David A. Brown
Phys. Dept., Code PH/Br, Naval Postgraduate School, Monterey, CA 93943
The technique of using the resonant modes of a ``free--free'' bar to determine the elastic properties of the bar material will be described. A bar can be electrodynamically and selectively excited in three independent vibrational modes by mounting small coils of magnet wire on each end of the sample. When the sample ends are placed in a magnetic field, a current through one coil will induce vibrations that can be detected by monitoring the emf produced in a second coil. The elastic shear modulus is determined by measuring the frequency of the torsional mode. The Young's modulus is determined from the frequency of either the longitudinal or flexural mode. The loss tangent, tan (delta), of the material can be obtained by measuring the quality factor of each resonance. Results from a sample using a transfer function technique will be compared with results obtained using a phase-locked loop (PLL). The transfer function technique is convenient, since the voltage across the detection coil is proportional to the velocity of the sample and the current delivered to the excitation coil is proportional to the force delivered to sample. Their ratio is proportional to the impedance of the material. The lock-in method is attractive because it offers a means to continuously monitor the properties of the material.