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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.

Slots with viscoelastic filling media increase the local damping of circular saw blade, which stabilizes the cutting process. In order to model the damping behaviour more accurately, a fractional viscoelastic model is introduced. Applying viscoelastic reciprocal theorem and eigenfunction expansion theorem leads to exact eigensolutions of the system with viscoelastic filling media. The method is applied to a circular plate with viscoelastic filling media. The comparison with a finite element simulation shows good agreement.

Structural Health Monitoring systems are developed to cost-efficiently prevent failure of mechanical and civil structures, and to predict the structure’s residual life. In this work, a damage detection algorithm based on the Hilbert transform of the recorded signals from induced guided ultrasonic waves is presented. By means of this algorithm, damage localization in multi-wire cables is performed through a time-of-flight analysis of the wave packets. The algorithm is fully automated and distinguishes between wave packets from different waves independently. Its applicability is analyzed for laboratory experiments on a single cylindrical wire and on multi-wire cables. As an additional damage indicator, second harmonic waves are evaluated. Furthermore, the possibility to perform damage identification by evaluating the waves’ amplitudes is analyzed. The amplitudes are compared with reference data from a novel hybrid finite-boundary element method.

Damping properties of assembled structures are largely influenced by frictional damping between joint interfaces. Therefore, these effects must be considered during the modeling process. Applying thin-layer elements (TLEs) with a linear, orthotropic material model on mechanical interfaces to incorporate joint damping has shown good agreement with experimental modal analysis in previous work. In the TLE model, constant hysteretic damping is assumed. The damping and stiffness parameters for the TLEs are experimentally identified on an isolated lap joint. Imprecisions caused by model simplifications and parameter uncertainty are addressed by model updating or uncertainty analysis. This requires multiple evaluations of models that are equivalent in all respects but their TLE parameterization. In this work, a model reduction technique for the TLE modeling approach is presented which significantly reduces computational cost for the re-calculation of eigenvalues after joint parameters are changed. The reduction is based on an eigensensitivity analysis and results in a single, linear equation for each eigenvalue. The presented approach is applied to a model updating example. Here, the model reduction allows for a much larger number of design variables which means experimental data can be reproduced more accurately with a physically more meaningful model.

Wave-based Structural Health Monitoring (SHM) to detect damages in civil and mechanical structures is a growing research field. In order to apply SHM to multi-wire cables, in this work, ultrasonic wave propagation in such coupled waveguides is studied theoretically, numerically and experimentally. In addition to transient finite element simulations, novel energy-based models are presented. With these models, efficient simulations of cables with many wires can be performed. Both finite element and energy-based models are verified with sophisticated experiments.

