Vibration Response of Linear Damped Complex Systems

1963 ◽  
Vol 30 (1) ◽  
pp. 70-74 ◽  
Author(s):  
Robert Plunkett
Keyword(s):  
Linear System ◽  
Complex Systems ◽  
Normal Modes ◽  
Continuous System ◽  
Vibration Response ◽  
Degree Of Freedom ◽  
The Other ◽  
Maximum Response ◽  
Approximate Expressions ◽  
Two Degree Of Freedom

Hahnkamm has found the changes in the amplitudes of each of the two maxima of the unit vibration response of a two-degree-of-freedom linear system as the strength of the single linear dashpot is changed. This paper develops two approximate expressions for the change in all of the response maxima of a multidegree or continuous system as the dashpot constant of the single linear damper is changed. One of these approximations is derived from a perturbation solution around the minimax values, and the other is derived from an expansion in normal modes. These expressions are useful in determining the sensitivity of the maximum response value to small changes in the damping constant.

Nonlinear Normal Modes and Localization in Elastic Vibro-Impact Systems With Multiple Constraints

2007 ◽  
Author(s):  
David Wagg
Keyword(s):  
Mathematical Formulation ◽  
Normal Modes ◽  
Nonlinear Normal Modes ◽  
Degree Of Freedom ◽  
Lumped Mass ◽  
Localized Modes ◽  
Impact Oscillator ◽  
Mass System ◽  
Nonlinear Normal ◽  
Two Degree Of Freedom

In this paper we consider the dynamics of compliant mechanical systems subject to combined vibration and impact forcing. Two specific systems are considered; a two degree of freedom impact oscillator and a clamped-clamped beam. Both systems are subject to multiple motion limiting constraints. A mathematical formulation for modelling such systems is developed using a modal approach including a modal form of the coefficient of restitution rule. The possible impact configurations for an N degree of freedom lumped mass system are considered. We then consider sticking motions which occur when a single mass in the system becomes stuck to an impact stop, which is a form of periodic localization. Then using the example of a two degree of freedom system with two constraints we describe exact modal solutions for the free flight and sticking motions which occur in this system. A numerical example of a sticking orbit for this system is shown and we discuss identifying a nonlinear normal modal basis for the system. This is achieved by extending the normal modal basis to include localized modes. Finally preliminary experimental results from a clamped-clamped vibroimpacting beam are considered and a simplified model discussed which uses an extended modal basis including localized modes.

Articulated Models of Cantilevers Conveying Fluid: The Study of a Paradox

1970 ◽  
Vol 12 (4) ◽  
pp. 288-300 ◽  
Author(s):  
M. P. Paidoussis ◽  
E. B. Deksnis
Keyword(s):  
Degrees Of Freedom ◽  
Continuous System ◽  
Dynamical Behaviour ◽  
Degree Of Freedom ◽  
Complex Frequency ◽  
Good Convergence ◽  
Articulated Models ◽  
Two Degree Of Freedom ◽  
Conveying Fluid ◽  
Oscillatory Instabilities

A general theory is presented for the dynamics of nth-degree-of-freedom articulated (lumped flexibility) models of cantilevers conveying fluid, of which the two-degree-of-freedom model of a column subjected to follower forces (first investigated by Ziegler) is a particular case. The ability of the articulated system to predict the dynamical behaviour of the continuous system modelled is investigated, and in particular the paradox that, whereas the continuous system is subject to only oscillatory instability (at sufficiently high flow), the model is generally subject to both oscillatory and buckling instabilities, and sometimes only to the latter. Complex frequency calculations show that buckling is associated with the higher modes of the articulated system, which, irrespective of the number of degrees of freedom, do not model well the corresponding modes of the continuous system. The critical flow velocities for buckling and oscillatory instabilities are calculated extensively, the latter showing good convergence to the corresponding values of the continuous system. The theory is supported by a set of experiments. Agreement between theory and experiment is satisfactorily good.

scholarly journals Pendekatan Eksperimen Karakteristik Respon Getaran Sistem Two Degree of Freedom dengan Penambahan Independent Dual Dynamic Vibration Absorber

2019 ◽  
Vol 3 (2) ◽  
pp. 85
Author(s):  
Susastro Susastro ◽  
Novi Indah Riani
Keyword(s):  
Vibration Reduction ◽  
Degree Of Freedom ◽  
The Other ◽  
Vibration Absorber ◽  
Dynamic Vibration Absorber ◽  
Maximum Reduction ◽  
Dynamic Vibration ◽  
Translational Vibration ◽  
Mathematical Equations ◽  
Two Degree Of Freedom

Vibration is one of the problems that must be reduced in a vehicle. There are many ways to reduce vibration in vehicles, one of them is by adding Dynamic vibration absorber (DVA). While Dual Dynamic vibration absorber (dDVA) is a DVA period that is able to move in the translational direction given to the system to reduce translation vibration and when there is resonance. Translation DVA is an additional type of time used to reduce the vibration of the translation direction. So far there is not much research related to the use of translational DVA to reduce rotational vibrations as well as translation. In this study, a study was conducted related to the use of independent double translational DVA (dDVA) to reduce translation vibrations as well as rotation of the beam. The research was conducted by modeling the system obtained into mathematical equations and simulations were carried out to determine the characteristics of vibrations that arise. In the simulation, one of the DVA periods is placed at the center of the main system period, while the other DVA period is given a change between the center period and the end of the system. The results of the study show that the maximum reduction in translational vibration is 95.51% and occurs when the absorber is placed at the center of the system, while the maximum rotation vibration reduction is 56.62% and is obtained when the system is given with an arm ratio of 1 and zero.

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