Materialbased damping is now available for linear and nonlinear directintegration timehistory analysis. The concept of proportional damping is critically examined and a generalized form of proportional. With this method, the optimally approximated stiffness and hysteretic damping matrices can be easily constructed. Proportional damping an overview sciencedirect topics. This technical memorandum provides a quick reference for some of the more common approaches used in dynamics analysis. Hysteretic proportional damping, also mass and stiffnessproportional, is used for steadystate and powerspectraldensity analyses. As stiffness proportional damping usually should be neglected for its. One of the main limitation of the mass and stiffness proportional damping approximation comes from the fact that the arbitrary variation of damping factors with.
Pdf initial versus tangentstiffness based rayleigh damping in. Paper 15 mass, stiffness, and damping matrix estimates. For the cases of rotary inertia, point mass elements, and substructures, where there is no reference to a material. Summary of modal mass, stiffness, and damping given the three equations 20, 24, and 28 for diagonalizing the mass, stiffness and damping matrices, it is now a. Damping devices may also be modeled as a structural subsystem, as described. A twostage approach to updating of mass, stiffness and. Effect of mass and springs on the damping of mass spring. As far as the stiffness proportional part of rayleigh damping is. A two stage approach to updating of mass, stiffness and damping matrices is proposed. Department between october 1997 and september 2000. During simulation, it is important that dynamic rigid bodies accurately behave and interact with the environment as they would in the realworld.
First, the mass and stiffness matrices do not need to be calculated using the fem, so errors due to the inaccuracy of these matrices can be reduced. To maintain the same behavior as in previous versions of the software, set the modification factor to unity and use the initial stiffness for stiffnessproportional viscous damping. Please note that setting a constant hysteretic damping with both mass and stiffnessproportional damping set to 0. Damping effect of springmass system or is this elasticease. Sap2000 allows users to either specify coefficients. If you are not familiar with these topics, you are encouraged to explore them via any college algebra or precalculus textbook. Proportional damping is a widely used approach to model dissipative forces in complex engineering structures and it has been used in various dynamic problems for more than ten decades. The equations of motion of free vibration of a viscously damped system can be expressed by. Sometimes, people concerned with vibration analysis. Hysteretic proportional damping, also mass and stiffnessproportional, is used for. That is, the viscous damping forces are assumed to be proportional to the inertial and restoring forces, as represented in the following equation. Rayleighs classical damping revisited sondipon adhikari1.
One of many difficulties associated with dem is modeling of damping. The modal mass, stiffness, and damping definitions are derived in a previous paper 1, and are restated here for convenience. Model of a tuned mass damper on a simple structure youtube. The two frequencypoint based rayleigh damping proportional to mass and stiffness in the direct integration analysis approximates the replacement of the. Pdf computation of rayleigh damping coefficients for large. The damping ratio is a measure describing how rapidly the oscillations decay from one bounce to the next. Assign modal damping values typically 5% critical per mode. Understanding and using dynamic stiffness a tutorial. Both modal and rayleigh damping are used to avoid the need to form a damping matrix based on the physical properties of the real structure. Effect of mass and springs on the damping of mass spring system thread starter. Mass proportional damping in nonlinear timehistory. Mmo is the mass moment of inertia about the axis of rotation. How can i determine the stiffness and damping coefficient.
Understanding and using dynamic stiffness a tutorial sometimes called real and imaginary components. How can i determine the stiffness and damping coefficient of viscoelastic damper which is to be installed in a building. The structural analysis shall consider the relative stiffness of diaphragms. Specifically, the damping factor, which tells how many radians of phase the restoring force lags behind the displacement. Method of relating modal damping to local dampers in. Stiffness and damping video simulation khan academy. Gavin fall 2018 1 preliminaries this document describes the formulation of sti. One of the main limitation of the mass and stiffness proportional damping approximation comes from the fact that the arbitrary variation of damping factors with respect to vibration frequency cannot be modelled accurately by using this approach. Proportional damping matrix a proportional damping matrix is assumed to be a linear combination of the mass and stiffness matrices. Rayleigh damping, mass proportional damping, elasticplastic, timehistory. Orthogonality, mass stiffness, damping matrix mit opencourseware. In general, damping is a material property specified as part of the material definition. This became a stumbling block to the analysis of a damped mdof system.
Described are six methods of extracting damping from data. In this paper, a new method of identifying system matrices for nonproportional damping structures using modal parameters is proposed. Rayleigh damping, mass proportional damping, elasticplastic, time history. Structural dynamics department of civil and environmental engineering duke university henri p. Hysteretic proportional damping, also mass and stiffness proportional, is used for steadystate and powerspectraldensity analyses. To define rayleigh damping, you specify two rayleigh damping factors. Damping coefficients technical knowledge base computers and. Extracting damping ratio from dynamic data and numerical. Structural damping is a particular common pattern for how the damping in a solid material when it flexes depends on frequency. Find out how your company can benefit from plm built on salesforce.