The properties of a high damping metallic material are investigated experimentally and a plausible finite element (FE) representation based on the results is deduced. The material consists of hollow, bonded aluminium spheres filled with ceramic particles. The damping mainly occurs due to dissipation via particle interaction. Consequently, one has to model the damping in such a way that shearing contributes only a little to the energy dissipation and the damping properties are orthotropic while the material stiffness is isotropic. Using the model of constant hysteresis for frequency-domain calculations, the complex stiffness matrix is constructed from the real-valued isotropic stiffness matrix, and the complex-valued orthotropic damping matrix. Since the finite element code used only offers the possibility of the damping matrix of an element being proportional to its stiffness, two superimposed finite element models are utilized, one representing the material's stiffness the other it's damping properties. The material parameters are obtained from an experimental modal analysis (EMA) on three samples of the material. The modelling approach is verified on a single hexahedral element and a simulation of the experimental modal analysis. Finally, a sandwich frame structure consisting of the damping material sandwiched between two aluminium frames is investigated by means of an EMA and a respective finite element modal analysis which makes use of the aforementioned modelling approach. A comparison of the results is given in terms of eigenfrequencies and the corresponding modal damping measures. Die Eigenschaften eines hoch dampfenden metallischen Werkstoffs werden experimentell untersucht und die Ergebnisse in einer adaquaten Finite-Elemente (FE) Modellierung zuganglich gemacht. Das Material besteht aus miteinander verklebten Aluminium-Hohlkugeln, die mit Keramikpartikeln gefullt sind. Die Dampfung basiert uberwiegend auf Energiedissipation, die durch Interaktion der Keramikpartikel untereinander hervorgerufen wird. Infolgedessen tragen Schubdeformationen nur in geringem Mase zur Energiedissipation bei, so dass die Dampfungseigenschaften orthotrop modelliert werden mussen, wahrend sich die Steifigkeit des Werkstoffs isotrop verhalt. Fur Berechnungen im Frequenzbereich wird das Modell konstanter Hysterese verwendet. Dabei wird die komplexe Steifigkeitsmatrix aus der reellwertigen isotropen Steifigkeit des Werkstoffs und seinen komplexen orthotropen Dampfungseigenschaften konstruiert. Da der verwendete Finite-Elemente Code im Fall von hysteretischer Dampfung nur die Option bietet, die Dampfungseigenschaften eines Elements proportional zu seiner Steifigkeit zu modellieren, werden zwei uberlagerte Finite-Elemente Modelle verwendet: in einem wird die Steifigkeit der Struktur abgebildet, wahrend das andere dessen Dampfungseigenschaften reprasentiert. Die entsprechenden Materialparameter werden mit Hilfe von experimentellen Modalanalysen (EMA) an drei verschiedenen balkenformigen Probekorpern gewonnen. Der Finite-Elemente-Modellierungsansatz wird anschliesend an einem einzelnen Hexaeder-Element sowie einer numerischen Modalanalyse der Probekorper verifiziert. Schlieslich wird eine Sandwich-Struktur mit Hilfe einer experimentellen Modalanalyse sowie der entsprechenden Finite-Elemente-Modellierung untersucht. Die Struktur besteht dabei aus zwei Aluminiumrahmen, zwischen die der neue Werkstoff eingebracht ist. Ein Vergleich der Ergebnisse wird in Form von Eigenfrequenzen und den dazugehorigen modalen Dampfungsmasen vorgenommen.

This paper addresses scattering effects at arbitrarily shaped defects in waveguides with finite cross-sections. The main subject is to predict scattered wavefields induced by an incident wavefield in order to localize and characterize damages. The numerical approach involves the solution of a boundary value problem in combination with a decomposition method of scattered wavefields. In order to investigate mode conversion phenomena at defects, a boundary element model of the damaged waveguide section is built up. Implementation of the Boundary Element Method based on the elastodynamic boundary integral equation and the Waveguide Finite Element Method allows for a numerically efficient calculation of scattering coefficients. For defect characterization and mode sensitivity analysis, various types of surface opening defects as well as shear fractures are considered. Numerical results are presented for cylindrical waveguides and are verified experimentally.

Structural Health Monitoring (SHM) is a growing research field in the realm of civil engineering. SHM concepts are implemented using integrated sensors and actuators to evaluate the state of a structure. Within this work, wave-based techniques are addressed. Dispersion effects for propagating waves in waveguides of different materials are analyzed for various different cross-sections. Since analytical theory is limited, a general approach based on the Waveguide Finite Element Method is applied. Numerical results are verified experimentally.

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.

Local nonlinearities typically occur due to large deformation in certain parts of a structure or due to the presence of nonlinear coupling elements. Often the dynamic behavior of such elements is a priori unknown and has to be investigated experimentally before they can be included in numerical calculations. In this contribution an integrated method for estimation of linear as well as nonlinear system parameters based on the nonlinear normal modes (NNMs) of the structure is proposed. The characteristics of the nonlinear and linear parts of an assembly both contribute to its NNMs. Assuming that the functional form of the nonlinearity is known or can be estimated through non-parametric identification techniques, this feature can be exploited for the purpose of model updating. For the updating process the measured and calculated NNMs of a system are compared and their difference is minimized. In this context the numerical calculation of NNMs is performed using the Harmonic Balance Method (HBM). The properties of the proposed method are demonstrated on the numerical example of a 4DOF oscillator with a cubic nonlinearity. Furthermore, the effectiveness of the method is shown by updating the FE-model of a beam with cubic nonlinearity based on experimental data.

