Premium
Stochastic Response of a Continuous System with Stochastic Surface Irregularities to an Accelerated Load
Author(s) -
Schenk C.A.,
Bergman L.A.
Publication year - 2003
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200310214
Subject(s) - eigenfunction , mathematics , moment (physics) , mathematical analysis , boundary value problem , covariance , series expansion , surface roughness , series (stratigraphy) , kernel (algebra) , stochastic process , representation (politics) , eigenvalues and eigenvectors , physics , classical mechanics , paleontology , statistics , quantum mechanics , combinatorics , politics , political science , law , biology
The problem of calculating the second moment characteristics of the response of a general class of nonconservative linear distributed parameter systems with stochastically varying surface roughness, excited by a moving concentrated load, is investigated. In particular the case of an accelerated load is discussed. The surface roughness is modeled as a Gaussian stationary second order process. For the stochastic representation of the surface roughness a orthogonal series expansion of the covariance kernel, the so called Karhunen‐Loéve expansion, is applied. The resulting initial/boundary value problem is transformed by eigenfunction expansion into the modal state space. Second moment characteristics of the response are determined numerically by direct integration using a Runge‐Kutta method.