An Extension of Rayleigh's Principle

1994 ◽  
Vol 22 (2) ◽  
pp. 83-90
Author(s):  
Alfonso Díaz-Jiménez ◽  
Gentil A. Estévez-Bretón
Keyword(s):  
Present Article ◽  
Degrees Of Freedom ◽  
Mechanical Systems ◽  
Natural Generalization ◽  
Vibrational Frequencies ◽  
Exact Results ◽  
Two Degrees Of Freedom ◽  
Elegant Method ◽  
Three Degrees Of Freedom

Steidel's extension of Rayleigh's method for calculating the natural vibrational frequencies of mechanical systems with two degrees of freedom provides an elegant method to obtain exact results. In the present article this approach, which perhaps has not been exploited as much as it could be, is first reviewed and then several examples of the procedure are given. An extension of the method to three degrees of freedom is presented, and a natural generalization of Rayleigh's principle is suggested.

scholarly journals Analysis and optimization of the effects of frictional and viscous dampers on dynamical systems

2019 ◽  
Vol 38 (2) ◽  
pp. 255-269
Author(s):  
Marlon Wesley Machado Cunico ◽  
Jennifer Desiree Medeiros Cavalheiro
Keyword(s):  
Frequency Domain ◽  
Degrees Of Freedom ◽  
Transfer Functions ◽  
Mechanical Systems ◽  
Static Friction ◽  
Coulomb Force ◽  
Dynamic Responses ◽  
Dynamical Response ◽  
Viscous Dampers ◽  
Three Degrees Of Freedom

Over the last several years, the complexity of products has been increasing in parallel to the product cost thus becoming one of main focal points for development. On the other hand, although several applications struggle to fix vibration problems, highlighting the importance of damper design, literature that compares the benefits and disadvantages between of dry-frictional, viscous, and Coulomb–viscous dampers is still rare. Owing to this, the main goal of this work is to present a study that compares the dynamical response of mechanical systems against several damper types. For this research, we analyzed the effects of three types of damper (viscous, Coulomb–viscous, and dry-frictional dampers) on two mechanical systems. The first system consists of a mass-spring-damper with one degree of freedom, while the second system is a rotational machine with three degrees of freedom. The sensibility analyses of each damper were also studied, where the viscosity, Coulomb force, static friction, and Stribeck decay were the variables. In this work, mechanical systems were studied in a forced vibration condition and analyzed in the time and frequency domain in addition to identifying the main transfer functions in the frequency domain. In this analysis, the displacement, receptance, and force reaction were considered to be the study responses. After analyzing the main effect of damper coefficients on the general dynamic responses, we performed an optimization study in order to evidence the optimal configurations of either majorly viscous or frictional damper. Lastly, we analyzed the main behavior of this optimized damper on three-degrees-of-freedom rotational dynamic system.

Non-linear vibrations in mechanical systems with one or two degrees of freedom

2018 ◽  
Author(s):  
Д.А. Гришко ◽  
◽  
В.В. Лапшин ◽  
Е.С. Студенников ◽  
А.Н. Тарасенко ◽  
...  
Keyword(s):  
Degrees Of Freedom ◽  
Mechanical Systems ◽  
Two Degrees Of Freedom ◽  
Non Linear ◽  
Linear Vibrations

Top-Top Interaction in Hexa-Deutero Dimethyl Selenide from the Microwave Spectrum in the First Excited Torsional States

1976 ◽  
Vol 31 (11) ◽  
pp. 1413-1418
Author(s):  
G. K. Pandey ◽  
H. Lutz ◽  
H. Dreizler
Keyword(s):  
Fine Structure ◽  
Least Squares ◽  
Internal Rotation ◽  
Degrees Of Freedom ◽  
Molecular Model ◽  
Microwave Spectrum ◽  
Two Degrees Of Freedom ◽  
Least Squares Fit ◽  
Dimethyl Selenide ◽  
Three Degrees Of Freedom

Abstract An analysis of the internal rotation fine structure for the rotational transitions of hexa-deutero dimethyl selenide in the first excited torsional states is presented in terms of a molecular model with two degrees of freedom for the internal rotation or torsion of the two tops in addition to the three degrees of freedom for the overall rotation. By a least squares fit of the multiplet splittings of ten transitions in the vn=11 and nine transitions in the ṽn=12 excited torsional states, the following parameters have been obtained: F3=1493±9 cal mol-1; ϑ=50°1′±7′ V12′=28.4±0.3 cal mol-1. The splitting of the fine structure components could be nicely fitted, but not their absolute frequencies and the seperation between the two multiplets.

Stable Control of Under-Actuated Mechanical System Acrobot

2014 ◽  
Vol 971-973 ◽  
pp. 727-730
Author(s):  
Min Wu ◽  
Hai Pu
Keyword(s):  
Asymptotic Stability ◽  
Mechanical System ◽  
Degrees Of Freedom ◽  
Mechanical Systems ◽  
Vertical Plane ◽  
Drive System ◽  
Control Input ◽  
Underactuated Mechanical Systems ◽  
Two Degrees Of Freedom ◽  
Stable Control

The mechanical system with one control input and two degrees of freedom is one kind of simple under-drive system, As a typical of two-DOF underactuated mechanical systems , Two-link underactuated mechanical arms is a system scholars always research of.This paper mainly take the two link underactuated mechanical arms-Acrobot which motivate in the vertical plane as object to discusses the asymptotic stability of control

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