Structural dynamic analysis with generalized damping models. Using as the generalized coordinate, the lagrangian of the system can be written as follows. The prototype single degree of freedom system is a springmassdamper system in which the spring has no damping. The horizontal vibrations of a singlestory building can be conveniently modeled as.
Vibration of single degree of freedom systems copyrighted. The prototype single degree of freedom system is a springmassdamper system in which the spring has no damping or mass, the mass has no stiffness or damp. Multi degree of freedom systems that commonly arise in linear vibration theory with symmetric. Dynamics of structures theory and applications to earthquake engineering written by anil k. Dynamics of multiple degree of freedom linear systems. Single degree of freedom everting ring linkages with. In this paper, a general technique is proposed for constructing approximate stationary pdf solutions of single degree of freedom sdof nonlinear systems under external and parametric gaussian.
Banerji, department of civil engineering,iit bombay. In this thesis, a simplified method using the generalized single degree of freedom. Such systems are called single degree of freedom sdof systems and are shown in the following figure. Methods to evaluate the response of sdof systems under various types of dynamic loading are taught. A brief introduction to multi dof systems is also included. They are too simple to approximate most real systems, however. Oct 31, 2014 chapter 2 free vibration of single degree of freedom 1. Known established linkages with a single degree of freedom, which facilitates control, have so far consisted of six or fewer links. Response of single degreeoffreedom systems to initial conditions.
Sdof system is proposed for seismic analysis of concrete. Example problems are solved throughout the course to illustrate the theoretical concepts. The analysis can be easily visualized with the aid of a free body diagram. Although singledegreeoffreedom systems with classical dry coulombic friction have been studied extensively, the properties of systems. Spectral identification of nonlinear multidegreeof. L16earthquake response analysis for single degree of freedom structures. Find materials for this course in the pages linked along the left. Blake introduction this chapter presents the theory of free and forced steadystate vibration of single degreeoffreedom systems. Structural dynamics of linear elastic multipledegreesof. Undamped sdof system its acceleration and opposing its motion. Lagranges equations of motion in a dynamical system, the change of the lagrangian for each generalized coordinate equals to the time derivative of the. Dynamics of simple oscillators single degree of freedom systems.
Dependent force gravitational forces earthquake ground motion formulation of equation of motion generalized coord. The analysis as onedegreeof freedom systems can be made provided that by the specification of a single coordinate the generalized coordinate. A method for identification of nonlinear multidegreeoffreedom systems g dimitriadis and j e cooper school of engineering, aerospace division, the university of manchester. System identification methods for nonlinear aeroelastic systems could find uses in many. It is important in the analysis of systems of bodies in mechanical engineering, structural engineering, aerospace engineering, robotics, and other fields the position of a single railcar engine moving along a track has one degree of freedom because. Ferri school of mechanical engineering, georgia institute of technology, atlanta, georgia 303320405, u. Introductory remarks assemblageof rigidbodies continuous systems vibration analysisby rayleighs method selectionof modeshapes re. Structural dynamics october 2003 general formulation of equations of motion idealization of a structure to a system model with finite number of degrees of freedom timedomain methods types of dynamic loading single degreeoffreedom systems multidegreeoffreedom system free vibration of sdof systems. Structural dynamic analysis with generalized damping. The mass is allowed to travel only along the spring elongation direction. Structural dynamics of linear elastic singledegreeoffreedom sdof systems this set of slides covers the fundamental concepts of structural dynamics of linear elastic singledegreeoffreedom sdof structures.
The number of degrees of freedom that a structure possesses is equal. We will formulate the equations of motion of a simple 2story. A simplified analysis of mdof systems using the concept of generalized single degree. Structural dynamics of linear elastic singledegreeof. A separate topic covers the analysis of linear elastic multiple degree of freedom mdof systems. An introduction to the dynamics of continuous systems is provided in topic 9. By restricting the deformation to a single shape of varying amplitude, we introduce an in nity of internal contstraints that limit. Mod02 lec02 l2degrees of freedom, sdof system, types of. Although the equations of motion of a two degree of freedom system are. Degrees of freedom degrees of freedom analysis tells us the maximum number of variables which can be independently specified to uniquely determine a feasible solution to a given problem.
