas the Boundary Element Method (BEM) is used for the treatment of the infinite acoustic domain. Coupling formulations generally suffer from the dense and unsymmetric equation system of the BEM, To circumvent this drawback, the acoustic domain is discretized here with the Hybrid Stress Boundary Element Method (HSBEM), which is based on a variational principle. The discretized formulation consists of a symmetric stiffness-type equation based on a dynamic flexibility matrix in frequency domain. The HSBEM is thus easily coupled with other symmetric discretization methods, combining the advantages of a boundary formulation and a symmetric approach. An issue of the method is the evaluation of the flexibility matrix. This contribution extends former publications of the authors by a detailed analysis of the implementation of this matrix, leading to a new clustering scheme for an efficient treatment, based on the special structure of the integral kernel. Moreover, the treatment of hyper-singular integral kernels without integration, based on orthogonality properties for interior and exterior domains is outlined. Examples show the consistency of this approach. Finally, a coupled formulation for structural acoustics employing the HSBEM for the structure and the acoustic domain is introduced. Several numerical tests elucidate the applicability of the method and the proposed improvements.

In this work the application of resistively shunted piezoelectric material for reducing vibration amplitudes of a plate is studied. The ability to tailor the frequency-dependent loss factor is a consequence of the applied passive electrical network. To predict the damping performance of resistively shunted piezoelectrics, an approach based on the effective strain energy fraction is proposed. A finite element model may be used to accurately determine the effective modal strain energy fraction. However, for placing purposes of the piezoelectric elements, an analytical model, which does not account for local stiffening due to the piezoceramics, can be used. Design considerations include the frequency dependence of piezoceramic properties as well as the effect of stiff piezoceramic material on mode shapes. Experimental results are presented for a rectangular plate with eight pairs of resistively shunted piezoelectric elements.

In this research damage diagnostics is carried out by a novel design of a smart layer that consists of piezoelectric films. This thin layer is attached to the structure being monitored. First, some fundamental investigations are carried out in order to examine the influence of the thickness of the film, the influence of different adhesives, and the influence of the couplant. The wave field generated by the smart layer propagates into a solid. The directional dependency is investigated. Moreover, an improved type of polyvinylidene fluoride (PVDF) copolymer is presented and investigated for the potential application in the field of structural health monitoring. The use of this PVDF copolymer makes the manufacturing process of a self-sensing actuating layer in ultrasonics much easier than conventional PVDF films since the piezoelectric film is directly sputtered onto the surface of a metallic specimen or onto a metallic layer. This smart layer technique is a valuable tool for identifying the location and size of cracks and delaminations in composites as well as for determining local material thicknesses which might occur due to corrosion. It can be applied in order to monitor the so-called ‘hot spots’ on new structures as well as on already existing structures. The application of the smart layer is demonstrated on a plate-like structure containing a damage. The identified damage corresponds well with the actual damage.

Systems with friction are non-conservative as a consequence of the fundamental character of friction as a physical phenomenon: usually friction is associated with dissipative effects, but sometimes also with self-excitation. The present paper deals with the effect that sliding friction has on beating phenomena, which are very common in multidimensional systems with imperfect symmetries. It turns out that sliding friction has a significant influence on the energy budget of beating states, it may even lead to substantial transient amplification of the total vibrational energy. After describing the phenomenon a technique is provided to determine the initial conditions leading to optimal transient amplification of vibrational energy in sliding friction affected beating oscillations. Also intuitive as well as formal explanations for the effect's mechanism are given.

The objective of the present work is to reexamine the dynamic phenomenon of sprag-slip instability. To that purpose, a model consisting of an elastic beam sliding over a rigid belt at constant speed is set up and investigated. It turns out that there are parameter combinations for which the system does not posess a static solution corresponding to a steady sliding state, neither stable nor unstable, a phenomenon first discovered by Painleve considering sliding rigid bodies, sometimes referred to as the Painleve paradox. The nonexistence of a steady sliding state is a sufficient criterion for the appearance of sprag-slip oscillations, since in the corresponding configurations the fundamental behavior of the system is intrinsically dynamic in nature.

