Resonance measurements forced oscillations

There are several possible approaches to the measurement of dynamic properties using forced oscillation of the test piece and the methods can be classified in various ways. The first distinction is between forced vibration at or near resonance and forced vibration away from resonance, with measurements at frequencies away from resonance being by far the most common. 

Two unknowns require two measurements. For a free oscillator these measurements are the resonant frequency and the damping. For a forced oscillator the favored combination is the amplitude ratio and phase angle over a range of applied frequencies. This combination is not available for the evaluation of coatings because of the requirement that one surface be free. The two measurements described in the example below are damping and phase angle. 

Thus G and G are obtained by measuring /o. 00, and 8. The difficult quantity to determine is 8. The best method is to convert 0 into a voltage using a rotational transducer. The phase difference 8 between this voltage and the torque current can then be obtained by one of a number of precise electrical methods. This forced-oscillation technique is used most efficiently at frequencies somewhat remote from the resonant frequency of the system. 

ES, resonance electrostatic method FO, forced oscillation dynamic-mechanical analysis FV, free vibration TP, torsion pendulum TSC, thermally stimulated discharge current measurement D, dielectric VR, vibrating reed. 

Methods for measuring G (a) wave speed, (b) resonance, and (c) forced oscillations. AT is a geometry constant free. 

Force Microscope (EFM). Measurements can be performed under the application of a voltage between the sample and the tip. In the dc-EFM mode, a constant voltage is applied to the sample the AFM is operating in non contact mode with the cantilever oscillating near its resonant frequency. In the ac-EFM mode, the voltage is oscillating so that the cantilever always oscillates at its resonance frequency. 

BENDING OF A BEAM. The complex dynamic Young s modulus can be determined from the forced, non-resonant oscillations of a single or double cantilever beam. The apparatus considered in this paper is the Dynamic Mechanical Thermal Analyzer (DMTA) (6), manufactured by Polymer Laboratories, Inc. Figure 3 shows the experimental setup for the single cantilever measurement. A thin sample is clamped at both ends. One end is attached to a calibrated shaker through a drive shaft. 

The resonance method is useful when the data are required at only one frequency or at a small number of frequencies. In a typical device used to measure the dynamic tensile storage modulus, the rod, which has a circular or rectangular cross section, is hung by threads at nodal points. An oscillating force is applied at one end of the rod by means of a piezolectric transducer. The response is detected at the other end by a capacitive transducer. To achieve that, it is very convenient to paint the extremities of the rod in front of the transducers with cooloidal silver or another conductive paint. 

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