Modal Analysis Using the Signal Processing Toolbox of Matlab 2017 (original) (raw)
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In this paper, concept of experimental modal analysis is discussed to derive dynamic properties of mechanical structures and equipments. Dynamic properties (mode shape, damping, and resonant frequencies) are calculated using MATLAB program. Amongst present curve fitting method, Rational Fraction Polynomials (RFP) method is used in the derivation of modal parameters. Results obtained from this method are compared with those obtained form experiment and shown in form of standard deviation. This standard deviation is computed from different experimental FRF values and analytically obtained FRF values. 1. Introduction Vibration has many undesirable and harmful effects on life and performance of mechanical equipments and other structures. The effects of vibration are due to dynamic interaction between vehicles and bridges, structural motions due to earthquakes, noise generated by construction equipment , vibration transmitted from machinery to its supporting structures thereby interfering with their performance , damage as well as malfunction and failure due to dynamic loading, fatigue failure, oscillation of transmission lines[1]. The objective of this paper is to emphasis on dynamic analysis of such equipments and structures by capturing their actual dynamic behaviour during experimentation such that the adversity arising from vibration effects can be minimised to improve their life and performance. Dynamic analysis consists of experimental and operational modal analysis. In experimental modal analysis (EMA), structures are artificially excited by exciters (Impact hammers and shakers). In operational modal analysis (OMA), structure is analysed while it is operated upon. For large and heavy structures (civil structures such as bridge and dams), modal analysis is used to detect damage by ambient (traffic) condition [2] .Recent trends in dynamic analysis are extremely focused on better performance and life of structures. Self excited vibrations of tool result in unstable cutting process, poor surface finish, reduced productivity and damage on the machine itself. By considering spindle geometry (its diameter and length), bearing stiffness, tool holder geometry and selection of combination of depth of cut and spindle speed from stability lobe diagrams, machining operation can be made chatter free[3,4]. In vibration of rotating equipments (such as pump, turbine etc.), dynamic analysis is used to check their health as excessive noise of these equipments is experienced by personnel in large power plants and refineries due to damage or failure of seals [5]. 2. Methodology In this paper, EMA is focused upon. EMA is used to characterize resonant vibration in machinery and structures. In EMA, a mode of vibration is defined by three parameters; modal frequency, modal damping and mode shape. Modal parameter estimation is the process of determining these parameters from experimental data. Furthermore, a set of modal parameters can completely characterize the dynamic properties of a structure. This set of parameters is also called a modal model for the structure. Modes (or resonances) are inherent properties of a structure. 199
SOFTWARE FOR OPERATIONAL MODAL ANALYSIS AND AUTOMATIC IDENTIFICATION OF MODAL PARAMETERS
etsmtl.ca
In this paper, we present a software for the Operational Modal Analysis (OMA) of vibrating structures in operating conditions. The method used is based on a multivariate autoregressive model, with the model's parameters of the model are estimated by least squares via the computation of the QR factorization, and the modal parameters are identified from the eigendecomposition of the state matrix. The natural frequencies, damping rates and modes shapes are updated with respect to the model order and are successively constructed on stabilization diagrams with their corresponding confidence intervals. Furthermore, an optimal model order can be automatically selected from the evolution of a factor called the Noise rate Order Factor (NOF) from which the structural modes are automatically distinguished from the spurious ones in order to construct noise-free spectra. After the frequency ranges of interest are selected, the natural frequencies and damping rates are automatically identified. The proposed software is user friendly and the operator can easily determine the accuracy of the modal parameters that are automatically computed. Several experimental applications are described by way of examples.
Experimental Study on the Effect of Excitation Type on the Output-Only Modal Analysis Results
Transactions of FAMENA, 2019
Output-only Modal Analysis (OMA) has found extensive use in the identification of dynamic properties of structures. This study aims to investigate the effect of excitation force on the accuracy of modal parameters. For this purpose, the modal parameters of a simply supported beam are obtained through the Experimental Modal Analysis (EMA) and the OMA method using three different types of artificial and natural excitations, namely a shaker, acoustic waves, and environmental noise. Frequency Domain Decomposition (FDD) technique is used to identify dynamic characteristics. Finally, these results are compared with those obtained by the analytical method and the EMA method. The results demonstrated the following: 1) Acoustic excitation presents the natural frequencies with the smallest errors in comparison with the analytical results. 2) Inaccuracy is observed at certain natural frequencies during the excitation with a shaker with respect to the connecting point between the shaker and the beam. 3) Modal Assurance Criterion (MAC) showed that the mode shapes extracted by the acoustic excitations are more similar to the analytical results.
