Measurement of damping in structures by the power input method. Research article dimensionless analysis of segmented. Structural damping structural damping reduces both impactgenerated and steadystate noises at their source. Researcharticle dynamic optimization of constrained layer damping structure for the headstock of machine tools with modal strain energy method yakaixu,1 weiguogao,1 yuhanyu,2 daweizhang,1 xiangsongzhao,1. In the previous post in this series which was four months agotime flies, we looked at the free vibrations of damped singledegreeoffreedom sdof systems, systems that can be modeled as a springmassdashpot like this the position of the mass. Solution for 2 oscillations m 2 and x 1 x 2 1005 20 the actual damping coefficien t is c c x 251. The energy method introduction dynamic systems can be characterized in terms of one or more natural frequencies. Damping optimization of hardcoating thin plate by the. In mode superposition analysis, the damping matrix must have the following properties in order for the modal equations to be uncoupled. Researcharticle dynamic optimization of constrained layer damping structure for the headstock of machine tools with modal strain energy method yakaixu,1 weiguogao,1. Energy methods can also be used for the analysis of damped systems. Research article dimensionless analysis of segmented constrained layer damping treatments with modal strain energy method shitaotian, 1,2 zhenbangxu, 1 qingwenwu, 1 andchaoqin 1 innovation lab of space robot system, changchun institute of optics, fine mechanics and physics, chinese academy of sciences, no. It is used in mechanical engineering to approximate the eigenmodes of a physical system, such as finding. Reallife systems are not undamped but possess some kind of energy dissipation mechanism or damping.
Extracting damping ratio from dynamic data and numerical. A study of the modal strain energy method for viscoelastically damped structures article pdf available in journal of the chinese institute of engineers 243 may 2001 with 619 reads. Some of these methods directly yield the natural frequency. Undamped systems and systems having viscous damping and structural damping are included. Measurement of damping in structures by the power input. Finite element modeling of viscoelastic damping by modal. The mechanical energy of the system diminishes in neglect gravity the mechanical energy of the system diminishes in time, motion is said to be damped the motion of the system can be decaying oscillations if the damping is weak. One possibility is to force gr 0 below a certain cutoff distance and extend sq either using an iterative method or using the maximum entropy method. Changing the composition of a damping material may also alter its effectiveness.
Pdf a new energybased method for evaluating the damping. Described are six methods of extracting damping from data. However, the principle of energy conservation still applies on a larger scale, so the vibrating system must be transferring energy elsewhere, and cannot be treated as an isolated system. This tutorial focuses on the energy method, which is an example of a. In section4, a cantilever thin plate coated with mgal hard coating was taken as an example to demonstrate solution of the modal damping parameters for the composite plate. Three main types of damping are present in any mechanical system.
This material is operable to provide high damping, specifically acoustic, vibration or shock damping, by utilizing the energy absorption mechanism of hollow tube. In this case, the total energy of the system is not conserved, as energy is dissipated by the damping forces. The idea is to compute the energy input per cycle from inputoutput measurements, and equate it with the formulated dissipated energy of the damping model to obtain estimation equations for unknown parameter values. Rayleighs classical damping revisited sondipon adhikari1 university of bristol, bristol, united kingdom. Paper open access energy recovery method of damping. The most commonly used method of increasing the damping is to include highly damped polymeric material at strategic locations onto the structure.
Us10119589b2 microlattice damping material and method for. These frequencyaveraged damping values are widely used in the automotive industry in vehicle computer models based on finite element method fem and statistical energy analysis sea. Dynamic optimization of constrained layer damping structure. Therefore, in this study, a method based on energy dissipation is developed to simplify the estimation of the. What is vibration and what are different types of vibration. Blake introduction this chapter presents the theory of free and forced steadystate vibration of single degreeoffreedom systems. In this section, we will derive an alternate approach, placing newtons law into a form particularly convenient for multiple degree of freedom systems or systems in complex coordinate systems. This paper presents a practical application of the pim to measure a vehicle side glass damping quickly and accurately. When a vibrating system loses mechanical energy in this way it is said to. Lagranges equation not that the rayleigh, energy, and lagrange methods are closely related. The damping ratio model of the cfrp motor frame is established based on the strain energy method and verified by experiments.
