Shock and Vibration - Volume 17, issue 4,5
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International Conference on Structural Engineering Dynamics – ICEDyn 2009
DOI: 10.3233/SAV-2010-0529
Citation: Shock and Vibration, vol. 17, no. 4,5, pp. 329-329, 2010
Some modern problems in structural engineering dynamics
Authors: Elishakoff, I. | Pentaras, D.
Abstract: This review paper deals with two problems in structural engineering dynamics; one is deterministic, the other is of stochastic nature. One problem is linear, the other is nonlinear. Authors have a biased preferential view on these problems because of their active involvement in the discussed research topics. Still, these two problems reflect, at least in a small manner, some developments in this vast and fascinating field. The first part deals with deterministic linear vibrations of double-walled …carbon nanotubes either in classical or refined setting; the second part is devoted to the nonlinear random vibrations of structures. Show more
Keywords: Deterministic linear vibrations, nonlinear random vibrations
Absolute vibration suppression (AVS) control – modeling, implementation and robustness
Authors: Halevi, Y. | Peled, I.
Abstract: Absolute Vibration Suppression (AVS) is a control method for flexible structures governed by the wave equation. Such system may be a rotating shaft, a rod in tension or a crane for which the cable mass is not negligible. First an accurate, infinite dimension, transfer function, relating arbitrary actuation and measurement points, with general boundary conditions, is derived. The transfer function consists of time delays, due to the wave motion, and low order rational terms, which correspond …to the reflection from the boundary. Thus the compact mathematical representation has a clear physical interpretation. Furthermore, it leads to the special structure of the AVS controller which is a collocated, rate to force feedback that completely eliminates the vibration. The paper investigates the properties of the AVS controller and its robustness to modeling errors, in particular small non-collocation. Show more
Keywords: Control, wave equation, vibration suppression
Damping prediction of structures with bolted joints
Authors: Gaul, Lothar | Becker, Jens
Abstract: Friction in joints significantly contributes to the observed overall damping of mechanical structures. Especially if the material damping is low, the frictional effects in joints and clamping boundary conditions dominate the structural damping. The damping and the stiffness of the structure are nonlinear functions of the system states and consequently of the excitation signal and amplitude. If these nonlinear effects should be incorporated in the design process, transient simulations must be employed in order to predict …and analyze the damping for a given excitation, though they need excessive computation power due to the nonlinear constitutive laws and the high contact stiffnesses. As one approach to alleviate transient simulations, the application of component mode synthesis (CMS) methods to structures with friction is investigated exploiting the linearity of the jointed substructures. The friction and the nonlinear normal contact is modeled by constitutive laws that are implemented in node-to-node finite elements. The necessary considerations for accurate damping prediction by the reduced models, the accuracy and the computational times for transient simulations are discussed. The developed model reduction techniques allow a strong reduction of the computation time which in turn makes it a promising tool for model updating and predictive parameter studies. As an application example, a beam-like structure with attached friction damper is investigated in simulations and the obtained numerical results after model updating are compared to experiments. Show more
Modelling of damping force of dynamically loaded specimen of polyurethane foam in dependence on its density
Authors: Cirkl, David
Abstract: Article deals with measurement and modelling of damping force of polyurethane foam specimen being compressed. The specimens were taken from car seats and differ by material density. For modelling of damping force during harmonical kinematical excitation the explicit formula is used. Its parameters are found by means of method based on evaluation of energy dissipated during one loading cycle and also on evaluation of position of damping force extreme.
Keywords: Passengers comfort, car seat, polyurethane foam, damping force
Some remarks on experimental estimation of damping for seismic design of civil constructions
Authors: Rainieri, Carlo | Fabbrocino, Giovanni | Cosenza, Edoardo
Abstract: Experimental estimation of damping is currently not a comprehensively solved problem. Although modal frequencies and mode shapes can be measured confidently and quite easily by means of dynamic tests on civil structures, an accurate identification of damping ratios needs further development. Experimental values can be characterized by large error bounds mainly because damping is strongly influenced by the magnitude of the dynamic response of a structure. In this paper, the main issues concerning …identification of modal damping ratios are discussed in order to define methods for their reliable estimation, to reduce uncertainties and characterize error bounds. According to this aim, a procedure for optimized modal parameter estimation via Stochastic Subspace Identification is also proposed. Then data collected from an extensive literature review are analyzed depending on the type of structure in order to point out the main factors affecting damping. Moreover, a comparison with provisions about structural damping given in National and International seismic codes for structural design of civil structures is reported. This process demonstrates that the development of a damping database based on homogeneous and reliable estimates is required for calibration of predictive formulations to be used in the framework of performance-based seismic design. Show more
Keywords: Dynamic tests, damping estimation, operational modal analysis, performance-based design
Eigenpath following for systems with symmetric complex-valued stiffness matrices
Authors: Miller, U. | Bograd, S. | Schmidt, A. | Gaul, L.
