The stiffness proportional damping is constructed for the. Gavin fall 2018 1 preliminaries this document describes the formulation of sti. Dont you have some equations relating the frequency of the oscillations of the spring mass system and the spring constant of the spring. Structural analysis for performance based earthquake engineering.
By stiffness im assuming you mean the spring constant, often known as k. Trombetti and silvestri, 19 within the class of rayleightype linear damping, have analyzed the performance of stiffnessproportional and massproportional dampers. Free vibration of a mass spring system with damping damper. Unlike the studies of ookuma in which the coherence function was effectively applied as a filter the complete sets of frequency response data were used in the solution. The rigidresponse calculation in responsespectrum analysis has been enhanced for nrc and general use. As far as the stiffness proportional part of rayleigh damping is.
In this case, the equipment on the isolator is assumed to be a rigid body. Models without shell elements or without mass proportional damping in materials used by shell elements were not affected. Mass, stiffness, and damping matrix technical papers. There are concerns raised by the mass proportional part of rayleigh damping, but. Method of relating modal damping to local dampers in lumpedparameter systems by harry j. Pdf direct updating of damping and stiffness matrices.
If a 0, then viscous damping isa only proportional to the stiffness distribution, and eq. The method of calculating the coefficients of bearings is an experimental method. Consider the case in which the damping matrix d is of the form dm k 3 where. The resulting coulomb damping force is obviously a square wave of period. In cases such as automatic control system design, accurate estimates of the mass, stiffness, and damping properties for only a few dofs may be all that is required in order to build an effective controller. Suitability for an incremental approach to numerical solution merits its use.
Several practical difficulties encountered, due to inherent differences in the nature of dynamic response of each part, and the different damping ratios of the two parts. Then dynamic analysis was performed for the different types of cablestayed bridges. Stiffnessproportional damping now uses initial stiffness instead of tangent stiffness to improve the consistency of results and convergence behavior. All forces and deformations calculated from linear time history analysis can be modified by multiplying c1 and c2 coefficients. View in hierarchy view source view scaffolding xml export to pdf export to word. The f is the composition of two forces, the elastic one, proportional to the elastic constant k and the position, and the damping force, proportional to the velocity and a damping constant. Damping modelling using generalized proportional damping.
Derivation of mass, stiffness and damping from experimental. There are many ways to compute a classical damping matrix from mass and stiffness matrices csi refer sap2000 ebook download as pdf file. A new composite material that exhibits high stiffness and high damping might reduce issues with vibration in mechanical systems and structures. Derivation of mass, stiffness and damping parameters from. Structures consisting of concrete and steel parts, which are irregular in damping ratios are investigated. Bicchi abstract in this paper a model free approach for damping control of variable stiffness actuators is proposed. Hysteretic proportional damping, also mass and stiffnessproportional, is used for steadystate and powerspectraldensity analyses. See if you can come up with something that behaves a bit more realistically. The direct measurement of structural mass, stiffness and. The distinct element method dem has been used successfully for the dynamic analysis of rigid block systems.
Structural dynamics department of civil and environmental engineering duke university henri p. Mass proportional damping in nonlinear timehistory. High stiffness low mass materials or structures reduce structure weight in transportation, but show little inherent damping. To update the matrix of the structure, two ways are available. Paper 15 mass, stiffness, and damping matrix estimates from. Mar 31, 2015 structures consisting of concrete and steel parts, which are irregular in damping ratios are investigated. Nov 16, 2012 by stiffness im assuming you mean the spring constant, often known as k. 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 straightforward task to define. Both the sap2000 and gtstrudl ctg models consist of. Variable stiffness control for oscillation damping g.
Rayleigh damping, mass proportional damping, elasticplastic, timehistory analysis. Here you can control damping of each spring, number of hairs, number of springs per hair, and spring stiffness. This representation of damping is called rayleigh damping or proportional damping. Mass and stiffnessproportional damping, normally referred to as rayleigh damping, is commonly used in nonlineardynamic analysis. This work aims to present the expansion of the algorithm known from the literature for calculating the coefficients of stiffness and damping. Any modal damping specified as additional material damping will also be included in linear and nonlinear directintegration time history load cases. Jul 18, 2015 16 sap2000 verification manual mode sap2000 reference 1 reference 2 1 0.
Barkans theory barkan 1962, sec prakash, 1981a studied the dynamic behavior of foundations and base soils and developed a theory. Jun 22, 2014 viscous proportional damping is used for directintegration timehistory analysis. Pdf parametric study on equivalent damping ratio of different. The f is the composition of two forces, the elastic one, proportional to the elastic constant k and the position, and the damping force, proportional to the velocity and a. Models without shell elements or without massproportional damping in materials used by shell elements were not affected. Advanced damper with high stiffness and high hysteresis.
