Free vibration of SDOF systems with arbitrary time-varying coefficients
type: Item
instance of: scholarly article
title: Free vibration of SDOF systems with arbitrary time-varying coefficients
zbMATH Open document ID: 0996.70016
DOI: 10.1016/S0020-7403(00)00031-X
author: R. Smith
published in: International Journal of Mechanical Sciences
publication date: 2002-11-04T00:00:00Z
review text: The author presents a new exact approach for analyzing free vibrations of single-degree-of-freedom (SDOF) system with one-step and multi-step nonperiodically varying mass and stiffness coefficients. The variation of mass with time is arbitrary, but the variation of stiffness is connected by a functional dependence with the mass variation. Using an appropriate functional transformations, the author reduces the governing differential equation to Bessel equation or to an ordinary differential equation with constant coefficients for six important particular cases. In order to simplify the free vibration analysis for multi-step time-varying coefficients, the author constructs fundamental solutions that satisfy some normalization conditions. The displacement response of SDOF systems is then determined by using these fundamental solutions and a recurrence formula. Numerical examples show that the proposed procedure is simple, efficient and exact.
reviewed by: Vasile Marinca
Mathematics Subject Classification ID: 70J30
zbMATH DE Number: 1559218
zbMATH Keywords: time-varying mass coefficient
zbMATH Keywords: time-varying stiffness coefficient
zbMATH Keywords: Bessel equation
zbMATH Keywords: ordinary differential equation with constant coefficients
zbMATH Keywords: free vibration
zbMATH Keywords: fundamental solutions
zbMATH Keywords: normalization conditions
zbMATH Keywords: displacement response
zbMATH Keywords: recurrence formula
MaRDI profile type: Publication
Wikidata QID: Q127829962
description: scientific article; zbMATH DE number 1559218