The Normal Modes of Vibration of Certain Nonlinear Continuous Systems

1964 ◽  
Vol 31 (1) ◽  
pp. 139-140 ◽  
Author(s):  
Thein Wah
Keyword(s):  
Normal Modes ◽  
Distributed Parameter Systems ◽  
Structural Theory ◽  
Distributed Parameter ◽  
Continuous Systems ◽  
Simple Interpretation ◽  
Modes Of Vibration

Two examples from structural theory are invoked to show that “normal modes” of vibration could have a simple interpretation in nonlinear distributed parameter systems.

Transfer Function Formulation of Constrained Distributed Parameter Systems, Part II: Applications

1993 ◽  
Vol 60 (4) ◽  
pp. 1012-1019 ◽  
Author(s):  
C. H. Chung ◽  
C. A. Tan
Keyword(s):  
Transfer Function ◽  
Elastic Foundation ◽  
Normal Modes ◽  
Distributed Parameter Systems ◽  
Distributed Parameter ◽  
Displacement Method ◽  
Mode Localization ◽  
Function Formulation ◽  
Free Beam ◽  
Symmetric Systems

In this paper, the application of the transfer function formulation and the generalized displacement method (GDM) to the analysis of constrained distributed parameter systems is illustrated. Two kinds of classical examples are considered. In the constrained free-free beam example, it is shown how the GDM gives the eigensolutions without requiring knowledge of the normal modes of the unconstrained beam. In the string on a partial elastic foundation example, mode localization and eigenvalue loci veering phenomena are examined. It is shown that mode localizaation can occur in spatially symmetric systems and for modes whose frequency loci do not veer.

The Nature of the Temporal Solutions of Damped Distributed Systems With Classical Normal Modes

1982 ◽  
Vol 49 (4) ◽  
pp. 867-870 ◽  
Author(s):  
D. J. Inman ◽  
A. N. Andry
Keyword(s):  
Distributed Systems ◽  
Normal Modes ◽  
Distributed Parameter Systems ◽  
Time Response ◽  
Distributed Parameter

Conditions under which the time response of certain distributed parameter systems, which are assumed to possess “classical normal” modes, is critically damped, overdamped, or underdamped are presented. The conditions are derived from the definiteness of certain combinations of the coefficient operators of the describing equations. These conditions are compared to previous results and their usefulness is illustrated by examples.

Nature of coupling in non-conservative distributed parameter systems attached to external damping sources

2017 ◽  
Vol 25 (7) ◽  
pp. 1367-1383
Author(s):  
John Bellos ◽  
Daniel J Inman ◽  
Nikolaos Bakas
Keyword(s):  
Equations Of Motion ◽  
Normal Modes ◽  
Distributed Parameter Systems ◽  
Distributed Parameter ◽  
Modal Coupling ◽  
Theoretical Predictions ◽  
Coupling Parameters ◽  
The Mathematical Model ◽  
Euler Bernoulli Beam ◽  
Response Errors

Non-conservative distributed parameter systems connected to external damping sources and possessing non-normal modes are analyzed in this work. The mathematical model of such systems is presented and real valued modal analysis is used to obtain the coupled modal equations of motion. A decoupling technique is developed using Fourier expansion, fictitious damping ratios, modal coupling parameters and pseudo forces. The method is applicable to all types of excitation. A normal mode criterion in the form of non-proportionality indices is also provided. The theoretical predictions are verified through application to a non-conservative Euler–Bernoulli beam with non-proportional damping configuration and various types of boundary conditions. Numerical examples emphasize the response errors associated with the proportional damping assumption and reveal the advantages of the proposed approach over the exact method.

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