The Vibration of Unsymmetrical Rotating Shafts

1965 ◽  
Vol 32 (1) ◽  
pp. 157-162 ◽  
Author(s):  
S. T. Ariaratnam
Keyword(s):  
Forced Vibrations ◽  
Viscous Damping ◽  
Free And Forced Vibrations ◽  
Rotating Shafts ◽  
Principal Directions

This paper deals with the vibration of heavy unsymmetrical shafts possessing unequal flexural rigidities in the principal directions and running in symmetrical bearings. The existence of several bands of whirling speeds is shown and the effects of stationary and rotary viscous damping on the free and forced vibrations of the shaft are discussed.

Closed-Form Exact Solutions for Viscously Damped Free and Forced Vibrations of Longitudinal and Torsional Bars

2017 ◽  
Vol 17 (08) ◽  
pp. 1750093 ◽  
Author(s):  
Jae-Hoon Kang
Keyword(s):  
Free Vibration ◽  
Closed Form ◽  
Closed Form Solution ◽  
Forced Vibrations ◽  
Form Solution ◽  
Forced Response ◽  
Mode Shapes ◽  
Viscous Damping ◽  
Vibration Displacement ◽  
Free And Forced Vibrations

This paper studies the viscously damped free and forced vibrations of longitudinal and torsional bars. The method is exact and yields closed form solution for the vibration displacement in contrast with the well-known eigenfunction superposition (ES) method, which requires expression of the distributed forcing functions and displacement response functions as infinite series sums of free vibration eigenfunctions. The viscously damped natural frequency equation and the critical viscous damping equation are exactly derived for the bars. Then the viscously damped free vibration frequencies and corresponding damped mode shapes are calculated and plotted, aside from the undamped free vibration and corresponding mode shapes typically computed and used in vibration problems. The longitudinal or torsional amplitude versus forcing frequency curves showing the forced response to distributed loadings are plotted for various viscous damping parameters. It is found that the viscous damping affects the natural frequencies and the corresponding mode shapes of longitudinal and torsional bars, especially for the fundamental frequency.

The Concept of Complex Damping

1952 ◽  
Vol 19 (3) ◽  
pp. 284-286
Author(s):  
N. O. Myklestad
Keyword(s):  
Steady State ◽  
Complex Number ◽  
Forced Vibrations ◽  
Damping Factor ◽  
Viscous Damping ◽  
Mass System ◽  
Free And Forced Vibrations ◽  
Phase Angles ◽  
State Case ◽  
Complex Damping

Abstract In this paper it is shown that if the hysteresis loop for a material has a particular shape the damping can be considered adequately by multiplying the modulus of elasticity of the material by the complex number e2bi where 2b is called the complex damping factor. For small values of b it is shown that both for free and forced vibrations of a simple spring-mass system the motion in the case of complex damping is the same as in the case of viscous damping, with b = c/ccr, except that in the steady-state case the phase angles are slightly different. Also, it is shown how complex damping may be applied to cases of forced vibrations of uniform rods and beams. The greatest advantage of using complex damping, however, is in numerical calculations of forced vibrations of engine crankshafts, airplane wings, and other types of structures; and for such calculations it already has been extensively used.

Nonlinear Free and Forced Vibrations of Symmetric Laminated Panels

2011 ◽  
Vol 471-472 ◽  
pp. 616-621 ◽  
Author(s):  
Alireza Shooshtari ◽  
Soheil Razavi ◽  
Hadi Ghashochi Bargh ◽  
Mohammad Homayoun Sadr-Lahidjani
Keyword(s):  
Perturbation Method ◽  
External Force ◽  
Laminated Composite ◽  
Composite Plates ◽  
Forced Vibrations ◽  
Numerical Results ◽  
Transverse Displacement ◽  
Laminated Composite Plates ◽  
Free And Forced Vibrations ◽  
Laminated Panels

In this paper, free and forced vibrations of symmetric laminated composite plates are studied analytically by using a perturbation method where the analytical results for transverse displacement are compared with the numerical results. The external force is taken to be harmonic in time and having uniform amplitude.

scholarly journals Nonlinear dynamics of rectangular plates: investigation of modal interaction in free and forced vibrations

2013 ◽  
Vol 225 (1) ◽  
pp. 213-232 ◽  
Author(s):  
Michele Ducceschi ◽  
Cyril Touzé ◽  
Stefan Bilbao ◽  
Craig J. Webb
Keyword(s):  
Nonlinear Dynamics ◽  
Forced Vibrations ◽  
Rectangular Plates ◽  
Modal Interaction ◽  
Free And Forced Vibrations
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