When damaged bodies are subjected to dynamic loadings, a non-linear structural response is observed in the vicinity of the cracks. This non-linearity is caused by the contact between opposite crack surfaces. In case of a harmonic excitation, higher harmonics can be observed in the frequency spectrum. In non-destructive testing, this phenomenon can be employed to localise damaged areas. In the present paper, a methodology is described for the numerical simulation of non-destructive damage detection in the excitation frequency and the higher harmonics. The approach is based upon a transient finite element calculation, followed by an analysis of the structural response with the Fast Fourier transform. The suitable choice of analysis parameters is discussed, and examples are given for the detection of cracks in flat slabs.

A fast multilevel multipole (FMM) algorithm is derived for the Helmholtz equation and adopted to the symmetric Galerkin boundary element method (BEM) for acoustics. The FMM allows to evaluate a matrix – vector product of the BEM with a computational cost of OðN log 2 NÞ; thus leading to a significant reduction of computation time and memory requirements compared to standard BEM formulations. This allows the simulation of large scale acoustic models. The performance of the algorithm is demonstrated on the example of sound radiation from an L-shaped domain with BE discretizations of up to 45,000 elements. q 2003 Elsevier Ltd. All rights reserved.

The present approach for vibration suppression of flexible structures is based on friction damping in semi-active joints. At optimal locations conventional rigid connections of a large truss structure are replaced by semi-active friction joints. Two different concepts for the control of the normal forces in the friction interfaces are implemented. In the first approach each semi-active joint has its own local feedback controller, whereas the second concept uses a global, clipped-optimal controller. Simulation results of a 10-bay truss structure show the potential of the proposed semi-active concept.

A boundary element formulation is presented for the solution of the equations of fully coupled thermoelasticity for materials of arbitrary degree of anisotropy. By employing the fundamental solutions of anisotropic elastostatics and stationary heat conduction, a system of equations with time-independent matrices is obtained. Since the fundamental solutions are uncoupled and time-independent, a domain integral remains in the representation formula which contains the time-dependence as well as the thermoelastic coupling. This domain integral is transformed to the boundary by means of the dual reciprocity method. By taking this approach, the use of dynamic fundamental solutions is avoided, which enables an efficient calculation of system matrices. In addition, the solution of transient processes as well as, free and forced vibration analysis becomes straightforward and can be carried out with standard time-stepping schemes and eigensystem solvers. Another important advantage of the present formulation is its versatility, since it includes a number of simplified thermoelastic theories, viz. the theory of thermal stresses, coupled and uncoupled quasi-static thermoelasticity, and stationary thermoelasticity. The accuracy of the new thermoelastic boundary element method is demonstrated by a number of example problems.

The mode-coupling instability has generally been acknowledged as one of the most prominent mechanisms leading to self-excited oscillations in sliding friction systems. The influence of structural damping on this type of instability mechanism however has not yet been fully clarified. The objective of the present work therefore is to investigate qualitative and quantitative aspects of the mode-coupling instability in the presence of structural damping, which will be assumed as linear viscous. For the sake of simplicity a two-degree-of-freedom minimal model is set up and analyzed. It is shown that under specific conditions the mode-coupling instability may be regarded as a viscous instability in the sense that an increase in structural damping may render a stable system unstable. An explanation for this behavior is given by two lines of argument: First a description and explanation is given in terms of eigenvalue-analysis. Due to the mathematical formality of this approach, the insight gained remains phenomenological. Second, a feedback-loop formalism is developed that allows a more detailed understanding of the underlying mechanical processes. Based on this formalism, necessary and in sum sufficient conditions for the onset of instability can be deduced and also the role of damping can be clarified.

A method of feedback design for damping control in mechanical systems is presented. In particular, several issues regarding nonlinear stabilization are discussed. The design method is Lyapunov-function based, and the resulting technique is easily applicable to damping control problems with friction interfaces. As an example, the method is applied to a flexible structure with a semi-active joint connection which acts as a controllable friction damper.

