Nonlinear longitudinal vibrations of an elastic inhomogeneous rod

A model describing nonlinear longitudinal vibrations of an elastic inhomogeneous rod is described by a second-order nonlinear differential equation. Using a group classification of this nonlinear differential equation, all the basic models with different symmetry properties are obtained. Some invari...

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Bibliographic Details
Main Authors: Chirkunov, Yu. A., Pikmullina, E. O.
Format: Conference Proceeding
Language:English
Subjects:
Boundary value problems
Exact solutions
Invariants
Nonlinear differential equations
Robotics
Online Access:Get full text
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Summary:A model describing nonlinear longitudinal vibrations of an elastic inhomogeneous rod is described by a second-order nonlinear differential equation. Using a group classification of this nonlinear differential equation, all the basic models with different symmetry properties are obtained. Some invariant submodels for these basic models are found. An exact solution is obtained that describes an invariant submodel of rank 0. For the two invariant submodels of rank 1, the factor equations describing them are obtained. For some values of the parameters defining these submodels, the boundary value problems with a physical meaning showing the specific features of the rod deformation were solved numerically. The relevance of the study is due to the use of the considered model for calculating beams in the design of construction objects, robotics and aeronautic.
ISSN:0094-243X
1551-7616
DOI:10.1063/5.0028754