Accession Number : ADA185548
Title : Steady Waves in a Nonlinear Theory of Viscoelasticity.
Descriptive Note : Doctoral thesis,
Corporate Author : AIR FORCE INST OF TECH WRIGHT-PATTERSON AFB OH
Personal Author(s) : Warhola, Gregory T
PDF Url : ADA185548
Report Date : Jan 1987
Pagination or Media Count : 136
Abstract : This work considers the propagation of steady waves in viscoelastic material for which the nonlinear strain measure is not necessarily convex. The shape of such a wave is governed by an ordinary nonlinear integro-differential equation having a possibly singular difference kernel. The existence and structure of a solution depends upon the relation of the wavespeed, a parameter in the problem, to two speeds based upon the state of the material ahead of the wave. Solutions are constructed by a monotone iterative scheme which is proven to converge to a unique solution within restricted classes of functions depending upon the wavespeed. A simple numerical approximation to the iterative scheme is used to produce graphs of solutions. An algebraic quasielastic approximation produces upper bounds on discontinuous ( shock and acceleration wave) solutions. For a material such as polymethyl methacrylate (pmma) having a small power in a power-law model of its compliance, this approximation is found to be useful for accurately predicting the structure of shock solutions.
Descriptors : *POLYMETHYL METHACRYLATE, *VISCOELASTICITY, ACCELERATION, APPROXIMATION(MATHEMATICS), FINITE DIFFERENCE THEORY, GRAPHS, INTEGRAL EQUATIONS, ITERATIONS, NONLINEAR DIFFERENTIAL EQUATIONS, NONLINEAR SYSTEMS, POWER, SHOCK, SOLUTIONS(GENERAL), STEADY STATE, THEORY, VELOCITY, WAVE PROPAGATION, WAVES, SHOCK WAVES, STRAIN(MECHANICS), KERNEL FUNCTIONS, THESES
Subject Categories : Mechanics
Distribution Statement : APPROVED FOR PUBLIC RELEASE