In order to demonstrate the effect of stiffnessproportional damping using the. The prevalence of manual engineering methods in wiring harness manufacturing compounds these challenges, especially as harness complexity increases. Structural dynamics department of civil and environmental engineering duke university henri p. Mass, stiffness, and damping matrix technical papers. Paper 15 mass, stiffness, and damping matrix estimates. Material damping massachusetts institute of technology. Abstractin this paper a model free approach for damping control of variable stiffness actuators is proposed. Free vibration of a mass spring system with damping damper. Stiffness proportional damping now uses initial stiffness instead of tangent stiffness to improve the consistency of results and convergence behavior. Structural analysis for performance based earthquake engineering. Determine the position ut of the mass at any time t. Jun 22, 2014 viscous proportional damping is used for directintegration timehistory analysis.
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. Motion of the system will be established by an initial disturbance i. Determine the amplitude, quasiperiod, and quasifrequency of the motion. One of many difficulties associated with dem is modeling of damping. The scale factor applies equally to all six degrees of freedom, as well as the mass and weight.
Derivation of mass, stiffness and damping from experimental. 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. 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. Viscous proportional damping is used for directintegration timehistory analysis. The damping force acts in the opposite direction to that of oscillating mass.
The first 12 modes are considered in this study and mode 1 is used for analysis. Unlike mass and stiffness properties, damping cannot usually be modelled. The system modal damping ratio for uniform subsystem damping is thus a b a b a a b b s u k k m m k m k m 12 the two mass and stiffness values were varied randomly in an informal numerical study using 100,000 trials. Damping models for flow chart based structural analysis. Assume that the mass is pushed 50 cm to the left of equilibrium and given a leftward velocity of 2 msec. The problem of minimizing the terminal energy for a one degree of freedom springmass model with controlled stiffness. This property is proportional to mass and stiffness. The c viscous damping force is a cosine function, and the structural damping force is the product of the coulomb square wave force times. More detail on these and other enhancements can be found in the separate file releasenotes. Design of variable stiffness and variable damping vibration absorber. I the investigation of different analytical representations of damping has. When the materials, vibration control devices or vibration isolators in a structure have different damping ratios, elements with different damping ratios can be. I have a problem with constant modal damping in sap2000. Jun 29, 2016 damped free vibration example 5 the main span of a bridge structure has the following properties based on vibration tests.
Structural analysis for performancebased earthquake engineering. If the mass is pulled down an additional 3 in and then given an initial velocity downward of 4 insec. Aljaberi both the effective dynamic stiffness and the radiation damping coefficient of the soilfoundation system are functions of the frequency it is convenient to express sur dy k as a product of the static stiffness, sur. A device known as damper is shown in the figure below. Furthermore, if there is no resistance or damping in the system, the oscillatory motion.
Modeling inherent damping using rayleigh proportional damping note. This became a stumbling block to the analysis of a damped mdof system. Program will take a description of a system containing masses and springs with proportional dampening and will output the mass m, dampeningd and stiffness k matrices for that system with respects to its system of equations as shown below. Hi guys i have a problem with constant modal damping in sap2000. This investigation is a codebased seismic design of such structures. Program can handle both numeric and symbolic equations. If there is no external force applied on the system, the system will experience free vibration. Turkish ts 5002000 r2018, mexican rcdf 2017, australian as 36002018 and korean kbc 2016. 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. The problem of minimizing the terminal energy for a one degree of freedom springmass model with controlled.
All forces and deformations calculated from linear time history analysis can be modified by multiplying c1 and c2 coefficients. Proportional damping an overview sciencedirect topics. Effective mass 400 x 103 kg effective stiffness 40,000 knm ratio of. Pdf elastic velocity damping model for inelastic structures. The distinct element method dem has been used successfully for the dynamic analysis of rigid block systems. Damping technical knowledge base computers and structures. To this end, the mass of the concrete slab is supported on spring elements see fig.
If a 0, then viscous damping isa only proportional to the stiffness distribution, and eq. Hysteretic proportional damping, also mass and stiffness proportional, is used for steadystate and powerspectraldensity analyses. For hinges modeled as links, the stiffnessproportional damping used for directintegration timehistory analyses may now be specified by the user to be proportional to the initial stiffness. Other configurations, such as single vane vwds are also available. Pdf direct updating of damping and stiffness matrices. System parameters in the mathematical model of a vibrating structure include mass, damping and stiffness. Paper 15 mass, stiffness, and damping matrix estimates from. Structures consisting of concrete and steel parts, which are irregular in damping ratios are investigated. Method of relating modal damping to local dampers in lumped. A new implicit dynamic finite element analysis procedure. A new nonlinear multistep static load case type has been added.
Reference origin datum position the z height of the reference origin above the mean water level and the heel and trim relative to horizontal when the vessel is in the datum position that was used to calculate its displaced volume. Hysteretic proportional damping, also mass and stiffnessproportional, is used for steadystate and powerspectraldensity analyses. Stiffnessproportional damping now uses initial stiffness instead of tangent stiffness to. Sap2000 tutorials training videos, manuals and model files 38 gb civil engineering community from. Analysis of structural response with different forms of.