The research field of structural health monitoring (SHM) in the realm of civil engineering has emerged rapidly. SHM concepts are based on integrated sensors and actuators to evaluate the structural state. Beside common structural response methods and other nondestructive testing techniques, wave-based ultrasonic techniques are widely used especially because of their flexibility. Monitoring cable structures such as overhead transmission lines or stay cables in suspension bridges is one objective of those wave-based methods. These structures are subject to aging, corrosion and other static and dynamic loads (e.g., wind, temperature). The cylindrical structures act as waveguides whereby monitoring of large distances with a single ultrasonic transducer is possible. However, the wave propagation is multimodal and dispersive, which complicates analysis of the wave motion and development of monitoring applications. This work addresses several aspects of the propagation of guided waves in cylinders, especially the analysis of reflection and transmission at discontinuities using finite element and boundary element methods.

Kurze Darstellung der Grundlagen und der Entwicklung der Stromungsmechanik vom Altertum bis zum Ende des 19. Jahrhunderts (© 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

This article gives an overview of different approaches for modeling the dynamics of mechanical joints in assembled structures. It contains a literature review pertaining to joint characteristics, types of joint models, and briefly examines models used in the simulation of assembled structures. Further on, a more detailed insight in joint modeling with the finite element method based on three different approaches is given: node-to-node contact using a Jenkins friction model, thin layer elements, and zero thickness elements. These approaches presented with real life applications come from an extensive joint modeling research performed at the Institute of Applied and Experimental Mechanics in the last 15 years. The advantages as well as limitations of these methods are discussed and the authors give practical hints for which cases these methods can be implemented. The article is supplemented with easy to model examples, so that the interested reader can apply the proposed approaches and compare the results with solutions provided by the authors.

We present two simple and effective schemes to formulate absorbing boundary conditions for time harmonic finite element analyses of waveguide structures. An impedance matching condition, applicable to single mode waveguides, is derived as well as an enhanced method for multi-modal wave propagation, making use of guided wave mode orthogonality. Both types are implemented in models generated with standard finite element software. Two examples of ultrasonic transducers attached to cylindrical waveguides are presented.

The integration of a model for longitudinal hydroacoustic fluid damping in thin hydraulic pipes in 3D finite element models is presented in this paper. In order to perform quantitative prediction of the vibroacoustic behavior and resulting noise levels of such fluid–structure coupled system due to hydraulic excitation, an accurate frequency-dependent fluid damping model including friction effects near the pipe wall is required. This step is achieved by matching complex wave numbers from analytical derivation into a parameterized damped wave equation and consecutive translation into finite element modeling. Since the friction effect close to the pipe wall changes locally with the inner pipe radius, the fluid damping model is applied segment-wise in order to model the influence of cross-sectional discontinuity, such as orifices, on the oscillating pressure pulsations. A component synthesis approach, which uses pipe segments as substructures, allows a simple model generation and fast computation times. The numerical harmonic results are compared to experimental frequency response functions, which are performed on a hydraulic test bench driven by a dynamic pressure source in the kHz-range.

