S. L. Skalozub

CALCULATING RESONANT FREQUENCIES OF AXISYMMETRIC OSCILLATIONS OF ISOTROPIC CYLINDRICAL RODS

Resonant longitudinal-transverse axisymmetric oscillations of cylindrical rods made of isotropic materials are analytically studied in accordance with the Pochhammer–Chree theory and the proposed hypothesis that there are no shear stresses at the rod ends during resonance due to reflection of standing shear surface waves attenuating as they move away from the end surface. Correlations relating dimensionless resonant frequencies to the geometric dimensions of the rods and the dynamic characteristics of the material (Poisson’s ratio and shear wave velocity) are presented in a form convenient for calculation. The developed algorithms and calculation programs are used to evaluate, by means of a personal computer and/or a desktop calculator, and tabulate the resonance frequencies of the first and second oscillation modes at different fixed values of Poisson’s ratio within 0.20–0.45 with a step of 0.05 and at discrete values of the rod length-to-diameter ratio within 0.9–5.0 with a step of 0.1. The frequency values are represented as seven-digit numbers with six digits after the decimal point. The evaluation of methodological errors in the calculation of resonant frequencies by comparison with the known results obtained by the Rayleigh–Ritz method reveals their fairly high agreement. The proposed procedure is used to calculate the instrumental errors in the determination of the dynamic characteristics of the material with respect to the experimental data found in the available literature.

Acknowledgment: I am grateful to R. S. Skalozubs for his assistance in the search and delivery of the necessary literature, to A. S. Skalozubs for the computer support of the preparation and formatting of the manuscript and to M. A. Skalozubs for compiling the program and performing calculations using a personal computer.

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