The material behavior of polymers and of rubber-like materials can often be classified as linear viscoelastic. Typical phenomena of viscoelastic material are the appearance of creep and relaxation processes. Considering periodic loads, a part of the deformation energy is stored in the material, whereas the rest is dissipated. This phenomenon is called material damping. When describing visoelastic materials, often rheological models consisting of springs and dashpots are used. They are known to have poor curve-fitting properties over a broad range of time or frequency. In this paper, a generalized rheological element will be deduced using fractional derivatives and the properties of some ‘fractional’ rheological models are discussed. Free decay experiments are carried out in order to perform a parameter identification of a ‘fractional’ 3-parameter model in the frequency domain. The 3d implementation of this model into an FE code is demonstrated and one of the experiments is simulated in order to verify the implementation.

To enhance the identification of material properties of orthotropic plates, a special method of fuzzy sensitivity analysis is presented which allows the determination of the dependencies between the material properties and the natural frequencies of each mode. The procedure is based on the classical thin-plate theory in conjunction with a recently developed method for calculating the natural frequencies of completely free orthotropic plates using the exact series solution. After presenting the fundamentals of fuzzy sensitivity analysis which include the numerical implementation of uncertain parameters as well as the simulation and the analysis of the model, the results of the proposed method applied to vibrations of an orthotropic plate are given.

A minimal two degree of freedom model is used to clarify from an intuitive perspective the physical mechanisms underlying the mode-coupling instability of self-excited friction induced oscillations. It is shown that simultaneous out-of-phase oscillations of friction force and displacement tangential to the friction force may lead to energy transfer from the frictional system to vibrational energy. Also it is shown that the friction force acts like a cross-coupling force linking motion normal to the contact surface to motion parallel to it and that a necessary condition for the onset of instability is that these friction-induced cross-coupling forces balance the corresponding structural cross-coupling forces of the system. Finally the origin and the role of phase shifts between oscillations normal and parallel to the contact surface is clarified with respect to the mode-coupling instability. It may be expected that the intuitive picture gained will be of considerable help for practical design purposes.

A coupled symmetric BE–FE method for the calculation of linear acoustic fluid–structure interaction in time and frequency domain is presented. In the coupling formulation a newly developed hybrid boundary element method (HBEM) will be used to describe the behaviour of the compressible fluid. The HBEM is based on Hamilton's principle formulated with the velocity potential. The state variables are separated into boundary variables which are approximated by piecewise polynomial functions and domain variables which are approximated by a superposition of static fundamental solutions. The domain integrals are eliminated, respectively, replaced by boundary integrals and a boundary element formulation with a symmetric mass and stiffness matrix is obtained as result. The structure is discretized by FEM. The coupling conditions fulfil C 1 -continuity on the interface. The coupled formulation can also be used for eigenfrequency analyses by transforming it from time domain into frequency domain.

Modeling and identification of a joint with load normal to the contact interface of two connected rods is discussed in this paper. An experimental setup for the analysis of the joint is proposed and measurement results are presented. The perception that both the damping behavior and the stiffness of the joint are influenced by a large number of effects that can hardly be modeled motivates the use of a rather simple model, but with fuzzy-valued model parameters, instead of crisp ones. In this concept, the uncertainty and variability of the model parameters can be taken into account by representing the parameters as fuzzy numbers that can be identified on the basis of the measured data. The identification of the fuzzy parameters proves to be a non-trivial problem which can be solved by applying the transformation method as a special implementation of fuzzy arithmetic.

Fractional time derivatives are used to deduce a generalization ofviscoelastic constitutive equations of differential operator type. Theseso-called fractional constitutive equations result in improvedcurve-fitting properties, especially when experimental data from longtime intervals or spanning several frequency decades need to be fitted.Compared to integer-order time derivative concepts less parameters arerequired. In addition, fractional constitutive equations lead to causalbehavior and the concept of fractional derivatives can be physicallyjustified providing a foundation of fractional constitutive equations. First, three-dimensional fractional constitutive equations based onthe Grunwaldian formulation are derived and their implementationinto an elastic FE code is demonstrated. Then, parameter identificationsfor the fractional 3-parameter model in the time domain as well as inthe frequency domain are carried out and compared to integer-orderderivative constitutive equations. As a result the improved performanceof fractional constitutive equations becomes obvious. Finally, theidentified material model is used to perform an FE time steppinganalysis of a viscoelastic structure.

