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Session 3226

Data Sampling Techniques for Fourier Analysis John Hartin, Kenneth Belanus University of Pittsburgh at Johnstown/Oklahoma State University

Abstract

Fourier analysis methods and data sampling techniques are introduced in two laboratory courses in the Mechanical Engineering Technology curriculum. Data acquisition with personal computer hardware permits high speed sampling and analysis of large quantities of data obtained from various transducers, strain gages, and accelerometers. Data sampling methodology determines the efficacy of the results. Sampling frequency and the number of data points acquired strongly influence the resolution of frequencies and their amplitudes in the spectra calculated for a signal. The use of simple laboratory structures for which experimental and analytical frequencies are readily obtained enhances the understanding of vibrations, data sampling, and interpretation of Fourier analysis results. Since structural vibrations may produce closely spaced harmonics, an understanding of the presented method is critical for a priori determination of frequency resolution.

Introduction

Much can be learned about the characteristics of a vibrating structure by experimental determination of dynamic strains or kinematics. Often, extremely high loads can exist due to impact loading or excitation of a structure near one of its resonant frequencies. High speed data acquisition with personal computer hardware permits sampling and analysis of large quantities of data from strain gages or accelerometers for comparison to an appropriate model or verification of a finite element analysis. Fourier analysis provides a powerful tool for obtaining both a qualitative and quantitative understanding the dynamic behavior of a structure.

In the Mechanical Engineering Technology program at the University of Pittsburgh at Johnstown (UPJ), the techniques and application of data acquisition and analysis are taught in a sequence of courses intended to produce a student capable of acquiring and manipulating appropriate, useable, quantities of high-speed data from a transducer. There are pitfalls in data taking and interpretation that can be identified, and the methodology can be tailored to provide optimum results. In the course sequence, the basic techniques of Fourier analysis are introduced, and a methodology for data acquisition suited to optimizing the usefulness of the resulting frequency spectrum is presented. Classroom examples from the authors’ laboratory and professional experiences illustrate the methods, problems, and outcomes.

Background

Data acquisition of experimental measurements results in a set of sampled data at regularly spaced times as illustrated in Figure 1. The continuous analog signal x(t) from a transducer is fed through an analog to digital converter to give discrete values of xi(t) at discrete times t=i∆, where ∆ is the sampling interval (generally dependent on the data acquisition hardware), and i = 1,2,...,N where N is the total number of samples. Analysis can now be conducted on the sampled data to determine its characteristics. In many mechanical and structural applications, the primary interest is the frequency content of the signal and the magnitude and location of the system resonances. To accomplish this, the signal is converted from the time domain to the frequency domain.

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Belanus, K., & Hartin, J. (1997, June), Data Sampling Techniques For Fourier Analysis Paper presented at 1997 Annual Conference, Milwaukee, Wisconsin. 10.18260/1-2--6487