AN APPROACH FOR WAVE VELOCITY-MEASUREMENT IN SOLID CYLINDRICAL RODS SUBJECTED TO ELASTIC IMPACT

Certain cross-sectional resonances of a long, solid, cylindrical rod, excited by transverse, elastic impact loading, may be measured by an e xperimental technique. The values of these resonance frequencies can b e predicted knowing the material characteristics of the rod, but it is of greater interest to inversely solve for the material characteristi cs of the tested material from the experimentally obtained frequency v alues, In the case of portland cement concrete testing specifically, t he bulk shear wave velocity of the material is important to know but d ifficult to measure. In this paper, the governing resonance equation w ill be manipulated and inverted, ultimately resulting in an expression of bulk shear wave velocity in terms pf the nth ordered resonance fre quency, Poisson's ratio, and cross-sectional solid. rod radius. The op eration is not tractable when performed symbolically, however, because of the presence of Bessel functions; therefore, this novel inversion will be achieved through the approximation of Bessel functions within the resonance equation with 2nd order Taylor series, resulting in a qu adratic equation in normalized resonance frequency Omega. The roots of the quadratic equation may then be solved explicitly, resulting in tw o symbolic expressions for Omega, one of which is selected as the appr opriate approximation. Manipulation of the selected root expression re sults in the desired symbolic expression for bulk shear wave velocity. With numerical examples from the literature, it is demonstrated that use of the series provides good approximation of the roots of the orig inal resonance equation across a significant span of coefficient value s and allows for sufficient inverse calculation of bulk shear wave vel ocity based on experimental results. The symbolic form of the inverted expression for bulk shear wave velocity is given in the Appendix. Cop yright (C) 1996 Elsevier Science Ltd.