The use of absorbers to reduce vibrations of machines is common in industry and can be found in various applications. In most cases passive absorbers are used to cancel one particular eigenfrequency. The disadvantage of this solution is that due to the introduction of an additional degree-of-freedom two resonance peaks occur next to the absorbed eigenfrequency. Given the case that the machine operates in a wider frequency band these two eigenfrequencies could be excited and feature similarly high amplitudes. To address this concern, in the present case an adaptive absorber is used, which is able to adjust its eigenfrequency to the actually excited frequency. Therefore, the anti-resonance can be shifted such that a full cancellation of the resonance is possible. The absorber consists of a mass and two springs. One spring is fixed to the mass permanently and the second can be coupled to the system by an adaptive joint connection. The normal force in the frictional contact serves as control variable to achieve adaptivity of the dynamic eigenfrequency of the absorber. Two control concepts are presented. Both concepts include isolated curves characterizing the nonlinear relation between the dynamic stiffness and the related normal force based on simulations using the Harmonic Balance Method. Due to the isolation of the nonlinearity, linear control concepts like LQR can be applied, which is done in the present case. Furthermore, a direct control of the eigenfrequency is done. The adaptive absorber is applied to a simplified machine tool carriage.Copyright © 2014 by ASME

The damping properties of materials, joints, and assembled structures can be modeled efficiently using fractional derivatives in the respective constitutive equations. The respective models describe the damping behavior accurately over broad ranges of time or frequency where only few material parameters are needed. They assure causality and pure dissipative behavior. Due to the non-local character of fractional derivatives the whole deformation history of the structure under consideration has to be considered in time-domain computations. This leads to increasing storage requirements and high computational costs. A new concept for an effective numerical evaluation makes use of the equivalence between the Riemann–Liouville definition of fractional derivatives and the solution of a partial differential equation (PDE). The solution of the PDE is found by applying the method of weighted residuals where the domain is split into finite elements using appropriate shape functions. This approach leads to accurate results for the calculation of fractional derivatives where the numerical effort is significantly reduced compared with alternative approaches. Finally, this method is used in conjunction with a spatial discretization method and a simple structure is calculated. The results are compared to those obtained from alternative formulations by means of accuracy, storage requirements, and computational costs.

The contribution summarizes the route from synthetic mechanics based on Newton’s and Euler’s axioms via analytical mechanics based on Rayleigh-Ritz method to Finite Elements.

The paper at hand shows how structural damping and stiffness parameters in shrunk joints can be determined by a generic joint experiment. With thin-layer elements these parameters from the joint experiment are coupled to the structures finite element model. Equivalent modal damping factors can be determined by performing a complex numerical modal analysis, by which the stability of the rotor can be tested. The two-disc rotor is examined as an application sample. This rotor consists of a shaft with two shrunk-on discs. With the above mentioned approach, and by considering structural damping added to material damping, the modal damping of the first torsional eigenfrequency is calculated and then compared to the results of an experimental modal analysis. The paper shows that the presented approach leads to a reliable approximation of the examined structure’s dissipation properties. It serves as a prediction tool for the response behavior of a turbo-generator.

In this work, an efficient FE-modeling technique for assembled metallic structures is presented. Linear thin-layer elements containing damping and stiffness parameters are placed on the interfaces of bolted joints. The interface parameters are identified experimentally on an isolated lap joint and then used as an input for the FE-simulation. Since the presented modeling technique is linear, it delivers acceptable results only for small relative displacements in the joint interface, i.e. microslip. Therefore investigations on the transition from micro- to macroslip are conducted. A promising approach to detect macroslip is based on the significant increase of higher harmonic frequency generation. The application of this criterion results in a linear relation between the normal force and the maximum tolerable tangential force.