To predict the vibro-acoustic behavior of structures, both a structural problem and an acoustic problem have to be solved. For thin structures immersed in water, a strong interaction between the structural domain and fluid domain occurs. This significantly alters the resonance frequencies. In this work, the structure is modeled by the finite element method. The exterior acoustic problem is solved by a fast boundary element method employing hierarchical matrices. An FE-BE formulation is presented, which allows the solution of the coupled eigenvalue problem and thus the prediction of the coupled eigenfrequencies and mode shapes. It is based on a Schur complement formulation of the FE-BE system yielding a generalized eigenvalue problem. A Krylov-Schur solver is applied for its efficient solution. Hereby, the compressibility of the fluid is neglected. The coupled eigensolution is then used for a model reduction strategy allowing fast frequency sweep calculations. The efficiency of the proposed formulations is investigated with respect to memory consumption, accuracy, and computation time.

In this study, the possibility of continuously monitoring load-carrying cables in bridges is considered. A sending/receiving transducer is used to generate an ultrasonic, longitudinal, elastic wave through the cable. The interaction between the L(0, 1)-wave and vertical cracks in a single rod is investigated using the Waveguide-FE-Method to predict the reflection and transmission coefficients. Moreover, this work analyzes how the elastic energy of a propagating wave is distributed between adjacent rods via friction. An energy-based model is developed to approximate the coupling behavior in a two-rod system. Finally, the numerical predictions are verified by experimental data.

The operation of pumps and valves leads to strong acoustic excitation in fluid-filled piping systems. Efficient substructuring and model order reduction strategies are required for the sound prediction in piping systems, and in order to reduce the sound transmission to attached components, such as the floor panel in vehicles, for example. This research presents a finite element based automatic substructuring and component mode synthesis technique, which is a combination of an extended Craig–Bampton method for fluid–structure coupled piping systems and a novel, consecutive interface reduction. Hereby, the remaining interface degrees of freedom between different substructures are further reduced using appropriate Ritz vectors. The proposed model order reduction strategy accelerates the computation of transfer functions in fluid-filled extended piping systems. In order to validate the simulation results, experimental results are obtained by a hydraulic test bench for dynamic measurements, where fluid pulsation is induced by piezo-driven transducers. The observed fluid–structure interaction phenomena correspond to the predictions by the proposed computation approach.

A model-based approach is proposed for the compensation of the piezoelectric hysteresis and creep effects in a feedforward control design for piezoelectric structures. The designed control commands can be favorably used in motion control for applications, e.g. for fast positioning with piezo flexures. They successfully realize fast rest-to-rest motion in the whole voltage operation range of the piezoelectric actuator material, i.e. specifically outside of the linear small-signal regime. The proposed control design combines a flatness-based inversion procedure for the structural dynamics under the assumption of linear piezoelectricity and an inverse piezoelectric operator for compensation of the piezoelectric hysteresis and creep large-signal effects. For that, the overall nonlinear system model is recast in a series connection of an input nonlinearity and the linear dynamics of the mechanical structure, which allows to design the feedforward control in two steps: First, a feedforward control for the linear model part is derived based on an approach exploiting the notion of flatness in combination with modal analysis of the linear dynamics. Thereby, the finite-element method is used to analyze the linear structural dynamics assuming small-signal operation of the piezoelectric material. Secondly, an inverse filter is designed based on the inversion of an operator-based hysteresis and creep model that is capable to compensate these nonlinear effects. By insertion of this filter, very good tracking control performance is achieved in both small and large-signal operation of the piezoelectric actuator. Simulations and experiments for a piezoelectrically actuated plate strip prove that the designed feedforward controls yields excellent tracking performance in large voltage ranges. The achieved time for the rest-to-rest transition is less than half the period of the first structural mode which is a typically limit of comparable methods.

Fluid–structure coupled problems are investigated to predict the vibro-acoustic behavior of submerged bodies. The finite element method is applied for the structural part, whereas the boundary element method is used for the fluid domain. The focus of this paper is on partly immersed bodies. The fluid problem is favorably modeled by a half-space formulation. This way, the Dirichlet boundary condition on the free fluid surface is incorporated by a half-space fundamental solution. A fast multipole implementation is presented for the half-space problem. In case of a high density of the fluid, the forces due to the acoustic pressure, which act on the structure, cannot be neglected. Thus, a strong coupling scheme is applied. An iterative solver is used to handle the coupled system. The efficiency of the proposed approach is discussed using a realistic model problem. Copyright © 2009 John Wiley & Sons, Ltd.

