Variations in steepness of the probability density function of beam random vibration
type: Item
instance of: scholarly article
title: Variations in steepness of the probability density function of beam random vibration
zbMATH Open document ID: 0992.74041
DOI: 10.1016/S0997-7538(00)00166-2
author: Alexander Steinwolf
author: N. S. Ferguson
author: Robert G. White
published in: European Journal of Mechanics. A. Solids
publication date: 2000-09-04T00:00:00Z
review text: The authors consider nonlinear random vibrations of a clamped-clamped beam. The large deflections of the beam are simulated taking into account the axial stretching forces. The governing partial differential equation is derived using the Euler-Bernoulli theory and neglecting rotary inertia and shear deformation when curvature in bending is small. By applying Galerkin method, ignoring in-plane effects, and expanding the flexural deflection in eigenfunction series, the authors reduce the corresponding initial-boundary value problem to a set of nonlinear ordinary differential equations. The differential equations are solved by Runge-Kutta method. As an application, the authors study different random vibrations by applying a random non-Gaussian concentrated force at the middle point of the beam.
Mathematics Subject Classification ID: 74H50
Mathematics Subject Classification ID: 74K10
Mathematics Subject Classification ID: 74H15
zbMATH DE Number: 1462589
zbMATH Keywords: nonlinear random vibrations
zbMATH Keywords: clamped-clamped beam
zbMATH Keywords: axial stretching
zbMATH Keywords: Euler-Bernoulli theory
zbMATH Keywords: Galerkin method
zbMATH Keywords: flexural deflection
zbMATH Keywords: eigenfunction series
zbMATH Keywords: initial-boundary value problem
zbMATH Keywords: nonlinear ordinary differential equations
zbMATH Keywords: Runge-Kutta method
zbMATH Keywords: random non-Gaussian concentrated force
reviewed by: Yuri N. Sankin
MaRDI profile type: Publication
full work available at URL: s0997-7538(00)00166-2
OpenAlex ID: W2037858804
description: scientific article; zbMATH DE number 1462589