Lagranges equations the motion of particles and rigid bodies is governed by newtons law. The natural frequency is the frequency at which the system would vibrate if it were given an initial disturbance and then allowed to vibrate freely. This force causes an energy dissipation that is known as fluid damping. The proposed method overcomes the weaknesses and limitations in the previous studies. An alternate method is to plot the displacement as a function of time and vary the damping constant until it appears to have died out at about 3 seconds.
Modeling technique of material damping properties in ansys. Energybased damping evaluation for exciter control in power. The use of the maximum entropy method is an attractive, but. Solving by using the finite element method, damping matrix manuscript received may 9, 2010. Rayleigh xe rayleigh damping this type of damping is normally referred to as rayleigh damping. Liang and feeny 37 proposed a damping estimation method based on the balance of energy. An example of the effectiveness of an extensional damping treatment is. Understanding damping techniques for noise and vibration control. If the damping is sliding friction, fsf constant, then the work done by the frictional is equal to the difference in the potential energy at the turning points. Evaluation of methods for analysis of multidegreeof.
Introduction there are many ways to extract damping parameters from data or models. Therefore, in this study, a method based on energy dissipation is developed to simplify the. Previous force equation gets a new, damping force term dxt d2xt dt kxt b dt f net m. In the previous post in this series which was four months agotime flies, we looked at the free vibrations of damped singledegreeoffreedom sdof systems, systems that can be modeled as a springmassdashpot like this. In this paper, a cfrp motor frame is designed and the natural frequency and damping are studied. For solution of vibration problems by the normal mode technique. A piezoelectric active sensing method for quantitative. The inverse of the damping function 1a profile in dynamic mode and the normal force profile f s d in the quasi static mode are simultaneously determined figure 3. Introduction damping is the energy dissipation of a material or system under cyclic stress. Application of energy method for determining loss factor in. Described is a microlattice damping material and a method for repeatable energy absorption. Consequently, the amount of mechanical energy transferred to heat in one oscillation period for front and rear suspension shock absorbers will be 72. Review of strain energy methods and introduction to sti. Evaluation of methods for analysis of multidegreeoffreedom.
In this method, the maximum kinetic energy at the mean position is made equal to the maximum potential energy or strain energy of the extreme position. Both of these parameters are acquired through experimental investigations for each type of boundary. Particle impact damping pid is a method to increase structural damping by inserting particles in an enclosure attached to a vibrating structure. These vibrations would most likely correspond to relatively low frequencies and would. The article studies the energy method for determining loss factor due to hysteretic damping in systems of vibration and seismic isolation. The structure and polymer must interact with one another in such a way as to cause the polymer to dissipate as much energy as possible. A vibration damping method on a vehicle wheel suspension is provided in which, in a hydraulic vibration damper, the damping force increases highly progressively as a function of the piston speed, especially in the range of a piston speed of essentially 0 to 2 ms, increasing at first slowly and essentially linearly and then especially beyond a piston speed of essentially 2 ms. The particles absorb kinetic energy of the structure and convert it into heat through inelastic collisions between the particles and the enclosure. The strain energy method is employed for modeling the damping properties of composite structures, using the finite element code abaqus in addition to some routines written in matlab.
Strain energy method to model composite structures damping. Review of strain energy methods and introduction to. A new energybased method is proposed in the current study to evaluate the damping properties of a cabledamper system. Bogard et al 39 studied the damping of the bolted joint interface by experimental technique and. Internal damping structural damping fluid damping 1. In a conservative system system with no damping the total mechanical energy i. Others yield a governing equation of motion, from which the natural frequency may be determined. Summary of energy dissipation damping of a generator proposed damping evaluation index for exciter by calculating the energy dissipation within a time window during the transient remark the proposed is a general damping evaluation method, which can be applied to any type of exciter controller 12 from exciter. The vibration amplitude reduction during its operation is compared with the metal frame motor. Estimation of additional equivalent damping ratio of the. Damping estimation of plates for statistical energy analysis.