Stiffness proportional damping now uses initial stiffness instead of tangent stiffness to improve the consistency of results and convergence behavior. Finite element steadystate vibration analysis considering. The damping ratio is a system parameter, denoted by. Damping faq technical knowledge base computers and. Program will take a description of a system containing masses and springs with proportional dampening and will output the massm, dampeningd and stiffnessk matrices for that system with respects to its system of equations as shown below. When the materials, vibration control devices or vibration isolators in a structure have different damping ratios, elements with different damping ratios can be. Stiffnessproportional damping now uses initial stiffness instead of tangent stiffness to improve the consistency of results and convergence behavior. The physical connectivity of the original model is preserved and the measured.
Multiple enhancements made for indian concrete frame design per code is 456 2000. Updating stiffness and hysteretic damping matrices using. I understand stiffness as the extent to which an object e. The distinct element method dem has been used successfully for the dynamic analysis of rigid block systems. A read is counted each time someone views a publication summary such as the title, abstract, and list of authors, clicks on a figure, or views or downloads the fulltext. All analysis for this example was performed on sap2000. Conference proceedings is brought to you for free and open access by scholars mine. Drain lewis research center summary the longitudinal dynamic characteristics of a linear structure may be approximated by a lumpedparameter model, which usually includes only the stiffness and mass distri bution of the system. Stiffness and damping parameters for dynamic analysis of retaining walls e. Once a set of modal data has been measured for a vibrating structure, it is possible to compute the full mass, stiffness and damping matrices for the structure by using. A proportional damping model is the first analytical model used to study damping for an mdof system. Any modal damping specified as additional material damping will also be included in linear and nonlinear directintegration time history load cases. Materialbased damping is now available for steadystate and psd analysis. Stiffness proportional damping now uses initial stiffness instead of tangent stiffness to improve the consistency of results and.
Experimental results, however, suggest that damping factors can vary with frequency. Derivation of mass, stiffness and damping parameters from experimental modal data. In addition, rayleigh damping 44 has been adopted to consider the structural damping, and the mass proportional coefficient and stiffness proportional. Viscous proportional damping is used for directintegration timehistory analysis.
It considers a massproportional and a stiffnessproportional damping in order to achive the real damping lets say 5%. Base reactions no longer include constraint forces at restraints. A good resource to show how this varies with different values of mass, stiffness and damping constant can be found here. Implementation of configuration dependent stiffness. Mass and stiffnessproportional damping, normally referred to as rayleigh. Model of a tuned mass damper on a simple structure. Damping modelling using generalized proportional damping. And i understand damping as the energy dissipative properties of an objectsystem e. Introduction there are many ways to extract damping parameters from data or models. There are concerns raised by the mass proportional part of rayleigh damping, but they are not considered in this paper. Now well add spring stiffness and damping to our system. Then i can find the spring stiffness k by sett all the derivatives to zero. In vortex, spring refers to the entire springdamper system.
In this white paper, learn how you can configure freely without requiring any custom development, and quickly update configurations as your needs evolve. Damping technical knowledge base computers and structures. Stiffnessproportional damping now uses initial stiffness instead of tangent stiffness to. You specify a critical damping ratio for each mode. For classically damped structures, modal mass, stiffness and damping can be defined directly from formulas that relate the full mass, stiffness and damping matrices to the transfer function matrix. The critical damping ratio of a system is often used to compare system damping to that which would result in a critically damped case i. Direct identification of nonproportional modal damping. Derivation of mass, stiffness and damping parameters from. Proportional damping is the most common approach to model dissipative forces in complex engineering structures and it has been used in various dynamic problems for more than 10 decades. Structural analysis for performancebased earthquake engineering. This property is proportional to mass and stiffness. In this paper, new procedures are proposed for the damping modeling and its numerical implementation in distinct element analysis of rigid multiblock systems.
It considers a mass proportional and a stiffness proportional damping in order to achive the real damping lets say 5%. A new direct method for the finite element fe matrix updating problem in a hysteretic or material damping model based on measured incomplete vibration modal data is presented. Damping models for structural vibration university of cambridge. Related threads on effect of mass and springs on the damping of mass spring system system massspringdamper and energy. The global damping matrix is constructed as a proportional combination of the mass and stiffness matrices, for example. Practical design method of yielding steel dampers in concrete. Modal analysis of mdof systems with proportional damping. The same method is further extended using complex frf data to update a proportional damping matrix. Stiffness and damping parameters for dynamic analysis of. Structural analysis for performance based earthquake. Nevertheless, if the real system is lightly damped, authors propose an ef. Our mission is to provide a free, worldclass education to anyone, anywhere. Unlike mass and stiffness properties, damping cannot usually be modelled.
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