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- W2016345440 abstract "This paper deals with the longitudinal vibrations of a nonlinear rod. The nonlinearity is strong and of cubic type. The motion of the rod is described by a second-order strong nonlinear partial differential equation. The exact numerical solution is obtained. Four approximate analytical methods for solving the differential equation are developed: the eigenmode solutions are denoted by applying the known space or time distribution functions, respectively, the method based on invariant manifolds, and the method for optimizing the two-mode eigenfrequency solution. The analytical and numerical solutions are compared. The amplitude-time-position diagrams and amplitude-frequency diagrams are plotted." @default.
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- W2016345440 title "Nonlinear Longitudinal Vibrations of a Rod" @default.
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- W2016345440 doi "https://doi.org/10.1177/107754639900500601" @default.
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