An examination of the concept of driving point receptance. (28th April 2018)

• Record Type: Journal Article
• Authors: Sheng, X.; He, Y.; Zhong, T.
• Is Part Of: Journal of sound and vibration. Volume 420(2018)
• Page Start: 185
• Page End: 203
• Publication Date: 2018-04-28
• Subjects: Driving point receptance -- Driving point mobility -- FE mesh density effect -- Wheel/rail interaction; Sound -- Periodicals; Vibration -- Periodicals; Son -- Périodiques; Vibration -- Périodiques; Sound; Vibration; Periodicals; Electronic journals; 620.205
• DOI: 10.1016/j.jsv.2018.01.042
• Languages: English
• ISSNs: 0022-460X

Abstract

Abstract: In the field of vibration, driving point receptance is a well-established and widely applied concept. However, as demonstrated in this paper, when a driving point receptance is calculated using the finite element (FE) method with solid elements, it does not converge as the FE mesh becomes finer, suggesting that there is a singularity. Hence, the concept of driving point receptance deserves a rigorous examination. In this paper, it is firstly shown that, for a point harmonic force applied on the surface of an elastic half-space, the Boussinesq formula can be applied to calculate the displacement amplitude of the surface if the response point is sufficiently close to the load. Secondly, by applying the Betti reciprocal theorem, it is shown that the displacement of an elastic body near a point harmonic force can be decomposed into two parts, with the first one being the displacement of an elastic half-space. This decomposition is useful, since it provides a solid basis for the introduction of a contact spring between a wheel and a rail in interaction. However, according to the Boussinesq formula, this decomposition also leads to the conclusion that a driving point receptance is infinite (singular), and would be undefinable. Nevertheless, driving point receptances have been calculated using different methods. Since the singularity identified in this paper was not appreciated, no account was given to the singularity in these calculations. Thus, the validity of these calculation methods must be examined. This constructs the third part of the paper. As the final development of the paper, the above decomposition is utilised to define and determine driving point receptances required for dealing with wheel/rail interactions. Highlights: Decomposition of the displacement of an elastic body near a point harmonic force into a half-space part and a second part. Revelation of a singularity in driving point receptance of any elastic body. Demonstration of non-convergence of driving point receptance calculated with solid FE elements. A procedure to better define and estimate driving point receptances required for wheel/rail interaction.