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Transmission Matrices and Lumped Parameter Models for Continuous Systems


Rocke, Richard Dale (1966) Transmission Matrices and Lumped Parameter Models for Continuous Systems. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/4K3H-1E57.


The use of transmission matrices and lumped parameter models for describing continuous systems is the subject of this study. Non-uniform continuous systems which play important roles in practical vibration problems, e.g., torsional oscillations in bars, transverse bending vibrations of beams, etc., are of primary importance.

A new approach for deriving closed form transmission matrices is applied to several classes of non-uniform continuous segments of one dimensional and beam systems. A power series expansion method is presented for determining approximate transmission matrices of any order for segments of non-uniform systems whose solutions cannot be found in closed form. This direct series method is shown to give results comparable to those of the improved lumped parameter models for one dimensional systems.

Four types of lumped parameter models are evaluated on the basis of the uniform continuous one dimensional system by comparing the behavior of the frequency root errors. The lumped parameter models which are based upon a close fit to the low frequency approximation of the exact transmission matrix, at the segment level, are shown to be superior. On this basis an improved lumped parameter model is recommended for approximating non-uniform segments. This new model is compared to a uniform segment approximation and error curves are presented for systems whose areas very quadratically and linearly. The effect of varying segment lengths is investigated for one dimensional systems and results indicate very little improvement in comparison to the use of equal length segments. For purposes of completeness, a brief summary of various lumped parameter models and other techniques which have previously been used to approximate the uniform Bernoulli-Euler beam is a given.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:(Applied Mechanics)
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Applied Mechanics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Crede, Charles E. (advisor)
  • Hudson, Donald E. (advisor)
Thesis Committee:
  • Unknown, Unknown
Defense Date:16 May 1966
Funding AgencyGrant Number
Hughes Aircraft CompanyUNSPECIFIED
NASANAS 8-2451
Record Number:CaltechTHESIS:10192015-155737101
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:9230
Deposited On:20 Oct 2015 18:47
Last Modified:07 Mar 2024 23:23

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