Do you have a pdf file of book modal analysis theory and testing. Abstract this thesis presents two novel nonlinear modal analysis methods, aimed at the identification of representative engineering structures. Structural dynamics of linear elastic multipledegreesoffreedom mdof systems u1 u2 u3 this topic covers the analysis of multipledegreesoffreedom mdof elastic systems. We use modal analysis to help design all types of structures including automotive struc. The response for each modal coordinate satisfying the modal eqn. A freebody diagram of mass 1 is given in figure a2. Topic 6 structural dynamics iii analysis of elastic mdof. The equations of motion can be uncoupled and solved by modal analysis. The output, frf, is an h 1 estimate computed using welchs method with window to window the signals. Extension of second moment analysis to vector valued and matrix valued functions, internationa journal of nonlinear mechanics, 1987, 223, 251260. Xmodal experimental modal analysis software structual. Frequencyresponse functions for modal analysis matlab. Knowledge summary a a ndof system has nnatural frequencies. Either static coupling, dynamic coupling or both static and dynamic coupling can exist.
July 30, 2002 ahmed elgamal 2 modal analysis these notes cover sections from ch. The concept of linear modal superposition is combined with the normal nonlinear mode technique, an approach that allows the formulation of a system identi. Heylen, lammen, sas modal analysis theory and testing. Author links open overlay panel bortsuen wang dengkai cheng. The system also has damping, but it is modeled as modal damping. For example, there is a 100dof structure the size of mass and stiffness matrixes are 100 100. Multidegreeoffreedom mdof systems and modal analysis. Extracting modal properties from experimental frequency response data. However, you want to do the modal analysis only for first 10 modes not all the modes which is very common in real situation.
Matlab implementation of an operational modal analysis technique for vibrationbased structural health monitoring by alejandro p. Free vibration of mdof systems system without damping the equation of motion of a twodof system in free vibration no external force is. Similar to the sdof system, mdof systems have natural frequencies. Modal analysis solution of mdof equation of motion by mode superposition the solution u will be represented by a summation of the mode shapes f n, each multiplied by a scaling factor q n known as the generalized coordinate. Xmodal iii is an experimental modal analysis research software package that the university of cincinnati, structural dynamics research lab ucsdrl has, and continues to, develop in conjunction with a group of sponsoring companies and the ucsdrl research software consortium. The multiple degree of freedom mdof wizard, for example, handles the most sophisticated modal analysis tasks, such as detecting repeated or closely spaced modes. The procedure of modal analysis can be divided in various steps as follows, step 1 free vibration analysis modal analysis requires the normal modes, which are obtained first by free vibration analysis. Modal analysis of mdof systems with proportional damping.
The fundamentals of modal testing application note 243 3. Vibrations of mechanical systems basics of modal analysis joerg bienert. Compute internal forces story shears and moments by static analysis of the structure subject to the equivalent forces. Analytical modal analysis modal analysis is the process of characterizing the dynamic response of a system in terms of its modes of vibration. The overall objective is to detect, localize, identify and quantify the. View notes me 5514 lecture 10 mdof forced from me 5514 at virginia tech. Modal analysis provides a detailed overview of the theory of analytical and experimental modal analysis and its applications. For the mdof case, however, a unique displacement vector called the mode shape exists for each distinct frequency and damp ing as illustrated in figure 1.
In mdof systems, a natural state implies a certain configuration of shape taken by the system during 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. Matlab implementation of an operational modal analysis. Uncoupling of equations through use of natural mode shapes. Modal analysis is the processes of determining the inherent dynamic characteristics of any system and using them to formulate a mathematical model of the dynamic behavior of the system. So, basically, modal analysis is the study of the natural characteristics of structures. Understanding both the natural frequency and mode shape helps to design my structural system for noise and vibration applications. Modal analysis for random response of mdof systems. Determine the total value of any response quantity by combining the modal. An important concept of analysis of mdof systems is the change of basis from normal cartesian coordinates to modal coordinates. Application of frequency response data and modal parameters. Geometry type 8719, modal analysis types 8720, 8720a and 8720b, and advanced modal analysis types 8721, 8721a and 8721b pulse reflex modal analysis is an easytouse postprocessing application that enables you to perform single and polyreference classical modal analysis even in the most demanding situations.
Development and application of a nonlinear modal analysis. If you have a question on some aspect of modal analysis, just contact us. If x or y is a matrix, each column represents a signal. Mdof system using classical modal analysis under external forces and base excitation. Request pdf modal analysis of mdof system by using free vibration response data only conventional modal testing requires the actuator and sensor to perform frf measurement so as to determine. Structural dynamics of linear elastic mdof systems civil.
Nonlinear modal analysis with ritz vectors requires the use of free vibration study, which is produced by a ramp load followed by an instantaneous removal of the load this is valid for sdof since for mdof the shape of load is also important. Structural dynamics of linear elastic multipledegreesof. Modal analysis of mdof system by using free vibration response data only. From observations, free vibration of undamped mdof system is a. Vandiver goes over the modal expansion theorem, computing mass and stiffness matrices, obtaining uncoupled equations of motion, modal initial conditions, damping in modal analysis, rayleigh damping, and experimental fitting of damping ratios. In the past two decades it has become a major technological tool in the quest for determining, improving and optimizing dynamic characteristics of engineering. A set of linear algebraic equations of free vibration, is rewritten here. Me617 handout 7 undamped modal analysis of mdof systems. In the analysis below, for a proper choice of generalized coordinates, known as principal or natural coordinates, the system of n ode describing the system motion is independent of. Modal analysis normal mode matrix mathematics free.
829 821 320 1392 1079 285 18 249 1061 131 556 1101 1360 236 1362 1253 796 910 707 475 1124 1261 1125 881 380 178 1125 747 836 673 510 415 251 1076 197 158 318 1348 808 891 269 366 10 489 26 637 1184 1481 918 1088 24