Dynamic equation of equilibrium free vibration of single degree of freedom systems forced vibration. Derivation derive the dynamic governing equation of. In these types of systems the modes of vibration would be a function of the spin rate and the resulting gyroscopic moments. A degree of freedom corresponds to one quantity that changes the configuration of the system, for example the angle of a pendulum, or the arc length traversed by a bead along a wire. Previously saw in unit 19 that a multi degreeoffreedom system has the same basic form of the governing equation as a single degreeoffreedom system. Free vibration of single degree of freedom sdof chapter 2 2. Dynamics of simple oscillators single degree of freedom systems cee 541. The simple pendulum is a single degree of freedom sdof system. The concept of generalized coordinate presented in this chapter permits the analysis of multiple interconnected rigid or elastic bodies with distributed properties as singledegreeoffreedom systems. Mod01 lec17 generalized single degree of freedom systems equations. Chapter 2 free vibration of single degree of freedom.
Introductory remarks assemblageof rigidbodies continuous systems generalized single degree of freedom systems giacomobo. Linkages are the basic functional elements of any machine. Undamped systems and systems having viscous damping and structural damping are included. Mod02 lec02 l2degrees of freedom, sdof system, types of vibrations. 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. We need to consider degrees of freedom when solving many different types of problems. Novel method for random vibration analysis of singledegree. The present study introduces a novel and simple numerical method for the solution of this. Free vibration of a single degree of freedom system is a fundamental topic in mechanical vibrations. In addition to springmass singledegreeoffreedom systems, work has also been done on unbalanced flexible rotors whose spin rate swept through its critical speeds, e. Chapter 9 multidegreeoffreedom systems equations of motion. Free vibration of singledegreeoffreedom sdof systems procedure in solving structural dynamics problems 1. Dynamics of simple oscillators single degree of freedom.
Single degree of freedom sdof system m k ft ut figure 1. Types of dynamic loads basic background of methods available and motivation for structural dynamics. Generalized sdof system for dynamic analysis of concrete. A secondary purpose is to compare the results of this method to simplified methods for multidegreeoffreedom shock response. However, most actual structures have several bodies and several restraints and therefore several degrees of freedom. Singledegreeoffreedom linear oscillator sdof for many dynamic systems the relationship between restoring force and deflection is approximately linear for small deviations about some reference. Furthermore, the mass is allowed to move in only one direction.
Although thethe equationsequations ofof motionmotion ofof aa twotwo degreedegree ofof freedomfreedom systemsystem areare generally coupled so that each equation involves all coordinates, it is. Generalized sdofs giacomo bo introductory remarks assemblage of rigid bodies continuous systems assemblages of rigid bodies i planar, or bidimensional, rigid bodies, constrained to move in a plane, i the exibility is concentrated in discrete elements, springs and dampers, i rigid bodies are connected to a xed reference and to each other by means of springs, dampers and smooth, bilateral. Jul 16, 2012 summary this chapter contains sections titled. Keywords equivalent nonlinear stochastic system, first passage failure, fractional derivative, singledegreeoffreedom, stochastic averaging method references agrawal, op 1999 an analytical scheme for stochastic dynamic systems containing fractional derivatives. Jul 03, 2012 mod01 lec19 generalized single degree of freedom systems equations of motions. Pdf in most of the current design codes and standards for concrete liquid storage tanks.
Jun 04, 20 mod02 lec02 l2degrees of freedom, sdof system, types of vibrations. The prototype single degree of freedom system is a springmassdamper system in which the spring has no damping or mass, the mass has no sti. Recently, a nonlinear and timevariant singledegreeoffreedom sdof oscillator parameter identification technique has been developed in. Vibration of single degree of freedom systems assoc. Example problems are solved throughout the course to. Such systems are called single degreeoffreedom sdof systems and are shown in the following figure, equation of motion for sdof systems. Mod01 lec19 generalized single degree of freedom systems. Generalized coordinates and rayleighs method springerlink. Generalized sdofs outline generalized sdofs giacomo bo giacomo bo continuous systems generalized single. View notes generalized single degree of freedom systems from ce 642 at university of tabriz. Modal superposition analysis uses design response spectrum as basic ground motion input. Structural dynamics department of civil and environmental engineering duke university henri p. Peak response of singledegreeoffreedom systems to swept.
The simplest vibratory system can be described by a single mass connected to a spring and possibly a dashpot. Therefore, it is called a single degree of freedom sdof system. New results for such systems are obtained using extensions of the results for single and two degree of freedom systems. Derivation derive the dynamic governing equation of the simpli. Consider a single degreeoffreedom system with a cubic stiffness nonlinearity and assume that the position and. Example of overhead water tank that can be modeled as sdof system 1.
Pdf generalized sdof system for dynamic analysis of concrete. The form of equations in 27 can be generalized to write the equations of. Abstractionmodeling idealize the actual structure to a simpli. Journal of sound and vibration 1990 1402, 287304 behavior of a singledegreeoffreedom system with a generalized friction law. Chapter 8 generalized single degree of freedom systems september 1, 2018 the material included in this presentation has been extracted from the fourth edition of the book.
