For a system with n degrees of freedom, they are nxn matrices the springmass system is linear. Sep 26, 2010 what is a single degree of freedom sdof system. Dynamics of simple oscillators single degree of freedom. We use the minimax criterion to illustrate the design procedure using the expansion. Flexure system compliant mechanism exact constraint screw theory projective geometry freedom topology constraint topology abstract in part ii of this paper we demonstrate how to use freedom and constraint topology fact to synthesize concepts for the multidegree of freedom, parallel precision. Introduction exact solution of the free vibration problems is where coefficients can be determined from the initial conditions. Example of overhead water tank that can be modeled as sdof system 1. Multidegreeoffreedom system with enforced motion by tom irvine email. Application of multiinput volterra theory to nonlinear. Development of a miniature multi degree of freedom measurement system for ultra precision stages. Design of multidegreeof freedom tunedmass dampers using perturbation techniques by justin matthew verdirame submitted to the department of mechanical engineering on june 5, 2003, in partial fulfillment of the requirements for the degree of master of science in mechanical engineering abstract.
Understand vibration of systems with more than one degree of freedom. Mod01 lec11 free and forced vibration of single degree of freedom systems. Mod01 lec11 free and forced vibration of single degree of. The generic model for a one degree of freedom system is a mass connected to a linear spring and a linear viscous damper i. Two degree of freedom system some examples of two degree of fdfreedom systems are shown in the figure. Thus a two degree of freedom system has two normal modes of vibration corresponding to two natural frequencies. Structural dynamics of linear elastic multipledegreesof. Chapter 9 multidegreeoffreedom systems equations of motion. We have developed a multidegree freedom system by developing a program in mat lab platform.
The method is not practical for large systems since two unknown coefficients must be introduced for each mode shape. Flexure system compliant mechanism exact constraint screw theory projective geometry freedom topology constraint topology abstract in this paper we introduce a new design principle, and complementary geometric entities, that form the basis for a new approach to the synthesis of multidegree of freedom, purely parallel precision. Shock response spectrum the shock response spectrum is inherently a single degree of freedom concept, as discussed in reference 1. Dynamic analysis of multidegreeoffreedom systems using. Response of single degree of freedom systems to initial conditions. Obtaining the natural frequencies of a multiple degree of freedom system interpreting the meaning of the eigenvectors of a multiple degree of freedom system understanding the mechanism of a vibration absorber 4. The generic model for a one degreeoffreedom system is a mass connected to a linear spring and a linear viscous damper i. Damped fourdegreeoffreedom system excited by foundation motion 55 10. However, it is also possible to form the coefficient matrices directly, since each parameter in a massdashpotspring system has a very distinguishable role. Chapter 9 multidegreeoffreedom systems equations of.
Multidegreeoffreedom system with free body diagram 5. In this chapter, the methods of vibration analysis of single degree of freedom systems presented in the first chapter are generalized and extended to study systems with an arbitrary finite number of degrees of freedom. Dynamics of simple oscillators single degree of freedom systems. Furthermore, the mass is allowed to move in only one direction. The new proposed method is applied to a second order system using fuzzy logic controller flc, which is designed to yield precise. The simple 1dof systems analyzed in the preceding section are very helpful to develop a feel for the general characteristics of vibrating systems. Multi degree of freedom system with enforced motion by tom irvine email. Simple vibration problems with matlab and some help.
For a system with two masses or more generally, two degrees of freedom, m and k are 2x2 matrices. Previously saw in unit 19 that a multi degree of freedom system has the same basic form of the governing equation as a single degree of freedom system. May 22, 20 mod01 lec11 free and forced vibration of single degree of freedom systems. A nonlinear system has more complicated equations of motion, but these can always be arranged into the standard matrix form by assuming that the displacement of the system is small, and linearizing. In this line of thought, some algorithms are devel oped that, using a transmissibility concept. Frequency response 1 when we considered a single degree of freedom system with one input force and one output response, the relationship between the steady state response and force was written as. This relationship can also be developed for multiple degree of.
These characteristics make the multi dof systems different from one dof systems. Previously saw in unit 19 that a multi degreeoffreedom system has the same basic form of the governing equation as a single degreeoffreedom system. Pdf development of a miniature multidegreeoffreedom. Because of its mathematical form, the massspringdamper system will be used as the baseline for analysis of a one degree of freedom system. Many systems are too complex to be represented by a single degree of freedom model. Evaluation of methods for analysis of multidegreeof. In a four dof system the damping in the first mode is. Computation of natural frequencies of multi degree of freedom.
Shock response spectrum the shock response spectrum is inherently a singledegreeoffreedom concept, as discussed in reference 1. We have developed a multi degree freedom system by developing a program in mat lab platform. The object of this paper is to compare a singledegreeoffreedom sdof system with multipledegreeoffreedoms mdofs structures using the incremental dynamic analysis ida method. We will formulate the equations of motion of a simple 2story. Forming equations of motion for multiple degreeoffreedom. A freebody analysis of this system in the framework of newtons second law, as performed in chapter 2 of the textbook, results in the following equation of motion. Sozen introduction this is a short presentation of the principles of structural dynamics applied to systems having several degrees of freedom for use by students in an earthquake engineering introductory course. Moreover, several survey articles and books, foremost among them the recent, admirable work by minorski l have served this purpose.
Dynamics of simple oscillators single degree of freedom systems cee 541. On nonlinear vibrations of systems with many degrees of. Forced response of multi degree of freedom systems 1 2. Structural dynamics department of civil and environmental engineering duke university henri p. Two dof system theory rev 070606 1 two degree of freedom system forced vibration theory introduction some dynamic systems that require two independent coordinates, or degrees of freedom, to describe their motion, are called two degree of freedom systems.
