21 Experimental Techniques in Damping Randall D. Peters

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Mercer University

21.1 Electronic Considerations .................................................. 21-2

Sensor Linearity † Frequency Issues † Data Acquisition

21.2 Data Processing................................................................... 21-3

Language Type † Integration Technique † Fourier Transform

21.3 Sensor Choices .................................................................... 21-7

Direct Measurement † Indirect Measurement

21.4 Damping Examples............................................................. 21-8

Case 1: Vibrating Bar — Linear with Significant Noise †

Case 2: Vibrating Reed — Example of Nonlinear Damping †

Case 3: Seismometer † Case 4: Rod Pendulum with Photogate

Sensor † Case 5: Rod Pendulum Influenced by Material under

the Knife-Edge † Hard Materials with Low Q † Anisotropic

Internal Friction

21.5 Driven Oscillators with Damping ..................................... 21-19

MUL Apparatus † Driven Harmonic Oscillator

21.6 Oscillator with Multiple Nonlinearities ............................ 21-21

21.7 Multiple Modes of Vibration............................................. 21-24

The System † Some Experimental Results † Short Time

Fourier Transform † Nonlinear Effects — Mode Mixing

21.8 Internal Friction as Source of Mechanical Noise............. 21-28

21.9 Viscous Damping — Need for Caution ........................... 21-29

21.10 Air Influence ....................................................................... 21-31

Brass and Solder Rod Pendula

Summary

This chapter is a continuation of Chapter 20 and is concerned with practical experimental techniques for measuring

damping. It begins with a discussion of the requirements placed on electronics. After demonstrating the importance

of sensor linearity using a computer simulation, the issues of data acquisition and processing are addressed. The

power of the Fast Fourier Transform is illustrated, not just for spectral analysis, but also (in “short time” form) for

measuring the damping of each component when a system oscillates with multiple modes. Various sensor types are

discussed in relation to their advantages and disadvantages for specific applications through the treatment of

seven different systems studied in free decay. These seven cases differ with respect to factors such as

(i) eigenfrequency, (ii) material type, and (iii) method of estimating the logarithmic decrement, and thus the Q

of the decay. In the case of some solids, damping is shown to result largely from defects in the structures. A powerful

test for nonlinear damping is demonstrated: simply looking at a graph of Q to see whether it changes with time. Two

examples of driven oscillators are given. The first being very nearly linear, and the second being highly nonlinear,

due to an anharmonic restoring force involving magnets plus several simultaneously acting damping mechanisms.

The nonlinear system is used to illustrate difficulties in interpretation that can arise in driven systems due to

21-1

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phenomena such as frequency and/or amplitude jumps involving hysteresis. Then an illustration is given of how

elastic-type nonlinearities may couple with damping-type nonlinearities in order to determine which modes of a

complex system survive during the transient approach to steady state. Mechanical noise, another important feature

of nonlinear damping, is also examined. The magnitude of the 1=f character in an evacuated pendulum is shown to

decrease with time, as the oscillator is allowed to stabilize against creep. The final sections address the common

misconception that viscous air friction is the most important form of mechanical oscillator damping. Cases are

chosen to demonstrate that (i) internal friction is nearly always also important, if not the most important, and

moreover, that (ii) fluid damping is rarely simple — involving the density as well as the viscosity of the fluid. It is

shown that damping has a complicated frequency dependence, as opposed to the simple (overly idealized) form

predicted by common theory.

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