Evaluation of Experimental Modal Analysis
2014
Experimental modal analysis has grown steadily in popularity since the advent of the digital FFT spectrum analyser in the early 1970's. Today, impact testing (or bump testing) has become widespread as a fast and economical means of finding the modes of vibration of a machine or structure. Mechanical resonance is the tendency of a mechanical system to absorb more energy when the frequency of its oscillations matches the system's natural frequency of vibration than it does at other frequencies. It may cause violent swaying motions and even catastrophic failure in improperly constructed structures. When designing objects, engineers must ensure the mechanical resonance frequencies of the component parts do not match driving vibrational frequencies of oscillating parts, a phenomenon known as disaster. Different techniques, experimental and theoretical have been developed to analyse problems related to vibration. But in the present era computational techniques are quite common and...
A Study of Joint Time-Frequency Analysis-Based Modal Analysis
IEEE Transactions on Instrumentation and Measurement, 2006
Traditional modal-analysis methods use either timedomain or frequency-domain approaches. Because vibration signals are generally nonstationary, time and frequency information is needed simultaneously in many cases. This paper presents an overview of the applications of joint time-frequency methods for modal analysis. Since a joint time-frequency analysis can decouple vibration modes, it has an advantage, especially when information about the excitation is not available. In this paper, wavelet and Gabor analyses for the modal parameter identification are compared. Two reconstruction approaches-the FFT method and the Gabor expansion method-are also compared. Numerical simulations and experiments have been carried out.
Trends in experimental modal analysis
Mechanical Systems and Signal Processing, 1987
The scope of this paper is to comment on current trends and new developments in the field of experimental modal analysis. The first section covers modal measurement and estimation procedures, with special emphasis on the use and limitations of recent techniques such as multiple input processing, total least square, global time-and frequency domain parameter estimation. In the second section reference is made to applications and use of modal parameters in techniques such as structural modification, fatigue and acoustic analysis. Emphasis is put on applications used at the Katholieke Universiteit, Leuven. This explains the wide use of experimental modal analysis procedures where the modal parameters are determined from measured impulse or frequency response functions. In this last method however, the physical structure is required. In design applications this is a major drawback where it implies the construction of prototypes. Current and more advanced experimental modal analysis procedures are reviewed in this paper and the use of these modal parameters in mathematical system optimisation and identification techniques are emphasised. 2. EXPERIMENTAL MODAL ANALYSIS METHODS 2.1. INTRODUCTION The experimental modal analysis technique can be regarded as a "Black Box" or input-output approach. This means that information about structural dynamics behaviour 5
Easymod: A Matlab/Scilab Toolbox for Teach- Ing Modal Analysis
2020
Teaching experimental modal analysis (EMA) to engineering students needs a basic knowledge and it is rarely possible to illustrate it with commercial software packages which are often presented as a black box following a specific industrial demand. These tools are naturally not adapted to education as they hide most of their fundamentals. This paper presents the development of an educational MatLab toolbox called EasyMod designed for determining the modal parameters of a structure by analysing frequency response functions (FRFs) obtained experimentally. Various Single-Input Single-Output methods, on increasing complexity, have been implemented in this toolbox: the peak picking/mode picking, circle-fit and line-fit methods use interesting properties of FRFs with emphasis on estimating eigenfrequencies, damping ratios and compliances. More complex methods are also proposed, for instance the least square complex exponential method (multi-input multi-output method), for a progressive ad...
Université de Mons EASYMOD: A MATLAB/SCILAB TOOLBOX FOR TEACH- ING MODAL ANALYSIS
Teaching experimental modal analysis (EMA) to engineering students needs a basic knowledge and it is rarely possible to illustrate it with commercial software packages which are often presented as a black box following a specific industrial demand. These tools are naturally not adapted to education as they hide most of their fundamentals. This paper presents the development of an educational MatLab toolbox called EasyMod designed for determining the modal parameters of a structure by analysing fre-quency response functions (FRFs) obtained experimentally. Various Single-Input Single-Output meth-ods, on increasing complexity, have been implemented in this toolbox: the peak picking/mode picking, circle-fit and line-fit methods use interesting properties of FRFs with emphasis on estimating eigenfre-quencies, damping ratios and compliances. More complex methods are also proposed, for instance the least square complex exponential method (multi-input multi-output method), for a progressive...
