Irregular vibrations in multi-mass discrete-continuous systems torsionally deformed

Abstract

In the paper irregular vibrations of discrete-continuous systems consisting of an arbitrary number rigid bodies connected by shafts torsionally deformed are studied. In the systems a local nonlinearity described by the polynomial of the third degree is introduced. It is assumed that the characteristic of the local nonlinearity is of a hard type. Governing equations are solved using the wave approach leading to equations with a retarded argument. Exemplary numerical calculations are done for the three-mass system. The possibility of occurring of irregular vibrations is discussed on the basis of the Poincaré maps, bifurcations diagrams and the exponents of Lyapunov.

Chaotic Vibrations in Multi-Mass Discrete-Continuous Systems Torsionally Deformed with Local Nonlinearities

“…Exemplary investigations are performed for a three-mass system, shown in Fig. 1, assuming the following dimensionless parameters, similarly as in [12,13]…”

“…When damping is small, irregular vibrations including chaotic vibrations one can observe in the discussed system. The possibilities of occurring irregular vibrations are seen in bifurcations curves given for the three-mass system in papers [12,13] for damping coefficients equal to…”

“…The studied system is a discrete-continuous system, so the required quantities can be determined in different cross-sections. In papers [12,13] the numerical results are presented mainly for the cross-section x = 0, separately for the hard characteristics case and for the soft characteristics case.…”

“…0 3  k and with 0 d = 0.001, 0 M = 1. From [13] it follows that chaotic vibrations can be expected for p < 1.2, so in Fig. 2 the Poincaré maps are plotted out for four selected values of the frequency p smaller than 1.2.…”

“…Irregular vibrations, including chaos, are studied in the technical literature mainly for discrete models, [3][4][5][6][7][8][9][10][11]. In [12,13] some attempts are done for the investigation of irregular vibrations in discrete-continuous systems after the adaptation the approach used in [8][9][10]. The aim of the present paper is to widen the results given in [12,13] for the both types of the characteristics of local nonlinearities in multi-mass systems torsionally deformed.…”