Large Amplitude Free Vibration Of A Rotating Non-Homogeneous Beam With Non-Linear Spring And Mass System

2008 ◽  
pp. 35-48
Author(s):  
Rasajit Kumar Bera* ◽  
P. C. Ray ◽  
A. Chakrabarti ◽  
B. Mukhopadhyay
Keyword(s):  
Free Vibration ◽  
Large Amplitude ◽  
Mass System ◽  
Non Linear ◽  
Linear Spring ◽  
Homogeneous Beam

Non-Linear Spring and Damping Forces Estimation During Free Vibration

1995 ◽  
Author(s):  
Michael Feldman ◽  
Simon Braun
Keyword(s):  
Free Vibration ◽  
Hilbert Transform ◽  
Time Domain ◽  
Free Vibration Analysis ◽  
Single Degree Of Freedom ◽  
Non Linear ◽  
Linear Spring ◽  
The Time Domain ◽  
The Hilbert Transform ◽  
Vibrating Systems

Abstract A method for dynamic analysis of sophisticated nonlinear single-degree-of-freedom systems, based on the Hilbert transform in the time domain is described. Using the Hilbert transform together with the proposed method for system identification, we obtain both instantaneous modal parameters together with non-linear force characteristics during free vibration analysis under impulse excitation without long resonance testing. Using the Hilbert transform in the time domain is a new method of studying linear and non-linear vibrating systems exposed to impulse or shock inputs.

Large Amplitude Free Vibration Analysis of a Rotating Beam with Non-linear Spring and Mass System

2005 ◽  
Vol 11 (12) ◽  
pp. 1511-1533 ◽  
Author(s):  
S. K. Das ◽  
P. C. Ray ◽  
G. Pohit
Keyword(s):  
Free Vibration Analysis ◽  
Linear Constraint ◽  
Multiple Time Scales ◽  
Multiple Time ◽  
Rotating Beam ◽  
Mass System ◽  
Linear Partial Differential Equations ◽  
Non Linear ◽  
Out Of Plane ◽  
Linear Spring

The free, out-of-plane vibration of a rotating beam with a non-linear spring-mass system has been investigated. The non-linear constraint appears in the boundary condition. The solution is obtained by applying the method of multiple time-scales directly to the non-linear partial differential equations and the boundary conditions. The results of the linear frequencies match well with those obtained in the literature. Subsequent non-linear study indicates that there is a pronounced effect of the spring and its mass. The influence of the spring-mass location on frequencies is also investigated for the non-linear frequencies of the rotating beam.

A novel tuned mass-conical spring system for passive vibration control of a variable mass structure

2021 ◽  
pp. 107754632110004
Author(s):  
Sanjukta Chakraborty ◽  
Aparna (Dey) Ghosh ◽  
Samit Ray-Chaudhuri
Keyword(s):  
Variable Mass ◽  
Design Procedure ◽  
Time History ◽  
Tuned Mass Damper ◽  
Water Tank ◽  
Mass System ◽  
Mass Damper ◽  
Linear Spring ◽  
Spring System ◽  
Elevated Water

This article presents the design of a tuned mass damper with a conical spring to enable tuning to the natural frequency of the system at multiple values, as may be convenient in case of a system with fluctuations in the mass. The principle and design procedure of the conical spring in the context of a varying mass system are presented. A passive feedback control mechanism based on a simple pulley-mass system is devised to cater to the multi-tuning requirements. A design example of an elevated water tank with fluctuating water content, subjected to ground excitation, is considered to numerically illustrate the efficiency of such a tuned mass damper associated with the conical spring. The conical spring is designed based on the tuning requirements at different mass conditions of the elevated water tank by satisfying the allowable load bearing capacity of the spring. Comparisons are made with the conventional passive tuned mass damper with a linear spring tuned to the full tank condition. Results from time history analysis reveal that the conical spring-tuned mass damper can be successfully designed to remain tuned and thereby achieve significant response reductions under stiffening conditions of the primary structure, whereas the linear spring-tuned mass damper suffers performance degradation because of detuning, whenever there is any fluctuation in the system mass.

Non-linear torsional oscillation of a two-degree-of-freedom system incorporating a Hooke joint

1964 ◽  
Vol 277 (1368) ◽  
pp. 92-106 ◽  
Keyword(s):  
Large Amplitude ◽  
Critical Speed ◽  
Torsional Oscillation ◽  
Degree Of Freedom ◽  
Non Linear ◽  
Two Degree Of Freedom

The non-linear torsional oscillation of the system is analyzed by means of a variant of Kryloff and Bogoliuboff’s method. It is shown that each mode of the system can perform oscillations of large amplitude in a number of critical speed ranges, and that hysteresis effects and discontinuous jumps in amplitude are to be expected in these speed ranges if the damping is light.

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