Experimental Modal Analysis using Ambient and Earthquake Vibrations: Theory, Software, Applications
University of Thessaly, 2012
This thesis addresses the problem of identifying the modal properties of structures using vibration measurements. Modal identification methodologies are proposed based on vibration measurements induced by artificial, ambient or earthquake loads applied on the structure. A modal model of the structure is identified using a weighted least-squares approach and measured time histories at selected locations of a structure. For artificially induced and ambient vibration measurements, the identification is performed in the frequency domain using respectively frequency response functions and cross power spectral densities. For earthquake induced vibrations, the identification is performed in both time and frequency domains. The modal identification methods presented in this work treat generalized non-classically damped modal models. The identification of the modal parameter (modal frequencies, modal damping ratios, modeshape components and modal participation factors) is accomplished by introducing a computationally very efficient three step approach as follows. In the first step, stabilization diagrams are constructed containing frequency and damping information. The modeshape components and participation factors are estimated in a second least-squares step, based on the user selection of the stabilized poles. The first two steps involve non-iterative procedures and result in solving linear algebraic systems of equations. Finally, in order to improve the estimation of the modal characteristics, especially for the challenging case of closely spaced and overlapping modes, a third step is introduced to solve a fully nonlinear optimization problem using available iterative gradient-based optimization algorithms. In this thesis, theoretical developments as well as software implementation issues are presented. The methodologies and software developed are applied for the identification of the modal characteristics of a small laboratory structure for the case of artificial induced vibration measurements, as well as the identification of the modal characteristics of three bridges, the under construction R/C bridge of Egnatia Odos located at Metsovo (Greece), and two other representative R/C bridges of Egnatia Odos located at Polymylos and Kavala (Greece) for the cases of ambient and earthquake induced vibration measurements. Results provide qualitative and quantitative information on the dynamic behaviour of the systems and their components under different types of excitations. All modal identification methodologies presented in this work are implemented in user-friendly software, termed Modal Identification Tool (MITooL). The software which includes graphical user interface allows the full exploration and analysis of signals that are measured on a structure when it is excited by artificial, ambient or earthquake loads. A user manual is also presented which gives details for the operations and prospects of the MITooL software. Step-by-step examples of modal identification are presented to demonstrate the applicability of the software.
2009
This work addresses the problem of identifying the modal properties of structures using vibration measurements. Modal identification methodologies are proposed based on vibration measurements induced by artificial, ambient or earthquake loads applied on the structure. A modal model of the structure is identified using a weighted least-squares approach and measured time histories at selected locations of a structure. For artificially induced and ambient vibration measurements, the identification is performed in the frequency domain using respectively frequency response functions and cross power spectral densities. For earthquake induced vibrations, the identification is performed in both time and frequency domains. The modal identification methods presented in this work treat generalized non-classically damped modal models. The identification of the modal parameter (modal frequencies, modal damping ratios, modeshape components and modal participation factors) is accomplished by introducing a computationally very efficient three step approach as follows. In the first step, stabilization diagrams are constructed containing frequency and damping information. The modeshape components and participation factors are estimated in a second least-squares step, based on the user selection of the stabilized poles. The first two steps involve non-iterative procedures and result in solving linear algebraic systems of equations. Finally, in order to improve the estimation of the modal characteristics, especially for the challenging case of closely spaced and overlapping modes, a third step is introduced to solve a fully nonlinear optimization problem using available iterative gradient-based optimization algorithms. In this thesis, theoretical developments as well as software implementation issues are presented. The methodologies and software developed are applied for the identification of the modal characteristics of a small laboratory structure for the case of artificial induced vibration measurements, as well as the identification of the modal characteristics of three bridges, the under construction R/C bridge of Egnatia Odos located at Metsovo (Greece), and two other representative R/C bridges of Egnatia Odos located at Polymylos and Kavala (Greece) for the cases of ambient and earthquake induced vibration measurements. Results provide qualitative and quantitative information on the dynamic behaviour of the systems and their components under different types of excitations. All modal identification methodologies presented in this work are implemented in user-friendly software, termed Modal Identification Tool (MITooL). The software which includes graphical user interface allows the full exploration and analysis of signals that are measured on a structure when it is excited by artificial, ambient or earthquake loads. A user manual is also presented which gives details for the operations and prospects of the MITooL software. Step-by-step examples of modal identification are presented to demonstrate the applicability of the software.