Journal ArticleDOI
On Uncoupling and Solving the Equations of Motion of Vibrating Linear Discrete Systems
TLDR
In this paper, the authors search for another coordinate system in the neighborhood of the normal coordinate system so that in the new coordinate system removal of the coupling terms in the equations of motion produces a minimum bound on the relative error introduced in the approximate solution.Abstract:
The method in effect searches for another coordinate system in the neighborhood of the normal coordinate system so that in the new coordinate system removal of the coupling terms in the equations of motion produces a minimum bound on the relative error introduced in the approximate solutionread more
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Structural Dynamic Analysis with Generalized Damping Models: Analysis
TL;DR: In the majority of practical cases this approach is adopted more for mathematical convenience than for modeling the physics of vibration damping as mentioned in this paper, and it has become standard practice to use this approach in dynamics, covering a wide range of applications from aerospace to civil engineering.
Journal ArticleDOI
The decoupling of damped linear systems in free or forced vibration
TL;DR: In this paper, the authors extend classical modal analysis to decouple any viscously damped linear system in non-oscillatory free vibration or in forced vibration, based upon an exposition of how exponential decay in a system can be regarded as imaginary oscillations, the concept of damped modes of imaginary vibration is introduced.
Journal ArticleDOI
Co-ordinate transformations for second order systems. part i: general transformations
TL;DR: It is presented a forceful case that this structure-preserving transformation should be considered to be the fundamental definition for the characteristic behaviour of general second order systems—in preference to the eigenvalue–eigenvector solutions conventionally accepted.
Journal ArticleDOI
The decoupling of damped linear systems in oscillatory free vibration
TL;DR: In this paper, the authors extend classical modal analysis to decouple any viscously damped linear system in oscillatory free vibration, based upon an exposition of how viscous damping causes phase drifts in the components of a linear system, the concept of non-classically damped modes of vibration is introduced.
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