Lets take an example of a closedbox, acoustic suspension system, one that has been optimized for an amplifier with an infinite. Me 563 mechanical vibrations fall 2010 14 this simple case, the package and crane both oscillate as rigid bodies. Victor giurgiutiu, in structural health monitoring with piezoelectric wafer active sensors second edition, 2014. The microlattice damping material is a cellular material formed of a threedimensional interconnected network of hollow tubes.
The total energy of the vibrating system is clearly not constant in this situation. The rayleighritz method is a numerical method of finding approximations to eigenvalue equations that are difficult to solve analytically, particularly in the context of solving physical boundary value problems that can be expressed as matrix differential equations. A new energy based method is proposed in the current study to evaluate the damping properties of a cabledamper system. It dissipates vibrational energy in the structure before it can build up and radiate as sound. Effects on system response dick pierce professional audio development. Application of energy method for determining loss factor. Energy recovery method of damping oscillations of the vehicle suspension d l okladnikov 1,3, v a zeer 1, e v grazhdantsev 2, r m avdeev 1 and s a akhremov 1 1 department of transport and technological machines, siberian federal university, svobodny 79, krasnoyarsk, 660041, russia. Research article dimensionless analysis of segmented constrained layer damping treatments with modal strain energy method shitaotian, 1,2 zhenbangxu, 1 qingwenwu, 1 andchaoqin 1 innovation lab of space robot system, changchun institute of optics, fine mechanics and physics, chinese academy of sciences. Evaluation of damping in dynamic analysis of structures. E mech not constant, oscillations not simple neglect gravity f bv spring oscillator as before, but with dissipative force f damp f damp viscous drag force, proportional to velocity such as the system in the figure, with vane moving in fluid. The panel computational model is a finite element model of a rectangular plate mechanically.
The logarithmic decrement is defined as the natural log of the ratio of the amplitudes of any two successive peaks. Sorbothane is the most efficient material currently available for energy absorptionthe best impact damper on the. At the turning points, the velocity is zero and therefore the energy is given by the potential energy. In the design of damped structures, the additional equivalent damping ratio edr is an important factor in the evaluation of the energy dissipation effect. In the absence of energy losses, such as from friction, damping or yielding, the strain energy is equal to the work done on the solid by. Energy methods for damped systems linkedin slideshare.
In letteratura esistono diversi metodi per stimare lo smorzamento e viene scelto ed implementato il metodo dellenergia di deformazione. Another approach is to extend sq artificially beyond the range over which it is actually experimentally determined so that obvious errors are reduced. Understanding damping techniques for noise and vibration. Engineered damping treatments edts that have high damping characteristics per unit volume are presented. In this case you can use a simple model, the damping coefficient of the material is given by a coefficient of viscosity on the frequency. Energybased damping evaluation for exciter control in. The cellular topologies of the edts are modeled using the finite element method in an attempt to determine the optimal topologies that maximize the strain energy, maximize the damping characteristics, and minimize the total weight. Us10119589b2 microlattice damping material and method. Multiple degreeoffreedom systems are discussed, including the normalmode theory of linear elastic structures and. Energy is dissipated as a result of extension and compression of the damping material under flexural stress from the base structure. However, previous additional edr estimation methods are complicated and not easy to be applied in practical engineering. You can counteract harmful effects of impact force by discovering a method for the safe effective absorption of impact energyutilizing a good impact damping material. Numerical damping stable damped energy 0 external internal damp f f f dt dx f damp damp p force displacement damping force is numerical not physical damping is intended for system instabilities not for rigid body motions unstable static solution.
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