The Experts below are selected from a list of 7500 Experts worldwide ranked by ideXlab platform
T K Datta - One of the best experts on this subject based on the ideXlab platform.
-
spectral analysis of systems with non classical Damping using classical mode superposition technique
Earthquake Engineering & Structural Dynamics, 1993Co-Authors: R S Jangid, T K DattaAbstract:A spectral method for random vibration analysis of a structural system with non-Proportional Damping is presented using classical (undamped) mode superposition technique. The method obtains the frequency response function of the system by solving the dynamic equilibrium equations in generalized co-ordinates through an iterative process. The iterative solution is written in closed form and the proof for convergence of the iterative process is given. Numerical examples show the convergence characteristics of the process and an excellent accuracy of the obtained results. The method turns out to be computationally more efficient than the conventional methods of spectral analysis using damped mode shapes and frequencies.
Mohamed A Elgawady - One of the best experts on this subject based on the ideXlab platform.
-
appropriate viscous Damping for nonlinear time history analysis of base isolated reinforced concrete buildings
Earthquake Engineering & Structural Dynamics, 2013Co-Authors: Deepak R Pant, Anil Wijeyewickrema, Mohamed A ElgawadyAbstract:SUMMARY There is no consensus at the present time regarding an appropriate approach to model viscous Damping in nonlinear time-history analysis of base-isolated buildings because of uncertainties associated with quantification of energy dissipation. Therefore, in this study, the effects of modeling viscous Damping on the response of base-isolated reinforced concrete buildings subjected to earthquake ground motions are investigated. The test results of a reduced-scale three-story building previously tested on a shaking table are compared with three-dimensional finite element simulation results. The study is primarily focused on nonlinear direct-integration time-history analysis, where many different approaches of modeling viscous Damping, developed within the framework of Rayleigh Damping are considered. Nonlinear direct-integration time-history analysis results reveal that the Damping ratio as well as the approach used to model Damping has significant effects on the response, and quite importantly, a Damping ratio of 1% is more appropriate in simulating the response than a Damping ratio of 5%. It is shown that stiffness-Proportional Damping, where the coefficient multiplying the stiffness matrix is calculated from the frequency of the base-isolated building with the post-elastic stiffness of the isolation system, provides reasonable estimates of the peak response indicators, in addition to being able to capture the frequency content of the response very well. Furthermore, nonlinear modal time-history analyses using constant as well as frequency-dependent modal Damping are also performed for comparison purposes. It was found that for nonlinear modal time-history analysis, frequency-dependent Damping, where zero Damping is assigned to the frequencies below the fundamental frequency of the superstructure for a fixed-base condition and 5% Damping is assigned to all other frequencies, is more appropriate, than 5% constant Damping. Copyright © 2013 John Wiley & Sons, Ltd.
Cornel Sultan - One of the best experts on this subject based on the ideXlab platform.
-
Proportional Damping approximation using the energy gain and simultaneous perturbation stochastic approximation
Mechanical Systems and Signal Processing, 2010Co-Authors: Cornel SultanAbstract:The design of vector second-order linear systems for accurate Proportional Damping approximation is addressed. For this purpose an error system is defined using the difference between the generalized coordinates of the non-Proportionally damped system and its Proportionally damped approximation in modal space. The accuracy of the approximation is characterized using the energy gain of the error system and the design problem is formulated as selecting parameters of the non-Proportionally damped system to ensure that this gain is sufficiently small. An efficient algorithm that combines linear matrix inequalities and simultaneous perturbation stochastic approximation is developed to solve the problem and examples of its application to tensegrity structures design are presented.
-
published in mechanical systems and signal processing 24 2010 2210 2224 Proportional Damping approximation using the energy gain and simultaneous perturbation stochastic approximation
2010Co-Authors: Cornel SultanAbstract:The design of vector second order linear systems for accurate Proportional Damping approximation is addressed. For this purpose an error system is defined using the difference between the generalized coordinates of the non-Proportionally damped system and its Proportionally damped approximation in modal space. The accuracy of the approximation is characterized using the energy gain of the error system and the design problem is formulated as selecting parameters of the non-Proportionally damped system to ensure that this gain is sufficiently small. An efficient algorithm that combines Linear Matrix Inequalities and Simultaneous Perturbation Stochastic Approximation is developed to solve the problem and examples of its application to tensegrity structures design are presented.
-
design of structures for Proportional Damping approximation using the energy gain
50th AIAA ASME ASCE AHS ASC Structures Structural Dynamics and Materials Conference, 2009Co-Authors: Cornel SultanAbstract:NLIKE inertial and stiffness characteristics, which can be easily measured in static conditions, Damping, a dynamic characteristic, is more difficult to quantify. Hence, in many cases the artificial Rayleigh Damping model, which assumes that the Damping matrix is a linear combination of the mass and stiffness matrices, is used. Rayleigh Damping (or a generalization of it) is preferred because it leads to the ideal situation of a Proportionally damped linear model of the structure’s dynamics, but it is neither a physics based nor a data based model. When the source of Damping can be identified and accurately modeled using physics principles the Rayleigh Damping assumption (or any artificial Damping model for that matter) is not recommended. One example is that of tensegrity structures: the major Damping sources can be easily identified, the joints and the tendons, and for these elements reliable physics based Damping models can be built. However, in most cases the resulting linearized dynamics models are not Proportionally damped. In general, the likelihood of obtaining non-Proportionally damped models will increase due to our enhanced ability to accurately model Damping using physics principles. Even if a system is not Proportionally damped, one would still like to be able to approximate it with a Proportionally damped system. For structures, usually described using models with many degrees of freedom, such models are very advantageous because they allow the replacement of non-Proportionally damped models with decoupled models, which can be easily used for control design, fast computations, etc. This paper, which is strongly related to Ref. 6, pursues the idea of designing the structure such that it yields a linearized dynamics model that is “close” to a Proportionally damped one. In Ref. 6 the design of structures for Proportional Damping approximation was investigated by exploiting only one, indirect factor that influences the accuracy of the approximation, namely the separation between natural frequencies. It was ascertained that separation
Mario Lazaro - One of the best experts on this subject based on the ideXlab platform.
