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. Modal analysis of mdof system by using free vibration. Understanding both the natural frequency and mode shape helps to design my structural system for noise and vibration applications. A set of linear algebraic equations of free vibration, is rewritten here. The multiple degree of freedom mdof wizard, for example, handles the most sophisticated modal analysis tasks, such as detecting repeated or closely spaced modes. Topic 6 structural dynamics iii analysis of elastic mdof. Matlab implementation of an operational modal analysis technique for vibrationbased structural health monitoring by alejandro p. Modal analysis provides a detailed overview of the theory of analytical and experimental modal analysis and its applications. Knowledge summary a a ndof system has nnatural frequencies. 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. Development and application of a nonlinear modal analysis. Do you have a pdf file of book modal analysis theory and testing.
Vibrations of mechanical systems basics of modal analysis joerg bienert. 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. Ojeda submitted to the department of civil and environmental engineering on may 09, 2012 in partial fulfillment of the requirements for the degree of master of engineering in civil and environmental engineering abstract. Frequencyresponse functions for modal analysis matlab. The system also has damping, but it is modeled as modal damping. Xmodal experimental modal analysis software structual. The fundamentals of modal testing application note 243 3. 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. Extracting modal properties from experimental frequency response data. View notes me 5514 lecture 10 mdof forced from me 5514 at virginia tech.
Either static coupling, dynamic coupling or both static and dynamic coupling can exist. However, you want to do the modal analysis only for first 10 modes not all the modes which is very common in real situation. Shock response spectrum analysis is the maximum response of a series of single degree of freedom systems having the same damping to a given transient signal. The output, frf, is an h 1 estimate computed using welchs method with window to window the signals. The response for each modal coordinate satisfying the modal eqn. Topic 6 structural dynamics iii analysis of elastic mdof systems equations of motion for mdof systems uncoupling of equations through use of natural mode shapes solution of uncoupled equations recombination of computed response modal response spectrum analysis by example use of reduced number of modes. July 30, 2002 ahmed elgamal 2 modal analysis these notes cover sections from ch.
Free vibration of mdof systems system without damping the equation of motion of a twodof system in free vibration no external force is. Determine the total value of any response quantity by combining the modal. Application of frequency response data and modal parameters. Multidegreeoffreedom mdof systems and modal analysis. Modal analysis of mdof system by using free vibration response data only. 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. In mdof systems, a natural state implies a certain configuration of shape taken by the system during motion. Moreover a mdof system does not possess only one natural. Abstract this thesis presents two novel nonlinear modal analysis methods, aimed at the identification of representative engineering structures. For example, there is a 100dof structure the size of mass and stiffness matrixes are 100 100. 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.
The concept of linear modal superposition is combined with the normal nonlinear mode technique, an approach that allows the formulation of a system identi. Analytical modal analysis depends on the generation of the equations of motion of a system through a finite element model. 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. Mdof system using classical modal analysis under external forces and base excitation. Matlab implementation of an operational modal analysis. So, basically, modal analysis is the study of the natural characteristics of structures. Geometry creation component based geometries for odsmodal analysis can be created in a simple stepbystep approach. In the past two decades it has become a major technological tool in the quest for determining, improving and optimizing dynamic characteristics of engineering. The equations of motion can be uncoupled and solved by modal analysis. A freebody diagram of mass 1 is given in figure a2. Twodegreeoffreedom system, modal analysis the method of generalized coordinates is demonstrated by an example. Structural dynamics of linear elastic multipledegreesof.
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. Author links open overlay panel bortsuen wang dengkai cheng. 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. Analytical modal analysis modal analysis is the process of characterizing the dynamic response of a system in terms of its modes of vibration. An important concept of analysis of mdof systems is the change of basis from normal cartesian coordinates to modal coordinates. Structural dynamics of linear elastic mdof systems civil.
Similar to the sdof system, mdof systems have natural frequencies. Heylen, lammen, sas modal analysis theory and testing. From observations, free vibration of undamped mdof system is a. If you have a question on some aspect of modal analysis, just contact us. The overall objective is to detect, localize, identify and quantify the. A freebody diagram of mass 2 is given in figure a3. Extension of second moment analysis to vector valued and matrix valued functions, internationa journal of nonlinear mechanics, 1987, 223, 251260. We use modal analysis to help design all types of structures including automotive struc. Me617 handout 7 undamped modal analysis of mdof systems. Compute internal forces story shears and moments by static analysis of the structure subject to the equivalent forces. Modal analysis for random response of mdof systems. 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.
207 1193 1001 1194 456 1185 1503 1494 821 511 424 1360 305 1021 1009 361 945 1369 369 1379 301 64 1473 657 292 175 810 1110 586 974 1384 1336 1350 657 440 1399 529 1273 327 240