In many engineering applications vibro-impact systems play an important role for functionality like for example in percussion machines or cause undesirable effects like noise or fatigue. Also in assembled structures clearance in joints can lead to vibro-impact problems that affect the overall dynamics of the systems. Either way, the understanding and simulation of such systems is essential. Furthermore, combinations of impacts with other nonlinearities like friction or nonlinear springs are relevant in practice. This contribution examines similar methods for the investigation of springs with cubic stiffness and vibro-impact nonlinearities as well as their combination. The Harmonic Balance Method is used along with a continuation method to simulate Frequency Response Functions of the nonlinear systems. Additionally, the influence of higher harmonics and subharmonics is considered. In systems with impact or cubic spring also chaotic motions can occur depending on the parameters. The occurrence of these motions is estimated by the calculation of Lyapunov-Exponents. Their appearance is visualized in Poincare-Maps and phase portraits. Further investigations will be carried out on the calculation of backbone curves for vibro-impact systems and systems with combined nonlinearities to capture the frequency-energy dependency of these systems.

Wave-based SHM concepts are widely used for an efficient evaluation of the state of a structure. In order to localize defects in waveguides, an exact knowledge of the propagation properties of ultrasonic waves is required.

In this paper, a non-singular boundary element formulation for 3D-elastostatics and 3D-elastodynamics is presented. The proposed method is based on a generalized variational principle. A weighted superposition of static fundamental solutions is used for the field approximation in the domain, whereas the displacement and stress field on the boundary are interpolated by well-known polynomial shape functions. By separating time- and space-dependence a symmetric equation of motion is derived with time-independent mass and stiffness matrix. The domain integral over inertia terms, leading to the mass matrix, is analytically transformed to the boundary. Thus, a boundary only formulation is derived. Comparing numerical results with analytical solutions clearly shows that the obtained system of equations is well-suited for dynamic problems.

An analysis for solving boundary value problems in structural mechanics which was proposed by Wang and Lin (1996 Journal of Sound and Vibration 196 , 285–293; 1999 Journal of Applied Mechanics 66 , 380–387) [1, 2] has been extended to the calculation of the eigenfrequencies of an orthotropic plate under all free boundary conditions. The convergence of the series solution is assured and the procedure leads to pointwise exact solutions. The calculated eigenfrequencies have been verified by a different approach and indicate that the present method is simple and effective.

The boundary element method (BEM) is an efficient tool for the calculation of acoustic wave propagation in fluids. Transient waves can be solved by either using a formulation in frequency domain along with an inverse Fourier transformation or a time domain formulation. To increase the efficiency for the solver and allow for an efficient coupling with finite element domains the symmetry of the system matrices is advantageous. If Hamilton's principle is used, a symmetric variational formulation can be established with the velocity potential as field variable. The single field principle is generalized as multifield principle as basis of a hybrid BEM for the calculation of acoustic fields in compressible fluids in time domain. The state variables are separated into boundary variables, which are approximated by piecewise polynomials and domain variables, which are approximated by a superposition of weighted fundamental solutions. In both approximations the time and space dependency is separated. This is why static fundamental solution can be used for the field approximation. The domain integrals are eliminated, respectively, transformed into boundary integrals and an equation of motion with symmetric mass and stiffness matrix is obtained, which can be solved by a direct time integration scheme or by mode superposition. The time derivative of the equation of motion leads to a formulation with pressure and acoustic flux on the boundary for an easier interpretation of the variables.

The symmetric hybrid boundary element method in the frequency and time domain is introduced for the computation of acoustic radiation and scattering in closed and infinite domains. The hybrid stress boundary element method in a frequency domain formulation is based on the dynamical Hellinger–Reissner potential and leads to a Hermitian, frequency-dependent stiffness equation. As compared to previous results published by the authors, new considerations concerning the interpretation of singular contributions in the stiffness matrix are communicated. On the other hand, the hybrid displacement boundary element method for time domain starts out from Hamilton's principle formulated with the velocity potential. The field variables in both formulations are separated into boundary variables, which are approximated by piecewise polynomial functions, and domain variables, which are approximated by a superposition of singular fundamental solutions, generated by Dirac distributions, and generalized loads, that are time dependent in the transient case. The domain is modified such that small spheres centered at the nodes are subtracted. Then the property of the Dirac distribution, now acting outside the domain, cancels the remaining domain integral in the hybrid principle and leads to a boundary integral formulation, incorporating singular integrals. In the time domain formulation, an analytical transformation is employed to transform the remaining domain integral into a boundary one. This approach results in a linear system of equations with a symmetric stiffness and mass matrix. Earlier 2D results are generalized in the present paper by a 3D implementation. Numerical results of transient pressure wave propagation in a closed domain are presented.

