This three-day, on-site, course is intended to introduce engineers and other technical personnel to the fundamentals of making shock and vibration measurements and to the use of Matlab to analyze and interpret the measured vibratory data. Practical demonstrations are presented on the use of accelerometers and related data acquisition instrumentation. Emphasis is placed on a student being able to understand the basics of Matlab programing and the use of the Matlab  “Signal Processing Toolbox” and the Matlab “Data Acquisition Toolbox.”   Applications relevant to the class participants are demonstrated and discussed. (This course would also benefit those involved in sound measurement and analysis, as well as those interested in learning about Matlab and its Toolbox applications.)


The goal of this course is for students to:

  1. Understand the fundamental principles upon which vibration analysis is based.
  2. Select and use accelerometers for shock and vibration measurement.
  3. Learn to use a digital Data Acquisition system (DAQ) to record vibration signals.
  4. Learn to use Matlab, including its Signal Processing and Data Acquisition Toolboxes, to:
    1. Perform basic mathematical calculations
    2. Perform filter and spectral analysis of recorded vibration signals
    3. Display and document analysis results
    4. Import raw measurement (signal) data and digitally store analysis results

Each participant receives a copy of the instructor’s course notes, including a CD containing all Matlab examples and appropriate reference articles, as well as a copy of the textbook: Getting Started with MATLAB  by Radra Pratap.  



Schedule of Topics:

Day 1:  Fundamentals of Vibration

  1. Introductory Concepts.   Review of signal types (periodic, random, etc.). Amplitude measurements.  Frequency and Fourier series (time and order based).  Types of frequency spectra (narrowband, PSD, CPBW). Measures of vibration (displacement, velocity, acceleration, and jerk).  Review decibels and complex numbers.
  2.  Shock and Vibration Transducer.   Review of vibration sensors (accelerometers, laser vibrometers, etc.).  Accelerometer types and signal conditioning.  Accelerometer amplitude and frequency response.  Accelerometer mounting considerations.
  3. Digital Signal Acquisition.   Digitization considerations.  Dynamic range resolution. Sampling frequency and aliasing.  Description and operation Data Acquisition systems (DAQ).


Day 2: Digital Signal Processing and Matlab Basics

  1. Frequency Spectra. Sampling relationships: frequency range and resolution. Fourier Series and DFT/FFT (amplitude and phase considerations). Power spectra (PS) periodogram and power spectra density (PSD). Calculation of PS from Fourier Series and DFT. Windowing and leakage. The "picket fence effect." Averaging and errors in PS and PSD.
  2. Time and Frequency Analysis: Time-domain functions. Time-frequency analysis. Frequency Response Functions (FRF). Digital filter characteristics (phase and time delays): Finite Impulse Response (FIR) and Infinite Impulse Response (IIR).
  3. Matlab Basics. Overview of Matlab using interactive demonstrations and/or experiments. Matlab workspace and variables and calculation syntax. Basic graphics. Procedures for importing and storing data.


Day 3: Matlab Applications and Examples

  1. Data Acquisition and Pre-Processing. Operating the DAQ and acquiring data using the Mathlab "Data Acquisition Toolbox." Importing and preparing data files for analysis using the Mathlab "Signal Processing Toolbox."
  2. Vibration Analysis using Matlab. Filter analysis techniques and commands. Demos of vibration data using IIR and FIR filters. Matlab FDATOOL for filter design and analysis. Examples of Matlab spectral analysis techniques and commands including periodograms and spectrograms.
  3. Selected Examples and Demonstrations. Matlab M-files will be provided to demonstrate the following: Stationary complex periodic and broadband (CPBW) autospectra; Transient ESD. Rotating machinery order analysis; Bandpass filtering analysis; Time integral and time-frequency analysis; Other Matlab applications based on discussions with the client.

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