Component mode-based model-order reduction (MOR) methods like the Craig–Bampton method or the Rubin method are known to be limited to structures with small coupling interfaces. This paper investigates two interface-reduction methods for application of MOR to systems with large coupling interfaces: for the Craig–Bampton method a direct reduction method based on strain energy considerations is investigated. Additionally, for the Rubin method an iterative reduction scheme is proposed, which incrementally constructs the reduction basis. Hereby, attachment modes are tested if they sufficiently enlarge the spanned subspace of the current reduction basis. If so, the m-orthogonal part is used to augment the basis. The methods are applied to FE–BE coupled systems in order to predict the vibro-acoustic behavior of structures, which are partly immersed in water. Hereby, a strong coupling scheme is employed, since for dense fluids the feedback of the acoustic pressure onto the structure is not negligible. For two example structures, the efficiency of the reduction methods with respect to numerical effort, memory consumption and computation time is compared with the exact full-order solution. Copyright © 2008 John Wiley & Sons, Ltd.

In this study, the feasibility of continuous, online monitoring of power lines using ultrasonic waves is considered. Local and global wave-based approaches for wire break detection in overhead transmission lines are presented. Both methods use a sending/receiving transducer to generate an ultrasonic, longitudinal, elastic wave in the cable. Defects in the cable cause a portion of the incident ultrasonic wave to be reflected back to the transducer, which when received, can be used to identify the presence of the defect. Although the transducers can only be attached to the surface of the cable, subsurface wires can also be interrogated since elastic energy spreads to these wires through friction contact. This study also explores how the elastic energy of a propagating wave becomes distributed among contacting rods via friction contact. This work focuses specifically on a two-rod system in which the wave energy from an excited “active” rod is transmitted to a neighboring “passive” rod through friction contact. An energy-based model is used to approximate the time average elastic wave power in the two rods as a function of propagation distance. Power predictions from the energy-based model compare well with experimental measurements and finite element simulations.

In this paper, a new uncertainty analysis for the transformation method (TM) is proposed. As a practical implementation of fuzzy arithmetic, the TM is a convenient tool for the simulation and analysis of systems with uncertain parameters that are expressed by fuzzy numbers. The proposed uncertainty analysis and the sensitivity analysis of the TM complete each other in providing some quantification of the relationship between the uncertainties of the system input and the system output. The computation of gain factors is proposed, which allows the estimation of the absolute and relative measures of uncertainty. These measures allow the quantification of the influence of the uncertainty of the input on the uncertainty of the output.

Active vibration control using modal controllers has been successfully implemented on simple structures such as beams and plates. Since the dynamic behavior 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 is identified using experimental modal analysis. The transformation of the experimentally measured mode shapes into closed-form analytical formulations and the extraction of modal input and output factors for sensors and actuators are used to connect experimental modal analysis with modal control theory. The implementation of the input and output factors in 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 film 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.

Lightweight structures typically have low inherent structural damping. Effective vibration suppression is required, for example, in certain applications involving precision positioning. The present approach is based on friction damping in semi-active joints which allow relative sliding between the connected parts. The energy dissipation due to interfacial slip in the friction joints can be controlled by varying the normal pressure in the contact area using a piezo-stack actuator. This paper focuses on the optimal placement of semi-active joints for vibration suppression. The proposed method uses optimality criteria for actuator and sensor locations based on eigenvalues of the controllability and observability gramians. Optimal sensor/actuator placement is stated as a nonlinear multicriteria optimization problem with discrete variables and is solved by a stochastic search algorithm. 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 for a 10-bay truss structure show the potential of the proposed semi-active concept.