Pdf polynomial solution of the single degree of freedom. Received 6 february 1989, and in final form 3 october 1989 although single degree of freedom systems with classical dry. Mod01 lec19 generalized single degree of freedom systems equations of motions. The dynamic response of single degree of freedom nonlinear systems subjected to earthquake motions is considered with the purpose of deriving factors for constructing inelastic design spectra, and. Behavior of a singledegreeoffreedom system with a generalized. A method for identification of nonlinear multidegreeof. Mod01 lec21 equations of motion for multi degree of freedom structures. L17generalized single degree of freedom systems equations of motions. Mechanical systems in general consist of structural elements which have distributed mass and elasticity. Generalized sdofs giacomo bo introductory remarks assemblage of rigid bodies continuous systems further remarks on continuous systems continuous systems have an in nite variety of deformation patterns. Multiple degreeoffreedom systems are discussed, including the normalmode theory of linear elastic structures and.
Journal of sound and vibration 1990 1402, 287304 behavior of a single degree of freedom system with a generalized friction law. Multidegree of freedom systems as sttdtated bfbefore, most engiiineering systems are contin o scontinuousand have an infinite number of degrees of freedom. 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. The vibration of structures with more than one degree of freedom many real structures can be represented by a single degree of freedom model. Structural dynamics of linear elastic singledegreeoffreedom. Sep 26, 2010 what is a single degree of freedom sdof system. A method for identification of nonlinear multi degree of freedom systems g dimitriadis and j e cooper school of engineering, aerospace division, the university of manchester abstract. Ventilation systems elevator and conveyance systems fluid pumping equipment machines and generators aerobics and exercise rooms, human activity external sources.
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. Mod01 lec17 generalized single degree of freedom systems. Pdf the effect of using hysteresis models bilinear and. The vibration analysis of continuous systems requires the solution of partial differential equations, which is quite difficult. The methods of vibration analysis of single degree of freedom systems can be generalized and extended to study systems with an arbitrary finite number of degrees of freedom. Seismic activity subway, road and rail systems, airplanes construction equipment wind, waves. Free vibration of singledegreeoffreedom sdof systems. The simple 1dof systems analyzed in the preceding section are very helpful to develop a feel for the general characteristics of vibrating systems. Mechanical systems in general consist of structural. Structural dynamics of linear elastic single degree of freedom sdof systems this set of slides covers the fundamental concepts of structural dynamics of linear elastic single degree of freedom sdof structures. A separate topic covers the analysis of linear elastic multipledegreeof. Generalized single degree of freedom systems equations of.
Generalized single degree of freedom systems generalized. The motion takes the form of a nonoscillatory or oscillatory decay. Sdof vibration can be analyzed by newtons second law of motion, f ma. Dynamics of multiple degree of freedom linear systems, eigenvalue problem, natural frequency and mode shapes, two dof systems slideshare uses cookies to improve functionality and performance, and to provide you with relevant advertising. Received 6 february 1989, and in final form 3 october 1989 although singledegreeoffreedom systems with classical dry. Single degree of freedom systems linkedin slideshare. Shock response spectrum the shock response spectrum is inherently a singledegreeoffreedom concept, as discussed in reference 1. Chapter 8 generalized singledegreeoffreedom systems september 1, 2018 the material included in this presentation has been extracted from the fourth edition of the book. Equations of motions for axial vibration of a beam.
The solution to the inverse problem for an n degree of freedom linear gyroscopic system is obtained as a special case. The author draws on his considerable research experience to produce a text covering. The vibration of structures with more than one degree of. Gavin fall, 2018 this document describes free and forced dynamic responses of simple oscillators somtimes called single degree of freedom sdof systems. The technique can be construed as a generalization of the multipleinputsingleouput miso methodology proposed by bendat and coworkers e. Most of the time, continuous systems are approximated as discrete systems, and solutions are obtained in a simple manner. Novel method for random vibration analysis of single. 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. Real systems have more than just one degree of freedom. In physics, the degrees of freedom dof of a mechanical system is the number of independent parameters that define its configuration or state. Riya catherine george, holds a phd degree from iit kanpur, in civil engineering. Any such set of coordinates is called generalized coordinates. Introduction a system is said to undergo free vibration when it oscillates only under an initial disturbance with no external forces acting after the initial disturbance 3. There is one for each degree of freedom, so the number of generalized coordinates equals the number of degrees of freedom, n.