Torsional Vibrations of a Multi-Rotor System Having a Non-Linear Flexible Coupling

1957 ◽  
Vol 61 (563) ◽  
pp. 779-781
Author(s):  
S. Mahalingam
Keyword(s):  
Forced Vibration ◽  
Elastic Characteristic ◽  
Approximate Solutions ◽  
Forced Vibrations ◽  
Rotor System ◽  
Torsional Vibrations ◽  
Flexible Coupling ◽  
Free And Forced Vibrations ◽  
Non Linear ◽  
Nonlinear Elastic

The free and forced vibrations of a multi-rotor system where one section of the shaft has a nonlinear elastic characteristic are considered in this paper. For any frequency of steady vibration the system is reduced to an equivalent rotor at either end of the nonlinear section. The vibrations at all points are assumed to be one-term approximate solutions and the amplitudes of steady forced vibration are determined by a method outlined by the author in an earlier paper.

scholarly journals FREE AND FORCED VIBRATIONS OF SHELLS OF VARIOUS SHAPES, TAKING INTO ACCOUNT THE VARIABILITY OF THE NON-LINEAR ELASTIC MATERIAL

2020 ◽  
Vol 3 (1) ◽  
pp. 70-75
Author(s):  
I. Sadygov
Keyword(s):  
Elastic Material ◽  
Oil And Gas ◽  
Oil And Gas Industry ◽  
Forced Vibrations ◽  
Relative Deformation ◽  
Dimensionless Frequency ◽  
Building Structures ◽  
Space Technology ◽  
Free And Forced Vibrations ◽  
Nonlinear Elastic

the article considers issues of shell vibrations, which are widely used in various industries and construction. Shells serve as elements of building structures with large spans. The chapter “Introduction” discussed issues related to the use of shells in all areas of industry, in aviation, rocket and space technology, railway transport, in the oil and gas industry and provides examples of shells for use in ceilings of circuses, stations, hangars; in industry: shells of rotation used as tanks, containers, columns, reactors, etc. In the section “Materials and research methods” free and forced vibrations of shells of variable thickness made out of nonlinear elastic material reviewed. In shell calculations the Kirchhoff – Law hypothesis was used. It was found that, during vibrations, the shells experience relative deformation of elongation and shear of the surface with coordinates (x, y), as well as bending and torsion strains. It is established that vibrations in the shells lead to a rotation of the main directions of elasticity and regarding to the adopted coordinate axis to angle θ, and the elastic constants of the material depend on the elastic constant Biy – the main directions of the nonlinear elastic shells. When solving the system of equations of motion of the shell relative to the displacements arising in it during vibration, based on theory R and various methods. The values of the dimensionless frequency parameter for a spherical shell taking into account changes in its curvature, variability and thickness of elastic properties are obtained.

scholarly journals A Multimode Approach to Geometrically Nonlinear Free and Forced Vibrations of Multistepped Beams

2021 ◽  
Vol 2021 ◽  
pp. 1-18
Author(s):  
Issam El Hantati ◽  
Ahmed Adri ◽  
Hatim Fakhreddine ◽  
Said Rifai ◽  
Rhali Benamar
Keyword(s):  
Approximate Method ◽  
Forced Vibration ◽  
Algebraic System ◽  
Strain Energy ◽  
Dynamic Behaviour ◽  
Forced Vibrations ◽  
Geometrical Parameters ◽  
Geometrically Nonlinear ◽  
Free And Forced Vibrations ◽  
Nonlinear Algebraic System

The scope of this study is to present a contribution to the geometrically nonlinear free and forced vibration of multiple-stepped beams, based on the theories of Euler–Bernoulli and von Karman, in order to calculate their corresponding amplitude-dependent modes and frequencies. Discrete expressions of the strain energy and kinetic energies are derived, and Hamilton’s principle is applied to reduce the problem to a solution of a nonlinear algebraic system and then solved by an approximate method. The forced vibration is then studied based on a multimode approach. The effect of nonlinearity on the dynamic behaviour of multistepped beams in the free and forced vibration is demonstrated and discussed. The effect of varying some geometrical parameters of the stepped beams in the free and forced cases is investigated and illustrated, among which is the variation in the level of excitation.

Forced Vibration of Rotor Suppressed by a Automatic Ball Balancer (Nonlinear Principal Resonances)

2013 ◽  
Vol 655-657 ◽  
pp. 551-557
Author(s):  
Xiao Long Zhang ◽  
Ya Bin Dong ◽  
Yu Min He ◽  
Mei Juan Tong
Keyword(s):  
Forced Vibration ◽  
High Speed ◽  
Rotor System ◽  
Restoring Force ◽  
Rotor Systems ◽  
Jeffcott Rotor ◽  
Rolling Elements ◽  
Rotary Speed ◽  
Nonlinear Elastic ◽  
And Control

The automatic ball balancer is equipment used to balance the rotor system online and control its forced vibration. Although the rotor system is a nonlinear system actually, especially the occurrence of the nonlinear elastic restoring force in the support of rolling elements bearings, many researches still focus on the linear rotor systems at present. The Jeffcott rotor acted by unsymmetrical nonlinear restoring force is studied in this paper. Through the resolving theoretically and simulating numerically, the principal resonance respond of the rotor system controlled by the balancer with two balls and its stability are studied, while the vibration characteristics and movement laws of the rotor and balls in every rotary speed region are analyzed. The results showed that the balancer can suppress the principal vibration of the nonlinear rotor system in high speed region very well.

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