The precision of the raster scan motion of piezoelectric tube scanners, e.g. in scanning probe microscopy, is degraded by structural vibrations excited by the driving voltage signals. In order to eliminate these vibrations, a model–based, flatness–based feedforward control scheme is proposed that tracks the tip of the piezoelectric tube along the desired scan trajectory in the lateral plane. This scheme is derived from a modal analysis of the tube scanner dynamics which is obtained by finite element (FE) discretization. In order to achieve robustness of the trajectory tracking performance with respect to model errors or unknown external disturbances, the feedforward control is supplemented by a feedback controller in a two–degree–of–freedom design which feeds back the measured displacements at the top of the scanner. The feedback additionally compensates for the coupling between the two scanning directions, e.g. due to tube eccentricity. The control performance is investigated in simulations where the sample mass attached to the top of the tube, which represents the most realistic model error, is varied. Various simulation results demonstrate the achieved improvements in tracking accuracy by the proposed control over conventional approaches.

Free wave propagation in fluid-filled corrugated pipes is analyzed using finite element methods in combination with a wave-based approach. By combining discretized models with a wave-based approach, complex mechanism of wave motion in the three-dimensional waveguide is fully included. The pipes are treated as waveguides having periodic properties in the direction of wave propagation. The analysis of these guided waves leads to dispersion curves which show the strong frequency-dependency of the different wave modes. The method also allows the inclusion of coupling between fluid-borne and structure-borne wave modes which occur at the acoustic-structure interface. Phase and group velocities of the wave modes are derived in postprocessing steps. Additionally, the energy ratio of the fluid-domain and solid-domain vibrational energies is computed. Finally, linear damping models are included in order to explore wave mode attenuation.

This paper presents an efficient approach to model contact interfaces of joints in finite element analysis (FEA) with segment-to-segment contact elements like thin layer or zero thickness elements. These elements originate from geomechanics and have been applied recently in modal analysis as an efficient way to define the contact stiffness of fixed joints for model updating. A big advantage of these elements is that no global contact search algorithm is employed as used in master–slave contacts. Contact search algorithms are not necessary for modelling contact interfaces of fixed joints since the interfaces are always in contact and restricted to small relative movements, which saves much computing time. We first give an introduction into the theory of segment-to-segment contact elements leading to zero thickness and thin layer elements. As a new application of zero thickness elements, we demonstrate the implementation of a structural contact damping model, derived from a Masing model, as non-linear constitutive laws for the contact element. This damping model takes into account the non-linear influence of frictional microslip in the contact interface of fixed joints. With this model we simulate the non-linear response of a bolted structure. This approach constitutes a new way to simulate multi-degree-of-freedom systems with structural joints and predict modal damping properties.

Rotor vibrations in electrical machines depend on structural damping and stiffness properties of the laminated cores. Structural damping determines torsional and transversal vibration amplitudes at resonances. Therefore, it is very important to know the structural damping and stiffness of the laminated cores to carry out structural dynamic simulations. In this paper, a measurement set-up is presented to determine the structural damping and direction-dependent stiffness for laminated cores and stacks. The dissipated damping energy is examined as a result of harmonic excitation of different excitation amplitudes, frequencies and axial pre-stressing conditions. Thereby, the measured structural damping factor is compared to the material damping factor from tables. To allow a conclusion for the reproducibility of the evaluated damping parameters, repeated measurements are carried out and the results are statistically analyzed using the Weibull distribution.

