NDLI: Quadratically Nonlinear Cylindrical Hyperelastic Waves: Derivation of Wave Equations for Axisymmetric and Other States

Content Provider	Springer Nature Link
Author	Rushchitsky, J. J.
Copyright Year	2005
Abstract	A rigorous approach of nonlinear continuum mechanics is used to derive nonlinear wave equations that describe the propagation and interaction of hyperelastic cylindrical waves. Nonlinearity is introduced by means of metric coefficients, the Cauchy—Green strain tensor, and the Murnaghan potential and corresponds to the quadratic nonlinearity of all basic relationships. Quadratically nonlinear wave equations are derived for three states (configurations): (i) axisymmetric configuration dependent on the radial and axial coordinates and independent of the angular coordinate, (ii) configuration dependent on the angular coordinate, and (iii) axisymmetric configuration dependent on the radial coordinate. Four ways of introducing physical and geometrical nonlinearities to the wave equations are analyzed. Six different systems of wave equations are written
Starting Page	646
Ending Page	656
Page Count	11
File Format	PDF
ISSN	10637095
Journal	International Applied Mechanics
Volume Number	41
Issue Number	6
e-ISSN	15738582
Language	English
Publisher	Kluwer Academic Publishers-Consultants Bureau
Publisher Date	2005-01-01
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	nonlinear continuum mechanics rigorous approach nonlinear hyperelastic cylindrical waves quadratically nonlinear wave equations geometrical and physical nonlinearities axisymmetric state Applications of Mathematics Mechanics
Content Type	Text
Resource Type	Article
Subject	Mechanics of Materials Mechanical Engineering

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