Accession Number : AD0820244
Title : THE APPLICATION OF FOURIER ANALYSIS TO ONE DIMENSIONAL INITIAL VALUE PROBLEMS FOR VISCOELASTIC WAVE PROPAGATION.
Descriptive Note : Technical rept.,
Corporate Author : STANFORD UNIV CA DIV OF ENGINEERING MECHANICS
Personal Author(s) : Chang, Shih-Jung
Report Date : JUL 1967
Pagination or Media Count : 12
Abstract : For one dimensional viscoelastic free vibration the necessary and sufficient condition that this problem is an eigenvalue problem requires that the wave number k squared be real and positive. This suggests Fourier representation for initial value problems with k as its integration variable. If the form e to the i(kx plus omega t) power is assumed as the elementary component of the solution, then, for each fixed k, the equation of motion reduces to a polynomial frequency equation for a discrete viscoelastic model. The roots omega(k)'s of the polynomial equation provide a complete set of elementary propagation components. It may happen that certain of the components do not possess the property of propagation but only of decay. It may also happen that in a certain range of k the component does not propagate, but for some other range of k it does. These properties give physical insight concerning the propagation and decay of the different components for an arbitrary viscoelastic disturbance. (Author)
Descriptors : *BOUNDARY VALUE PROBLEMS), (*WAVE PROPAGATION, (*VISCOELASTICITY, WAVE PROPAGATION), (*FOURIER ANALYSIS, BOUNDARY VALUE PROBLEMS), VIBRATION, ATTENUATION, PARTIAL DIFFERENTIAL EQUATIONS, PROPAGATION, MECHANICAL WAVES.
Subject Categories : Numerical Mathematics
Radiofrequency Wave Propagation
Distribution Statement : APPROVED FOR PUBLIC RELEASE