Piezoelectric patches shunted with passive electrical networks can be attached to a host structure for reduction of structural vibrations. This approach is frequently called ''shunted piezo damping'' and has the advantage of guaranteed stability and low complexity in implementation. For numerical treatment of such structures, a finite element modelling methodology is presented that incorporates both the piezoelectric coupling effects of the patches and the electrical dynamics of the connected passive electrical circuits. It allows direct computation of the achieved modal damping ratios as a major design criterion of interest. The damping ratios are determined from the eigenvalue problem corresponding to the coupled model containing piezoelectric structure and passive electrical circuit. The model includes local stiffening and mass effects as a result of the attached patches and, therefore, enables accurate prediction of the natural frequencies and corresponding modal damping ratios. This becomes crucial for choosing the patch thickness to achieve optimal modal damping for a given host structure. Additionally, structures with complex geometry or spatially varying material properties can easily be handled. Furthermore, the use of a finite element formulation for the coupled model of piezoelectric patches and a host structure facilitates design modifications and systematic investigations of parameter dependencies. In this paper, the impact of parameters of the passive electrical network on modal damping ratios as well as the variation of the patch thickness are studied. An application of this modelling method is realized by commercial software packages by importing fully coupled ANSYS^(C) - models in MATLAB^(C). Afterwards, modal truncation is applied, the dynamic equations of the passive electrical network are integrated into the piezoelectric model and eigenvalue problems are solved to extract the increase in modal damping ratios. The numerical results are verified by experiments.

Valve actuation and pump fluctuation in piping systems generate propagating sound waves in the fluid path which in turn can lead to undesired excitation of structural components. This vibro-acoustic problem is addressed by studying the propagation dynamics as well as the excitation mechanism. Fluid-structure interaction has a significant influence on both hydroacoustics and on structural deformation. Therefore, pipe models are generated in three dimensions by using finite elements in order to include higher-order deflection modes and fluid modes. The acoustic wave equation in the fluid is hereby fully coupled to the structural domain at the fluid-structure interface. These models are used for simulating transient response and for performing numerical modal analysis. Unfortunately, such 3D models are large and simulation runs turn out to be very time consuming. To overcome this limitation, reduced pipe models are needed for efficient simulations. The proposed model reduction is based on a series of modal transformations and modal truncations, where focus is placed on the treatment of the nonsymmetric system matrices due to the coupling. Afterwards, dominant modes are selected based on controllability and observability considerations. Furthermore, modal controllabilities are used to quantify the excitation of vibration modes by a white noise acoustic source at the pipe inlet. The excitation of structural elements connected to the piping system can therefore be predicted without performing transient simulations. Numerical results are presented for a piping system consisting of straight pipe segments, an elbow pipe, joints, and a target structure. This example illustrates the usefulness of the presented method for vibro-acoustic investigations of more complex piping systems.

The numerical evaluation of fractional derivatives requires a high number of computations due to their nonlocal character. Particularly in the case of a multi-degree-of-freedom (mdof) system that is described by a fractional differential equation in time and is solved numerically by time integration, the numerical effort and the storage requirements explode. Therefore, a new method for the numerical evaluation of fractional derivatives is presented which reduces the numerical effort of mdof systems drastically. The algorithm is based on the Grunwald definition of fractional derivatives and, in contrast to some other concepts, maintains its benefits. The algorithm is applied to the equation of motion of a viscoelastic member, the properties of which are described by a fractional constitutive equation. Comparative calculations demonstrate the accuracy of the algorithm and the reduction in computation time and storage requirements.

This paper presents the application of an alternative waveguide finite element method (WFE) using standard FE-code for the computation of dispersion curves in fluid filled elastic pipes. Only one element is needed in longitudinal direction of the pipe in the FE model, which includes structural–acoustic interaction by a full coupling interface. After rearranging the dynamic stiffness matrix of the segment model in transfer matrix form, a periodicity condition is applied leading to an eigenvalue problem. Here, eigenvectors correspond to wave modes and eigenvalues are a function of the complex wavenumber. From the eigenpairs, phase velocities and group velocities of branches are computed as well as sound power transmission. Instead of solving the eigenvalue problem for each frequency separately, an eigenpath analysis is presented in order to track dispersion curves through the frequency band of interest. The numerical results are compared to results from an analytical model of a thin walled fluid-filled shell. The method allows periodic wave guides with any cross section to be analyzed while employing standard FE discretization.