The stiffness proportional damping is constructed for the. As missile designs become more complicated, the multiple stage interfaces can produce slip. It doesnt seem to have an effect on the response when i change the damping, even if i set it t modal damping in sap2000 computers and structures. The global damping matrix is constructed as a proportional combination of the mass and stiffness matrices, for example. Dynamic behavior of cablestayed bridge with damping. Method of relating modal damping to local dampers in lumpedparameter systems by harry j.
If a secondary device with mass m 2, stiffness k 2 and viscous damping c is added to the system. Damped free vibration example 5 the main span of a bridge structure has the following properties based on vibration tests. The resulting coulomb damping force is obviously a square wave of period. 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. Damping faq technical knowledge base computers and. The proposed model does not dictate the form of the initial damping matrix c. Abstract in this paper a model free approach for damping control of variable stiffness actuators is proposed. 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. A proportional damping model is the first analytical model used to study damping for an mdof system. 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. 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. Design of variable stiffness and variable damping vibration absorber ijsrdvol. Implementation of configuration dependent stiffness.
The modeling information in this booklet was prepared for dis by button engineering. In this paper, new procedures are proposed for the damping modeling and its numerical implementation in distinct element analysis of rigid multiblock systems. Pdf damping models for flow chart based structural analysis. The idea is to take advantage of the possibility to change the stiffness of the actuators in controlling the damping. Schematic drawings for typical configurations of double vane vwds are shown in appendix c. Damping modelling using generalized proportional damping. First modal analysis was performed with different values of damping parameter i.
In examples 1 and 2, the stiffnessproportional coefficient, a 1, is much smaller than the massproportional coefficient, a 0, which reveals that massproportional damping dissipates more energy in lowerfrequency modes than does stiffnessproportional damping. One of the main limitation of the mass and stiffness proportional damping approximation comes from the fact that the arbitrary. Then determine the first time the maximum magnitude will occur. K is the initial stiffness of the system in drain and most other nonlinear dynamic analysis programs the inherent damping is represented as rayleigh damping, which produces a damping matrix that is proportional to mass and stiffness. There are many ways to compute a classical damping matrix from mass and stiffness matrices csi refer sap2000 ebook download as pdf file. A 14 kg mass is attached to spring with stiffness 8 nm. Free vibration of a mass spring system without damping november 22, 2014 september 20, 2018 engineeering projects fig. Damping devices may also be modeled as a structural subsystem, as described. Analysis of structural response with different forms of damping. Free vibration of a mass spring system without damping. Derivation of mass, stiffness and damping parameters from. Mar 31, 2015 structures consisting of concrete and steel parts, which are irregular in damping ratios are investigated.
R factor introduces damping forces caused by the absolute velocities of the model and so simulates the idea of the model moving through a viscous ether a permeating, still fluid, so that any motion of any point in the model causes damping. Pdf in the sap2000 folder and available by using the help. Gavin fall 2018 1 preliminaries this document describes the formulation of sti. 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. This allows the same link property to be used for multiple link objects that may, for example, represent different size tributary regions supported by the link objects. Parametric study on equivalent damping ratio of different. Fortunately, there are electrical systems and wiring harness engineering tools are available to help companies, large and small, as they tackle new challenges. Mini sap 2000 tutorial for an example beam hands on exercise.
For hinges modeled as links, the stiffness proportional damping used for directintegration timehistory analyses may now be specified by the user to be proportional to the initial stiffness of the hinge the current behavior, the tangent stiffness, or a mixture of the two. The viscous wall dampers discussed here are double vane dampers with a viscous fluid layer thickness of 5mm. The rigidresponse calculation in responsespectrum analysis has been enhanced for nrc and general use. As stated in the sap2000 analysis reference manual, for steadystate and powerspectraldensity cases, the hysteretic damping matrix is calculated as a linear combination of the stiffness matrix, scaled by coefficient d k, and the mass matrix, scaled by coefficient d m. However, the question fielded concerns modal damping. 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. Method of relating modal damping to local dampers in. If the system is lightly damped, authors propose a simple and ef. Mini sap 2000 tutorial for an example beam hands on. It doesnt seem to have an effect on the response when i change the damping, even if i set it to 0,99. Structural analysis for performance based earthquake. 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.
Then dynamic analysis was performed for the different types of cablestayed bridges. Massdampeningstiffness matrix eom file exchange matlab. 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. The origin to which the stiffness, added mass and damping matrices all refer, with respect to the vessel axes. The coefficients a 2p, b 0 were used to create a proportional damping matrix, and the damped fea model was solved for its modes. When exciting the first mode of vibration, the modal damping is also taken as a function of velocity. Displacement of the free bridge edge in response to a random excitation 2.