-
critical relationships in nonviscous systems with Proportional Damping
Journal of Sound and Vibration, 2020Co-Authors: Mario Lazaro, Lluis M GarciaraffiAbstract:Abstract Materials with time-dependent dissipative behavior currently play an important role in the design of new mechanisms for vibration control in civil, automotive, aeronautical and mechanical engineering. Damping forces are assumed to depend on the past history of the velocity response via convolution integrals over multiple exponential hereditary kernels. Hence, the computational complexity increases both in time and frequency domain with respect to the widely used viscous models. The derivations of this article are carried out under the hypothesis of nonviscous Proportional Damping, that is, the time-dependent Damping matrix becomes diagonal in the modal space of the undamped system. In this context, the Damping parameters, which control the behavior of dissipative forces, will be considered as variable. Critical manifolds can be defined as hypersurfaces in the domain of the Damping parameters, which represent boundaries between oscillatory and non-oscillatory motion. In particular, critical manifolds of two parameters are the so-called critical curves. In this paper a new method to obtain critical curves in Proportionally damped nonviscous multiple degree-of-freedom systems is presented. It is proved that the conditions of critical Damping lead to relationships that enables an analytical determination of such critical curves, in parametric form. In addtion, it is demonstrated that modal critical regions arise as the intersection of the critical curves. The proposed method is validated through two numerical examples involving discrete and continuous system with generalized Proportional Damping.
-
a viscous approach based on oscillatory eigensolutions for viscoelastically damped vibrating systems
Mechanical Systems and Signal Processing, 2013Co-Authors: Mario Lazaro, Jose L Perezaparicio, Marcelo EpsteinAbstract:Abstract Dissipative mechanisms in linear multiple-degree-of-freedom viscoelastic systems are characterized by the dependence on the history of the velocity degrees-of-freedom via convolution integrals over kernel functions. As a result, Damping matrices are frequency-dependent and, in general, state-space approach based methods are widely used for their resolution. This paper proposes a new approach suitable for modelling such systems via a viscous model with Proportional Damping, which approximates the response of the original viscoelastic system using the undamped eigenvectors together with the complex eigenvalues with oscillatory nature, neglecting those modes with non-viscous nature (negative real eigenvalues). It is rigorously demonstrated that the transfer function of any viscoelastic system can be expanded as the sum of the transfer function of certain viscous model and a residual term. The obtained viscous model, named Equivalent Viscous Model, is characteristic of each viscoelastic system. In order to study the bound of the residual term two indexes are introduced to describe, on one hand, the non-Proportionality, or the modal decoupling capability of the Damping matrix and, on the other hand, the Damping level of the system. The proposed viscous model is validated through numerical examples simulating different conditions of Proportionality and Damping.
Daniel J. Inman - One of the best experts on this subject based on the ideXlab platform.
-
Nature of coupling in non-conservative distributed parameter systems attached to external Damping sources:
Mathematics and Mechanics of Solids, 2017Co-Authors: John Bellos, Daniel J. Inman, Nikolaos BakasAbstract:Non-conservative distributed parameter systems connected to external Damping sources and possessing non-normal modes are analyzed in this work. The mathematical model of such systems is presented and real valued modal analysis is used to obtain the coupled modal equations of motion. A decoupling technique is developed using Fourier expansion, fictitious Damping ratios, modal coupling parameters and pseudo forces. The method is applicable to all types of excitation. A normal mode criterion in the form of non-Proportionality indices is also provided. The theoretical predictions are verified through application to a non-conservative Euler–Bernoulli beam with non-Proportional Damping configuration and various types of boundary conditions. Numerical examples emphasize the response errors associated with the Proportional Damping assumption and reveal the advantages of the proposed approach over the exact method.
-
symmetric inverse eigenvalue vibration problem and its application
Mechanical Systems and Signal Processing, 2001Co-Authors: Ladislav Starek, Daniel J. InmanAbstract:Abstract This paper summarises the authors' previous effort on inverse eigenvalue problem for linear vibrating systems described by a vector differential equation with constant coefficient matrices and non-Proportional Damping. The inverse problem of interest here is that of determining real symmetric coefficient matrices assumed to represent mass normalised velocity and position coefficient matrices, given a set of specified complex eigenvalues and eigenvectors. There are given two solutions of a symmetric inverse eigenvalue problem presented by Starek and Inman [1, 2]. The theory of inverse eigenvalue problem is applied to the model updating problem. The goal of this paper is to recognise that the model updating problem is a subset of the inverse eigenvalue problem. The approach proposed here is to use the results of inverse eigenvalue problem to develop methods for model updating. Comments are made on how their procedure may be used to solve the damage detection problem.