Today many electronic devices consist of plate-like printed circuit boards carrying electric and electronic components mounted in some sort of housing. Depending on the application, these electronic devices may be subjected to severe random vibration loads over their lifetime, e.g. in automotive or aerospace environments. The present work shows that although state-of-the-art printed circuit boards are typically structurally linear with respect to stiffness properties, they are usually characterized by strongly nonlinear damping characteristics that have to be taken into account for proper vibration modelling and testing of corresponding devices. An approach allowing the nonlinear damping characteristics observed to be properly taken into account for testing and life-time prediction purposes is presented.

This paper gives an overview of research in the area of smart structure dynamics. A general description of smart material systems is given. Particular focus is given to the following fields of application: semi-passive concepts, energy harvesting, semi-active concepts, active vibration control, and active structural acoustic control. The use of smart structures in structural health monitoring applications is also considered.

For the simulation of acoustic-structure interaction problems, the coupled field equations must be solved. The structure is commonly discretized using finite elements, whereas for the acoustic field the boundary element method (BEM) is favorable. A mortar BEM-FEM coupling algorithm is developed that allows the combination of non-conforming meshes. The high flexibility for the choice of discretizations offers a high efficiency, since specialized shape functions and adaptive mesh refinement can be used in the subdomains. The mortar coupling algorithm yields a saddle point problem that is solved using a preconditioned inexact Uzawa algorithm. The iterative solver enables the use of the fast multipole BEM and thus coupled simulations on large boundary element models. Uncertain model parameters can be represented by fuzzy numbers and subsequently fuzzy arithmetic based on the transformation method can be used to evaluate BEM-FEM models in the presence of fuzzy-valued parameters.

Recently Yuan and Agrawal [L. Yuan and O.P. Agrawal, A numerical scheme for dynamic systems containing fractional derivatives, Journal of Vibration and Acoustics 124 (2002) 321–324] presented a new numerical scheme to calculate the dynamic response of mechanical systems, the damping forces of which are described by fractional derivatives. When solving the resulting equation of motion by time integration, it is necessary to store the entire displacement history of the system due to the non-local character of the fractional derivatives. The cited scheme appears to overcome this drawback by transforming the equation of motion with the fractional term into a set of ordinary differential equations. It can be shown that this scheme is equivalent to a classical spring-dashpot representation and thus does not imply the benefits derived from fractional-derivative models. In addition, it is less flexible and incorrectly predicts the asymptotic behavior.

This paper presents a model reduction and substructure technique for reduced dynamical models of fluid-filled pipe components. Both linear acoustical domain and structural domain are modelled by finite elements (FE), and they are fully coupled by a fluid–structure interface. The discretised dynamic FE-equations, which use the acoustic pressure as field variable in the fluid, render both non-symmetric mass and stiffness matrices due to the FSI-coupling. Since the partial solutions to the eigenproblem of the coupled system are of special interest, either numerical preconditioning or non-dimensionalisation of the physical quantities is performed to improve the condition and to accelerate the numerical computation. An iterative subspace solver is adopted to generate a sufficient approximate of the low-frequency eigenspace of the constrained problem. Model reduction for component mode synthesis uses constraint modes together with the computed eigenspace. Single-point constraints for the nodal degrees of freedom hold at the interface between substructures. The null space resulting from a QR-decomposition of the single-point constraints at the interface is used as explicit coupling matrix to prevent the deterioration of the conditioning. Partitioning of the reduction space and coupling matrices leads to a structure of the coupled global system matrices, which is similar to the original system structure in physical quantities. Therefore, the iterative subspace eigensolver is used again for numerical modal analysis. Modal analysis is performed for a pipe segment assembled by fully coupled two-field substructures. The results are compared to the results obtained from the full model and to experimentally determined mode shapes.