Accession Number : ADA185625

Title :   The Paradoxical Asymptotic Status of Massless Springs,

Corporate Author : MARYLAND UNIV COLLEGE PARK DEPT OF MATHEMATICS

Personal Author(s) : Antman, Stuart S

PDF Url : ADA185625

Report Date : Mar 1987

Pagination or Media Count : 34

Abstract : The most fundamental problem in the entire theory of oscillations is to describe the motion of a mass point, the tip mass, attached to a spring. Within the classical theory of particle mechanics, the spring is regarded as massless, so that it serves only to transmit a force to the tip mass. This force typically depends on the position and velocity of the tip mass in perhaps a nonlinear way. In this case, the motion is governed by an autonomous ordinary differential equation. On the other hand, if the spring has mass, then its motion as a continuum is coupled to that of the tip mass. If the spring has a nonlinear constitutive equation, then the analysis of the resulting motion, governed by partial differential equations, can be formidable indeed. This paper studies the motion of both tip mass and spring when the mass density of the spring is small and when its constitutive equation describes nonlinearly elastic and viscoelastic materials. Although these constitutive equations do not account for past history, if its nevertheless proven that in the formal limit as the spring's mass density goes to zero the equation for the tip mass is an ordinary differential equation for elastic springs, but is generally not so for viscoelastic springs.

Descriptors :   *SPRINGS, *VISCOELASTICITY, DENSITY, DIFFERENTIAL EQUATIONS, ELASTIC PROPERTIES, EQUATIONS OF MOTION, EQUATIONS, MASS, MATERIALS, MECHANICS, NONLINEAR SYSTEMS, OSCILLATION, PARTIAL DIFFERENTIAL EQUATIONS, PARTICLES, THEORY

Subject Categories : Mechanics

Distribution Statement : APPROVED FOR PUBLIC RELEASE