During formulation, the damping matrix is assumed to be proportional to the mass and stiffness matrices as follows. How is damping specified for different parts of the structure. Implementation of configuration dependent stiffness. An innovative solution approach with hydraulic actuators offers the possibility of changing both, the stiffness and thus the natural frequency and the degree of damping. Hysteretic proportional damping, also mass and stiffness proportional, is used for steadystate and powerspectraldensity analyses. Mini sap 2000 tutorial for an example beam hands on exercise. Stiffness proportional damping now uses initial stiffness instead of tangent stiffness to improve the consistency of results and convergence behavior. As stiffness proportional damping usually should be neglected for its significant. Modal analysis of mdof systems with proportional damping. Classical rayleigh damping is viscous damping which is proportional to a linear combination of mass and stiffness. Computation of rayleigh damping coefficients for large systems. Mini sap 2000 tutorial for an example beam hands on. Damping faq technical knowledge base computers and.
Finite element steadystate vibration analysis considering. Sap2000 database documentation hyperlinked contents page 4 of 1907 1072004 case response spectrum 1 general case response spectrum 2 load assignments case response spectrum 3 interpolated damping case response spectrum 4 proportional damping. Dynamic analysis of foundations for the effects of. Extract the sap2000 stiffness matrix for a twostory frame and compare it to the manual solution. Effective damping of approximately two and stiffnessdamping product of approximately 200 gpa were achieved in such dampers consisting of stainless steel columns.
However, for the sliding mode of motion, the vertical geometrical damping relationship is applied for the backfill. Then, it is desirable to select the proper isolator so. The c viscous damping force is a cosine function, and the structural damping force is the product of the coulomb square wave force times. This means that when the building begins to oscillate, the mass will move in the opposite direction 3. This property is proportional to mass and stiffness. The variable stiffness mechanism consist of mass and cantilever beam as absorber, lead screws, motor, variable in the absorber, the spring constant at mass varies by. Mass and stiffness proportional damping, normally referred to as rayleigh damping, is commonly used in nonlineardynamic analysis. As stated in the sap2000 analysis reference manual, csi 2009 for. Report pacific earthquake engineering research center. Therefore, sliding and rocking stiffness and damping arc discussed only. Damping coefficients technical knowledge base computers.
Damping technical knowledge base computers and structures. Its found in hookes law f kx where f is the force the spring is exerting and x is the distance from the equilibrium point. The coefficients a 2p, b 0 were used to create a proportional damping matrix, and the damped fea model was solved for its modes. The mass is can move independently of the building.
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 video simulation khan academy. Identification of stiffness, damping and mass coefficients of. If the system is lightly damped, authors propose a simple and ef. Method of relating modal damping to local dampers in lumped. Show that if the damping matrix is proportional to the mass and. The first 12 modes are considered in this study and mode 1 is used for analysis. So the trick is to find a nice balance between spring stiffness and damping. Pdf initial versus tangentstiffness based rayleigh damping in. These systems consist of a heavy mass mounted on a floor connected to dampers that act like shock absorbers. When the materials, vibration control devices or vibration isolators in a structure have different damping ratios, elements with different damping ratios can be. For example, to model the damping of an aircraft fuselage one could fit generalized proportional damping models for all the ribs and panels by testing them separately and then combine the element or substructure damping matrices in a way similar to the assembly of the mass and stiffness matrices in the standard finite element method. Sap2000 revision no 0 example 6006 7 the direct integration time histories use mass and stiffness proportional damping that is specified to have 2.
One way is the direct methods 108, 109 that directly update stiffness and mass matrices of the elements in a onestep procedure to. Dont you have some equations relating the frequency of the oscillations of the springmass system and the spring constant of the spring. Hysteretic proportional damping, also mass and stiffnessproportional, is used for. This will help reduce the amplitude of the oscillations of the. Trombetti and silvestri, 19 within the class of rayleightype linear damping, have analyzed the performance of stiffness proportional and mass proportional dampers. E x a m p l e 3 threedimensional frame dynamic loads description this is a twostory, threedimensional frame structure with rigid diaphragm floors. These assumptions greatly simply the equations for calculating mass, stiffness, and damping matrices, but a matrix inversion in this case the mode shape matrix is still required. Stiffness and damping parameters for dynamic analysis of. Design of variable stiffness and variable damping vibration. Method of relating modal damping to local dampers in. Damping devices may also be modeled as a structural subsystem, as described. This investigation is a codebased seismic design of such structures. The article describes the method for determining the 24 coefficients of dynamic system composed of a rotor and two bearings based on impulse excitation between two bearings. I understand stiffness as the extent to which an object e.
And i understand damping as the energy dissipative properties of an objectsystem e. Parametric study on equivalent damping ratio of different. Dynamic behavior of cablestayed bridge with damping. But, in the real system, the equipment should have its resonant frequency. Free vibration of a mass spring system with damping november 22, 2014 september 20, 2018 engineeering projects fig. In this paper, new procedures are proposed for the damping modeling and its numerical implementation in distinct element analysis of rigid multiblock systems. All forces and deformations calculated from linear time history analysis can. Caution regarding stiffness proportional damping never use stiffness proportional damping in association with any elements that have artificially high stiffness and that may yield. The resulting mass, stiffness and damping matrices were used to define the eigenvalues and associated vectors and hence the modal model. Sap user manual, university of california, berkeley. Viscous proportional damping is used for directintegration timehistory analysis.
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