Abstract: A vibration analysis of a structure with joints is performed. The simulation is conducted with finite element software capable of performing a numeric modal analysis with hysteretic damping assumption. The joints are modeled with thin layer elements, representing dissipation and stiffness of the joints. The matrices describing the system consist of the mass, as well as real and complex-valued stiffness matrices. If the eigenvalues of this system are found in one step, due to the mode …crossing occurring for the closely spaced modes, it is difficult and time consuming to assign calculated modal damping factors to the corresponding undamped eigenvalues. In order to avoid this problem, an eigenvalue following method is used. The outcome of the solution is the graphical presentation of continuous eigenvalue paths, showing the change in the eigenvalues from the undamped to the fully damped case. For every undamped eigenvalue exists its equivalent eigenfrequency and damping factor that can be used for further numerical analysis. In scope of this article a Predictor-Corrector and a Rayleigh-Quotient Iteration algorithms are applied to the problem. The algorithms are tested specifically on the type of matrices resulting from the weakly damped hysteretic formulation arising from the simulation of metallic structures with joints. Show more
Keywords: Hysteretic damping, complex eigenvalues, path following, complex stiffness matrix
A generalized frequency-temperature viscoelastic model
Authors: Moreira, R.A.S. | Corte-Real, J.D. | Rodrigues, J. Dias
Abstract: The design of passive damping treatments using viscoelastic materials requires both an accurate numerical analysis approach, usually making use of the finite element method, and a realistic means of material description. While the former has been widely studied and several and valuable approaches have become available during the last years, the latter is still an issue requiring additional efforts. The experimental characterization, the data modeling and finally the constitutive models able to be directly used along …analytic and numerical analysis, are still important research areas. Several viscoelastic models, able to be directly applied into a finite element analysis either in a time or in a frequency domain analysis, are available and have been widely used during the last years in most of the published work. Despite the general description and straightforward use that such modeling approaches may provide, temperature effect is usually disregarded and isothermal analysis are usually performed. Moreover, this temperature effect is naturally not directly considered as an input parameter for most of the viscoelastic material models and isothermal conditions are also considered in the experimental characterization data analysis. This work presents an extended viscoelastic model, based on well known isothermal models, where the temperature-frequency superposition effect is directly considered. The extended model is applied to the analysis of the experimental data using a data fitting procedure to identify a set of global parameters able to represent the effect of the frequency and the temperature. Show more
Implementation of a new method for the computation of fractionally damped structures into the finite element method
Authors: Schmidt, A. | Lotsch, M. | Gaul, L.
Abstract: The damping properties of materials, joints, and assembled structures can be modeled efficiently by the use of fractional derivatives in their 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. The concept of fractional derivatives can be implemented into discretization methods such as the finite element method, the boundary element …method, or the finite difference method. 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 finite element discretization and a simple rod structure is calculated. The results are compared to those obtained from alternative formulations by means of accuracy, storage requirements, and computational costs. Show more
Keywords: Fractional derivatives, damping, finite element method
Stochastic modeling of surface viscoelastic treatments combined with model condensation procedures
Authors: de Lima, A.M.G. | Rade, D.A. | Bouhaddi, N.
Abstract: Engineering structures incorporating viscoelastic materials are characterized by inherent uncertainties affecting the parameters that control the efficiency of the viscoelastic dampers. In this context, the handling of variability in viscoelastic systems is a natural and necessary extension of the modeling capability of the present techniques of deterministic analysis. Among the various methods devised for uncertainty modeling, the stochastic finite element method has received major attention, as it is well adapted for applications …to complex engineering systems. In this paper, the stochastic finite element method applied to a structural three-layer sandwich plate finite element containing a viscoelastic layer, with random parameters modelled as random fields, is presented. Accounting for the dependence of the behaviour of the viscoelastic materials with respect to frequency and temperature, using the concepts of complex modulus and shift factor, the uncertainties are modelled as homogeneous Gaussian stochastic fields and are discretized according to the spectral method, using Karhunen-Loève expansions. The modeling procedure is confined to the frequency domain, and the dynamic responses are characterized by frequency response functions (FRF's). Monte Carlo Simulation (MCS) combined with Latin Hypercube Sampling is used as the stochastic solver. The typically high dimensions of finite element models of viscoelastic systems combined with the large number of Monte Carlo samples to be computed make the evaluation of the FRF's variability computer intensive. Those difficulties motivate the use of condensation methods specially adapted for viscoelastic systems, in order to alleviate the computational cost. After the presentation of the underlying formulation, numerical applications of moderate complexity are presented and discussed aiming at demonstrating the main features and, particularly, the computation cost savings provided by the association of MCS with the suggested condensation procedure. Show more
Keywords: Uncertainty propagation, viscoelasticity, model condensation, stochastic finite elements