Vibration properties of most assembled mechanical systems depend on frictional damping in joints. The nonlinear transfer behavior of the frictional interfaces often provides the dominant damping mechanism in a built-up structure and plays an important role in the vibratory response of the structure. For improving the performance of systems, many studies have been carried out to predict, measure, and/or enhance the energy dissipation of friction. This article reviews approaches for describing the nonlinear transfer behavior of bolted joint connections. It gives an overview of modeling issues. The models include classical and practical engineering models. Constitutive and phenomenological friction models describing the nonlinear transfer behavior of joints are discussed. The models deal with the inherent nonlinearity of contact forces (eg, Hertzian contact), and the nonlinear relationship between friction and relative velocity in the friction interface. The research activities in this area are a combination of theoretical, numerical, and experimental investigations. Various solution techniques commonly applied to friction-damped systems are presented and discussed. Recent applications are outlined with regard to the use of joints as semi-active damping devices for vibration control. Several application areas for friction damped systems due to mechanical joints and connections like shells and beams with friction boundaries are presented. This review article includes 134 references.

Active vibration control has been successfully tested for structures with simple geometry, such as beams and plates, by using modal controllers. Since the dynamical behaviour of a variety of mechanical structures can be expressed in terms of modal parameters, the application of modal control concepts can be extended to structures with more complex geometries. For such structures the evaluation of modal parameters from numerical calculations of local modes is complicated because the results strongly depend on proper boundary conditions of the truncated structure. Therefore the modal data are identified by an experimental modal analysis. The transformation of the experimentally evaluated mode shapes into a closed analytical formulation and the extraction of modal input and output factors for sensors and actuators connect experimental modal analysis and modal control theory. The implementation of the input and output factors into a modal state space formulation results in a modal filter for the point sensor array and a retransformation filter for the segmented actuator patches. In this study PVDF foil is used for sensors and actuators. The modal controller is implemented on a digital controller board and experimental tests with the floor panel and center panel of a car body are carried out to validate the proposed concept.

In this paper, a boundary element (BE) formulation is developed originally which treats three-dimensional problems of transient piezoelectricity. The approach at hand uses the fundamental solution of the static piezoelectric operator instead of the transient one. This results in a domain integral appearing in the representation formula, which contains the inertia term. This domain integral can be transformed to the boundary using the dual reciprocity method (DRM), which leads to a system of ordinary differential equations in time domain, similar to the systems obtained in standard finite element methods (FEM). The DRM has been chosen because of the difficulties and big computational effort involved in a BE implementation, which makes use of the anisotropic transient piezoelectric fundamental solution. It is an approach that appears to be much too time-consuming for use in a commercial BE code, in which computational costs is an important issue. The method presented in this paper is validated by a numerical example for transient piezoelectricy, which demonstrates excellent agreement with FE computations for the generalized displacements, and an improved accuracy for the flux quantities such as electric field and elastic stresses.

Since advanced technical systems, such as aircrafts, space structures and automobiles, have to combine high performance with low weight, passive vibration absorbers reach their limits. This is why active control has become more important in structural dynamics with successful applications. Vibration control requires sensors, actuators and a controller. In this paper Polyvinylidene fluoride (PVDF) is used as actuator and sensor material. The PVDF elements are segmented in arrays on the plate. The sensors act as point sensors and the sensor signals are filtered by a modal sensor matrix. The modal displacements and modal velocities are used as input data for the controller and for a so-called Actuator Management System (AMS) as well. A modal actuator matrix transforms the controller output into driving actuator voltages. The AMS switches elements of the modal actuator matrix which results in quasi modal actuator groups. A rectangular aluminum plate has been equipped with PVDF actuators and sensors and experimental tests have been carried out in order to validate the proposed concept.

