scholarly journals THE NONLINEAR EQUATIONS OF MOTION OF SHELLS OF REVOLUTION : NONLINEAR VIBRATIONS OF SHELLS OF REVOLUTION PART 1.

1979 ◽  
Vol 281 (0) ◽  
pp. 21-30
Author(s):  
YOUICHI MINAKAWA
Keyword(s):  
Nonlinear Equations ◽  
Nonlinear Vibrations ◽  
Equations Of Motion ◽  
Shells Of Revolution ◽  
Nonlinear Equations Of Motion

A New Displacement Form for the Nonlinear Equations of Motion of Shells of Revolution

1985 ◽  
Vol 52 (3) ◽  
pp. 507-509 ◽  
Author(s):  
J. G. Simmonds
Keyword(s):  
Boundary Conditions ◽  
Nonlinear Equations ◽  
Equations Of Motion ◽  
Shells Of Revolution ◽  
Governing Equations ◽  
Hoop Strain ◽  
Axisymmetric Motion ◽  
Nonlinear Equations Of Motion ◽  
Surface Loads ◽  
Theory Of Shells

In the theory of shells of revolution undergoing torsionless, axisymmetric motion, an extensional and a bending hoop strain are introduced that are linear in the displacements, regardless of the magnitudes of the strains and the meridional rotation. The resulting equations of motion and boundary conditions are derived and some common conservative surface loads are listed along with their potentials. The governing equations appear to be the simplest possible in terms of displacements.

scholarly journals Динамика трехкомпонентной делокализованной нелинейной колебательной моды в графене

2019 ◽  
Vol 61 (11) ◽  
pp. 2163
Author(s):  
С.А. Щербинин ◽  
М.Н. Семенова ◽  
А.С. Семенов ◽  
Е.А. Корзникова ◽  
Г.М. Чечин ◽  
...  
Keyword(s):  
Molecular Dynamics ◽  
Nonlinear Equations ◽  
Nonlinear Vibrations ◽  
Vibrational Mode ◽  
Equations Of Motion ◽  
Graphene Lattice ◽  
Nonlinear Equations Of Motion ◽  
Low Amplitude ◽  
Upper Boundary

AbstractThe dynamics of a three-component nonlinear delocalized vibrational mode in graphene is studied with molecular dynamics. This mode, being a superposition of a root and two one-component modes, is an exact and symmetrically determined solution of nonlinear equations of motion of carbon atoms. The dependences of a frequency, energy per atom, and average stresses over a period that appeared in graphene are calculated as a function of amplitude of a root mode. We showed that the vibrations become periodic with certain amplitudes of three component modes, and the vibrations of one-component modes are close to periodic one and have a frequency twice the frequency of a root mode, which is noticeably higher than the upper boundary of a spectrum of low-amplitude vibrations of a graphene lattice. The data obtained expand our understanding of nonlinear vibrations of graphene lattice.

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