Validity Domain of an Energetic Method for the Estimation of Modal Damping in the Case of Non Linear Localized Dissipation (original) (raw)
Related papers
Estimation of Modal Damping for Structures with Localized Dissipation
Conference Proceedings of the Society for Experimental Mechanics Series, 2015
Damping plays an important role in bolted joints of assembled structures due to their significant capacity to dissipate energy. The underlying mechanisms of these dissipative phenomena are generally poorly understood and result from contact and friction effects within the joint interfaces. In order to provide useful virtual prototyping tools for reducing response levels, accurate model-based estimation of modal damping is required. The present study employs an energetic method to calculate the loss factor associated with the localized dissipative interfaces of a global linear structure. The current method is based on the concept of the dissipated energy in the interfaces for which the closed-form expression of the loss factor is the ratio between dissipated energy and maximal potential energy, over a cycle of periodic vibration. The aim of this work is to investigate the advantages and drawbacks of this methodology for particular conditions such as: modal projection, localized damping level and model density. Simulated academic examples, where accurate estimations of the exact solutions are available, will be used to illustrate the methodology and to explore the potential difficulties that may arise in more complex industrial applications.
An integrated approach to structural damping
Precision Engineering, 1996
This paper considers a passive damping method that can be applied to a wide range of structural geometries including machine tool bases and components. The method uses viscoelastic materials to dissipate energy in the manner of classic constrained-layer damping; however, the layers are embedded within the structure as opposed to being applied externally. This provides a robust means of incorporating damping without encountering several of the common disadvantages associated with external damping treatments. An analytical solution to the amount of damping in bending modes is presented using a modal strain energy approach. The utility of this passive damping technique is demonstrated experimentally, and examples showing the accuracy of the modal strain energy solution are presented.
Assessment of the accuracy of damping estimation for lightly damped structures
Estimation of the damping levels in structures is required in many applications and the theoretical damping predictions in many cases are either difficult or not reliable. Therefore, experimental determination of the damping levels is employed quite often. However, there are also difficulties in experimental estimation of damping especially for lightly damped structures. The most widely used methods for damping determination are those of the frequency-based methods. These methods require vibration spectrums or the Frequency Response Function(s), which are obtained by transforming the time-domain data via Fourier Transform. During this process it is often necessary to modify the time-domain data by using an exponential window so as to minimize the leakage effect in the spectrum. It is well-known that the application of an exponential window to time-domain data introduces a known level of damping to individual modes. The so-called numerical damping added by this process can be subtrac...
Experimental Identification of Overall Structural Damping of System
Strojniski Vestnik Journal of Mechanical Engineering, 2013
The dynamic behaviour of large and complex structures largely depends on damping resistance in the structure. A portion of the structural energy is lost to deformations in material, friction between the contact surfaces, and relative motion within the structure. Often, in an analysis of numerical models, before the dynamic analysis of transient events (transient analysis), the damping resistance is adopted on the basis of recommendations, which implies an error of transient response (introduced by frequencies, logarithmic decrements and maximal amplitudes). Decreasing amortized vibratory movement is dependent on the extent of the structural damping. This paper presents the importance of structural damping in structural analysis and shows the experimental and theoretical procedure for identifying G values of the structural damping coefficient. A model for determining the G coefficient is shown in the example of a real tower crane structure. The experimentally obtained values were then used in the transient numerical FEM analysis, as the basis for adopting the conclusions about the dynamic behaviour of this class of structures (transportation machines). The effect of the external perturbation force of trapezoidal impulse form (lifting and quickly lowering of load) is introduced and the dynamic task, as an example of the use of the G coefficient G, is solved. The experimentally determined damping (theoretically isolated for tall truss structures) can be used in similar transient analyses.
Journal of Vibration and Acoustics, 2015
Measurements are presented from a two-beam structure with several bolted interfaces in order to characterize the nonlinear damping introduced by the joints. The measurements (all at force levels below macroslip) reveal that each underlying mode of the structure is well approximated by a single degree-of-freedom (SDOF) system with a nonlinear mechanical joint. At low enough force levels, the measurements show dissipation that scales as the second power of the applied force, agreeing with theory for a linear viscously damped system. This is attributed to linear viscous behavior of the material and/or damping provided by the support structure. At larger force levels, the damping is observed to behave nonlinearly, suggesting that damping from the mechanical joints is dominant. A model is presented that captures these effects, consisting of a spring and viscous damping element in parallel with a four-parameter Iwan model. The parameters of this model are identified for each mode of the s...
Structural Vibration: Analysis and Damping_C. Beards
Structural Vibration: Analysis and Damping, 2006
Many structures suffer from unwanted vibrations and, although careful analysis at the design stage can minimise these, the vibration levels of many structures are excessive. In this book the entire range of methods of control, both by damping and by excitation, is described in a single volume. Clear and concise descriptions are given of the techniques for mathematically modelling real structures so that the equations which describe the motion of such structures can be derived. This approach leads to a comprehensive discussion of the analysis of typical models of vibrating structures excited by a range of periodic and random inputs. Careful consideration is also given to the sources of excitation, both internal and external, and the effects of isolation and transmissability. A major part of the book is devoted to damping of structures and many sources of damping are considered, as are the ways of changing damping using both active and passive methods. The numerous worked examples liberally distributed throughout the text, amplify and clarify the theoretical analysis presented. Particular attention is paid to the meaning and interpretation of results, further enhancing the scope and applications of analysis. Over 80 problems are included with answers and worked solutions to most. This book provides engineering students, designers and professional engineers with a detailed insight into the principles involved in the analysis and damping of structural vibration while presenting a sound theoretical basis for further study. Suitable for students of engineering to first degree level and for designers and practising engineers Numerous worked examples Clear and easy to follow
European Journal of Mechanics - A/Solids, 2017
The evaluation of damping in the assembled structures presents a real challenge. Indeed, because of the nonlinear behavior of the dissipation and their localization in interfaces, the equations of motion of a dynamic system involve coupling terms. These coupling terms are generally neglected, in engineering applications, by the community because of their complexity. Hence, a proportional damping is usually assumed even if it may provide inaccurate results.The aim of this paper is to investigate the assumptions related to modal damping in the cases of localized linear and nonlinear dissipation. To achieve this goal, a perturbation method based on an asymptotic expansion of the frequency response function is proposed. Two indices of nonlinear coupling and modal coupling are proposed in order to quantify and correct a posteriori the error induced by modal damping assumption. Numerical examples are proposed in order to illustrate, first, the validation of the proposed method, by comparing the results with the reference solutions, and second, the usefulness of the proposed indices in quantifying and correcting errors induced by proportional damping hypothesis.
Damping models for structural vibration
2000
Abstract This dissertation reports a systematic study on analysis and identification of multiple parameter damped mechanical systems. The attention is focused on viscously and non-viscously damped multiple degree-offreedom linear vibrating systems. The non-viscous damping model is such that the damping forces depend on the past history of motion via convolution integrals over some kernel functions.
SOME OBSERVATIONS ON THE CHARACTERIZATION OF STRUCTURAL DAMPING
Journal of Sound and Vibration, 2002
This paper deals with the characterization of damping in dynamical structural systems. In particular, the problem of how the modal damping ratios change with di!erent boundary conditions is addressed. It is shown that only Rayleigh-type damping is actually independent of boundary conditions and modal damping ratios can be easily converted from one boundary condition to another. This condition applies independently to continuous, discrete and discretized systems.