Friction damping in bolted joint connections of large space structures turned out to be a major source of damping (Gaul and Bohlen, 1987). For vibration suppression, the joints are designed such that the normal force in a frictional interface is controlled which improves damping performance. The use of active control to vary the normal contact force in a joint by means of a piezoelectric element is explored. A model consisting of two elastic beams connected by a single active joint is considered. A friction model with velocity dependent dynamics is used to describe the friction phenomena. A control law for friction dampers which maximizes energy dissipation instantaneously by controlling the normal force at the friction interface is proposed. The effect of displacement- and velocity-induced friction dynamics is considered for the design of the control law. We arrive at a dynamic controller which prevents frictional energy stored as potential energy in a bristle model from being returned to the system.

In memoriam ERIC REISSNER The paper is devoted to Professor Eric Reissner's initation of halfspace theory for soil interacting with a vibrating foundation. His interest in vibration problems was fostered by his father H. REISSNER and A. HERTWIG in Berlin. Aiming at the interpretation of Degebo (Institute of Soil Mechanics) machine vibration tests, E. REISSNER generalized the halfspace theory for point loads by H. LAMB and calculated the frequency response function of a circular foundation on soil. His solution of the associated stress boundary value problem contains the so-called radiation damping. The publication (Ingenieur-Archiv 1936) became the classic paper in the field. It was not until 1955 that the halfspace theory was confirmed by experimental results after ARNOLD et al. corrected a sign mistake. A generalization of Reissner's solution for the viscoelastic halfspace excited on a rectangle is presented. The obtained Green's functions lead to the solution of mixed boundary value problems for rigid foundation slabs. The interaction of adjacent slabs can be treated by superposition as well. A link between Reissner's halfspace theory and boundary element formulations of general soil-structure interaction problems is provided.

Large space structures often consist of truss elements which are connected by bolted joints. The interface dissipation in these junctions turns out to be the major source of damping. For vibration suppression, the joints are designed such that the normal force in the frictional interface is controlled for improving damping performance. The norma1 contact is varied by active control using a bolt with a piezoelectric washer. A system consisting of two elastic beams connected by a single active joint is considered. The friction phenomena are described by a friction model with velocity dynamics. The effect of displacement- and velocity-induced friction dynamics is considered in the design of the control law. The result is a dynamic controller which prevents frictional energy, stored as potential energy in the bristles, from being returned into the system.

An experimental method has been developed for detecting impact-generated flexural waves in plates using piezoelectric films. The recorded signals are analyzed in order to determine the force-time history of the impact. The reconstructed response is compared with the measured response. A good prediction is found. This technique presents a valuable method for identification of source locations and may be applied to in-service structures under impact, to seismic data from earthquakes or to signals recorded from acoustic emission of propagating cracks.

As an alternative to domain discretization methods, the boundary element method (BEM) provides a powerful tool for the calculation of dynamic structural response in frequency and time domain. Field equations of motion and boundary conditions are cast into boundary integral equations (BIE), which are discretized only on the boundary. Fundamental solutions are used as weighting functions in the BIE which fulfil the Sommerfeld radiation condition, i.e., the energy radiation into a surrounding medium is modelled correctly. Therefore, infinite and semi-infinite domains can be effectively treated by the method. The soil represents such a semi-infinite domain in soil-structure-interaction problems. The response to vibratory loads superimposed to static pre-loads can often be calculated by linear viscoelastic constitutive equations. Conventional viscoelastic constitutive equations can be generalized by taking fractional order time derivatives into account. In the present paper two time domain BEM approaches including generalized viscoelastic behaviour are compared with the Laplace domain BEM approach and subsequent numerical inverse transformation. One of the presented time domain approaches uses an analytical integration of the elastodynamic BIE in a time step. Viscoelastic constitutive properties are introduced after Laplace transformation by means of an elastic–viscoelastic correspondence principle. The transient response is obtained by inverse transformation in each time step. The other time domain approach is based on the so-called `convolution quadrature method'. In this formulation, the convolution integral in the BIE is numerically approximated by a quadrature formula whose weights are determined by the same Laplace transformed fundamental solutions used in the first method and a linear multistep method. A numerical study of wave propagation problems in 3-d viscoelastic continuum is performed for comparing the three BEM formulations.