The two masses are connected by three springs to two walls and each other. Single degree of freedom sdof system m k ft ut figure 1. Forced response of multi degree of freedom systems forced response of multi degree of freedom systems figure 1. There are 3 degrees of freedom in this problem since to fully characterize the system we must know the positions of the three masses x 1, x 2, and x 3. Equations of motion of an undamped multidegree of freedom system the displacement vector can be written as a linear combination of the mode. This system is called a single input single output siso system. If we give an arbitrary initial excitation to the system, the resulting free. Because of its mathematical form, the massspringdamper system will be used as the baseline for analysis of a one degreeoffreedom system. Multidegreeoffreedom systems generalizing the concepts of mass, spring, and damping to systems via use of matrices how we generalize the concepts of positivity to matrices using principles like virtual work to derive equations opportunity for me to sneak in optimization.
Degrees of freedom may or may not be in the same coordinate direction. Design of multidegreeoffreedom tunedmass dampers using perturbation techniques by justin matthew verdirame bachelor of science, mechanical engineering. Singledegreeoffreedom linear oscillator sdof for many dynamic systems the relationship between restoring force and deflection is approximately linear for small deviations about some reference. Forced response of multidegreeoffreedom systems 1 2. Synthesis of multidegree of freedom, parallel flexure system. Multidegreeoffreedom systems equations of motion, problem statement, and solution methods twostory shear building a shear building is the building whose floor systems are rigid in flexure and several factors are neglected, for example, axial deformation of beams and columns. Mechanical systems in general consist of structural. Oct 10, 2010 obtaining the natural frequencies of a multiple degree of freedom system interpreting the meaning of the eigenvectors of a multiple degree of freedom system understanding the mechanism of a vibration absorber 4. The fi tfirst figure shows a two mass two spring system that is described by two linear coordinates x1 and x2. Multiple degrees of freedom structural dynamics 2 l. If we consider the case where x 1 x 2 then the free body diagrams become those seen in. Synthesis of multidegree of freedom, parallel flexure. Undamped sdof system its acceleration and opposing its motion.
The basic purpose of this series of slides is to provide background on the development of the codebased equivalent lateral force elf procedure and modal superposition. Design of multidegreeoffreedom tunedmass dampers using. A secondary purpose is to compare the results of this method to simplified methods for multidegreeoffreedom shock response. The simplest form of vibration that we can study is the single degree of freedom system without damping or external forcing. The method is applied to a twodimensional, 2 degreeoffreedom transonic airfoil undergoing simultaneous forced pitch and heave harmonic oscillations. This paper presents a reducedordermodeling approach for nonlinear, multidegreeoffreedom aerodynamic systems using multiinput volterra theory. This paper presents a multidegree of freedom mdof controller. Multi degree of freedom systems, frequency response. They are too simple to approximate most real systems, however. For a system having n degrees of freedom, there are n associated natural frequencies, each associated with its own mode shape. Development of a miniature multidegreeoffreedom measurement system for ultra precision stages. There are two equations for a two degree of fdfreedom system, one for each. The object of this paper is to compare a single degree of freedom sdof system with multiple degree of freedoms mdofs structures using the incremental dynamic analysis ida method. The pure mode shapes can be later superimposed to get the actual displacement pattern of the system.
Structural dynamics of linear elastic multipledegreesoffreedom mdof systems u1 u2 u3 this topic covers the analysis of multipledegreesoffreedom mdof elastic systems. Three free body diagrams are needed to form the equations of motion. There are 3 degrees of freedom in this problem since to fully characterize the system we must know the positions of the three masses x 1, x 2, and x 3 three free body diagrams are needed to form the equations of motion. Introduction of multidegree of freedom systems youtube. Multi degree of freedom systems equations of motion, problem statement, and solution methods twostory shear building a shear building is the building whose floor systems are rigid in flexure and several factors are neglected, for example, axial deformation of beams and columns. Gavin fall, 2018 this document describes free and forced dynamic responses of simple oscillators somtimes called single degree of freedom sdof systems. A secondary purpose is to compare the results of this method to simplified methods for multi degree of freedom shock response. W07m02 multi degree of freedom system solution of equilibrium. A system model with two degrees of freedom is depicted in figure 1.
When we considered a single degree of freedom system with one input force and one output response, the relationship between the steady state response and force was written as. Evaluation of methods for analysis of multidegreeoffreedom. Real systems have more than just one degree of freedom. For systems with more than one degree of freedom dof, we introduce multi natural frequencies, mode shapes, and mode interaction. Shock response of multidegreeoffreedom systems revision f. Apr 01, 2018 introduction of multi degree of freedom systems. The forces fi arising due to damping associated with the coordinates xl, x2, will have the form. Single degree of freedom systems linkedin slideshare. Mod01 lec11 free and forced vibration of single degree. Multi degree freedom systems free download as powerpoint presentation. Dynamic analysis of multidegreeoffreedom systems using a. Forced response of multidegreeoffreedom systems forced response of multidegreeoffreedom systems figure 1.
The horizontal vibrations of a singlestory building can be conveniently modeled as a single degree of freedom system. Simple vibration problems with matlab and some help from maple. Computation of natural frequencies of multi degree of. Vibration theory degrees of freedom, sdof system, types of vibrations. Structural dynamics of linear elastic multipledegrees of freedom mdof systems u1 u2 u3 this topic covers the analysis of multipledegrees of freedom mdof elastic systems.
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