scholarly journals Nonlinear forced oscillations of an unsymmetrical shaft and an unsymmetrical rotor with quartic nonliearity. 2nd report. Variations of resonance curves of summed-and-differential harmonic and super-summed-and-differential harmonic oscillations and the occurrence of unstable vibrations.

1988 ◽  
Vol 54 (506) ◽  
pp. 2448-2454
Author(s):  
Takashi IKEDA ◽  
Yukio ISHIDA ◽  
Toshio YAMAMOTO
1955 ◽  
Vol 22 (1) ◽  
pp. 107-110
Author(s):  
T. C. Huang

Abstract In this paper an investigation is made of equations governing the oscillations of a nonlinear system in two degrees of freedom. Analyses of harmonic oscillations are illustrated for the cases of (1) the forced oscillations with nonlinear restoring force, damping neglected; (2) the free oscillations with nonlinear restoring force, damping neglected; and (3) the forced oscillations with nonlinear restoring force, small viscous damping considered. Amplitudes of oscillations and frequency equations are derived based on the mathematically justified perturbation method. Response curves are then plotted.


2020 ◽  
Vol 11 (3) ◽  
pp. 181-186
Author(s):  
Yu. V. Chovnyuk ◽  
◽  
I. M. Sivak ◽  

The analysis of forced oscillations and waveformations of heavy ropes of hoisting mechanisms of cranes in the processes of starting the latter is carried out. The main parameters of the resulting waveforms in the ropes for different ways of lifting the load ("with a pickup", "by weight") are determined. The influence of gravity on the rope and the longitudinal oscillations arising in it, as well as on the longitudinal waveforms arising inside it are investigated. The rope of the lifting mechanism, in this case, is considered as a tensile rod. The laws of motion of cross-sections of ropes are established, according to which the forces arising in ropes are minimized during the startup of hoisting mechanisms of cranes. The application of the integrodifferential equation, which adequately describes the oscillations of the rope system of cargo cranes, and also takes into account the frequencyindependent internal friction in these systems, which accompanies the oscillatory processes in the ropes during transient reagents for their differentiation by different ways of lifting loads. The parameters of the established harmonic oscillations of the rope system of cranes for long-term lifting of the load and taking into account the inertial properties of the rope (considerable length), as well as the magnitude of the static movement of the rope (for different ways of lifting loads) are determined.


Author(s):  
Yukio Ishida ◽  
Imao Nagasaka ◽  
Seongwoo Lee

Abstract Harmonic resonances and subharmonic resonances of order 1/2 and order 1/3 in a continuous rotating shaft with distributed mass are discussed. The restoring force of the shaft has geometric stiffening nonlinearity due to the extension of the shaft center line. It is supposed that a distributed bias force, such as the gravity, works. The possibility of their occurrences, the shapes of resonance curves, and internal resonance phenomena are investigated.


Author(s):  
M.I. Vaskovskyi ◽  
A. B. Struk ◽  
M. V. Makoviichuk ◽  
I. P. Shatskyi

The article discusses the issues of forecasting the strength of underground pipelines laid in seismically active areas through sections composed of relatively rigid moving blocks. In such dangerous areas, in addition to the normal pressure load of the transported product, the pipe is subjected to additional effects from the movements of the fragments of the block foundation. As the literature data show, the problems of the influence of the interaction of faults on the stress state of the pipeline have not yet been studied. The aim of the study is to develop a model for the analysis of abnormal stresses in the underground pipeline on a damaged foundation caused by static or time-harmonic reciprocal turns of the blocks around the axis of the pipe on both sides of several faults. Static equilibrium and harmonic oscillations of the pipeline are investigated in a linear setting, modelling it with a rod with an annular cross section. The inertia of the transported product is not taken into account. To consider the issues of the ultimate equilibrium of the pipe, the momentless theory of shells and the energy theory of strength are used. The soil backfill is considered as Winkler’s elastic layer. Multiple damages to the solid foundation are presented in the form of several faults on which there is a rupture of the angle of rotation around the axis of the pipe. We formulated boundary value problems for differential equations of static torsion and torsional harmonic oscillations with discontinuous right-hand sides. Based on the analytical solutions of these problems for the cases of antisymmetric and symmetrical reversal of the foundation blocks, the distributions of the torsion angle and equivalent stress in the pipe, depending on the distance between faults and the frequency of forced oscillations of the system, are investigated.


Author(s):  
I.P. POPOV

It is noted that the traditional calculation of mechanisms in forced oscillations is often a difficult task. Most often, calculators are interested in steady-state oscillation modes. The aim of the work is to significantly simplify the calculations by replacing the need to solve differential equations with algebraic methods. A similar approach is widely used in electrical engineering. The use of a symbolic (complex) description of mechanical systems under forced harmonic oscillations (in the steady state) made it possible to abandon the extremely cumbersome and time-consuming calculation algorithm associated with solving differential equations and replace it with simple and clear algebraic operations. Due to this, the calculation time is reduced significantly. Vector diagrams, not being a necessary component of the study of mechanical systems, have significant methodological significance, since they show quantitative and phase relationships between the parameters of systems.


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