Summary This paper provides a unified approach for conventional and generalised linear models of viscoelastic constitutive behaviour. Creep, relaxation and hysteresis effects of materials and structures are described consistently. Advantages of the fractional derivative concept are outlined. Mathematical consequences resulting from operator non-locality in time domain and uniqueness questions arising in frequency domain are addressed. The elastic-viscoelastic correspondence principle serves as a tool to obtain as well analytical and numerical BEM and FEM solutions of wave propagation and vibration problems by transform methods. Characteristics of viscoelastic waves and vibrations are discussed. The paper focusses on material damping but includes aspects of radiation damping description by discretisation methods as well. Important aspects of damping description are beyond the scope of selected topics of this survey paper. This is why additional reading is recommended on the following subjects: Thermo-viscoelasticity and non-linear viscoelasticity [3, 4, 21], determination of mechanical properties by experimental methods [2, 4, 38, 43], damping devices and surface damping treatment [31, 38, 43], material damping data [3, 31] and structural damping [45] including the nonlinear dissipation in mechanical joints such as bolted or riveted connections [46–48]. A list which is by far not complete.

Unter Anwendung der Kugelgeometrie wird eine neue Methode beschrieben, mit der die integralfreien Terme aus den Somigliana-Identitaten fur drei-dimensionale Kontinua mit nicht glatten Randern analytisch berechnet werden konnen. Fur diese Terme aus der Somigliana-Verschiebungsidentitat und der Somigliana-Spannungsidentitat werden Berechnungsformeln entwickelt, die nur noch Transformationen von speziellen Tensorfunktionen enthalten, so das insbesondere keine Integrationen mehr durchzufuhren sind. Die erzielten Ergebnisse sind auf andere Probleme der Randelementmethode ubertragbar. New analytical formulas are derived for calculating the integral free terms of both the 3-D Somigliana displacement and the Somigliana stress identity with non-smooth boundary. The basis of the approach is to incorporate spherical geometry. Computation of the formulas is easy because the integration is replaced by simple tensor-function transformations. It is possible to apply the results to other problems associated with the Boundary Element Method.

A new smart structural configuration for beams with symmetrically embedded modal sensors and actuators is proposed. Pairs of symmetrically installed modal sensors and actuators having the same shape of electrode profile are individually connected by a control unit. They are used to control each corresponding vibration mode of the beam independently. Dynamic response of the structure is investigated by the modal analysis method. Numerical simulations for vibration and sound radiation controls presented for illustrations are limited to simply supported beams. Results indicate that modal sensors and actuators, properly selected on the basis of the location and frequency of external forces, can effectively suppress the beam vibration and reduce radiated sound pressure in the far-field.

A new procedure for calculating field points with the boundary element method (BEM) is outlined. In the conventional BEM (CBEM) field points are computed as post-processing by recurrently solving the boundary integral equation with known boundary data for every field point of interest. This procedure is very time-consuming. On the other hand, newly developed hybrid boundary element formulations (HBEMs) based on variational principles compute field points from the known boundary solution by simply transforming it to the domain using fundamental solutions as field approximation. The advantage of the HBEM is that the related system matrices are symmetric by construction but the computational effort to obtain the boundary solution is higher than in CBEMs. Thus, if symmetry of the system matrices has no priority, it is advantageous to compute the boundary solution with the CBEM and the field point solution with the HBEM. The additional implementation effort is relatively low, since only one extra matrix has to be computed, which is sparse and has analytical entries.

The electrical fields and configuration parameters such as location, size and thickness of piezoelectric actuators are very important for shape control of structures. By using a performance index, the configuration parameters of actuators and adhesive can be chosen by some rules for improving performance. In this study a procedure combining a finite element model and the gradient projection algorithm is proposed for optimum design of shape control. This finite element model contains the actuator element, the adhesive interface element, and an eight-node isoparametric plate element which is employed for the calculation of plate shape. The gradient projection algorithm is used to choose the optimal values of design variables. Some numerical examples are illustrated and results reveal that the present method is effective and can be applied to the problem of shape control.