Vibration of a periodically supported beam on an elastic half-space
type: Item
instance of: scholarly article
title: Vibration of a periodically supported beam on an elastic half-space
zbMATH Open document ID: 0978.74035
DOI: 10.1016/S0997-7538(99)00141-2
published in: European Journal of Mechanics. A. Solids
publication date: 2002-01-31T00:00:00Z
review text: The authors consider the actual problem of steady-state vibrations of a periodically supported beam on an elastic half-space under a uniformly moving harmonically varying load. Such models are common for the description of railroad track. The rail is simulated as a beam, while supports reflect the properties of pads, sleepers, and track subsoil. Three-dimensional subsoil is replaced by a set of springs with a frequency-dependent stiffness. The stiffness has an imaginary part and is derived using Fourier transform. The existence of zeros of the equivalent stiffness means that there exists a critical regime of motion. For example, if the beam is subjected to a moving constant load and the velocity of motion tends to the velocity of Rayleigh waves, the steady-state beam displacements become infinite. This effect is of practical importance for high-speed trains, especially if the track subsoil is soft and the velocity of Rayleigh waves is about 200 km/h.
Mathematics Subject Classification ID: 74H45
Mathematics Subject Classification ID: 74K10
zbMATH DE Number: 1443066
zbMATH Keywords: springs with frequency-dependent stiffness
zbMATH Keywords: steady-state vibrations
zbMATH Keywords: periodically supported beam
zbMATH Keywords: elastic half-space
zbMATH Keywords: uniformly moving harmonically varying load
zbMATH Keywords: railroad track
zbMATH Keywords: track subsoil
zbMATH Keywords: Fourier transform
zbMATH Keywords: critical regime of motion
zbMATH Keywords: Rayleigh waves
zbMATH Keywords: high-speed trains
author: A. V. Metrikine
author: Karl Popp
reviewed by: Yuri N. Sankin
MaRDI profile type: Publication
full work available at URL: s0997-7538(99)00141-2
OpenAlex ID: W2042328936
description: scientific article; zbMATH DE number 1443066