On harmonic vibrations out of phase with the exciting force

✍ Scribed by Fritz John

• Publisher: John Wiley and Sons
• Year: 1948
• Tongue: English
• Weight: 661 KB
• Volume: 1
• Category: Article
• ISSN: 0010-3640
• DOI: 10.1002/cpa.3160010403

✦ Synopsis

This paper is concerned with the solutions of a differential equation of the type

(1)

Here it is assumed that the function F(r, z ) is defined and of class C2 in the strip

, -1 5 2 I + I and satisfies there the inequalities (2) F, < 0 , F , > k > 0 with a certain fixed k. It is also assumed that 'Erxwungene Schwingungen mit verdnderlicher Eigenfrequenz, Brnunarhweig, 1918. For a general discussion of nonlinear vibrations the reader is referred to the paper by K. 0. Friedrichs nnd J. J. Stoker, Forced Vibrations of Systems wilh Nonlinear Resturing Force, Quarterly of Applied Mathematics, Volume I, pp. 97-115, 1943. *See Friedrichs-Stoker, loc. tit., p. 102. SSimilnr results for equations of the form (4) were obtained by the author in n previous paper, published in Studies in Nonlinear Vibrations, Institute for Mathematics and Mechanics, New York University, 1946. The present presentation is much Riinpler and lends to more general results than the one given there.