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A Caltech Library Repository Feedhttp://www.rssboard.org/rss-specificationpython-feedgenenThu, 28 Mar 2024 10:48:58 -0700Transmission Matrices and Lumped Parameter Models for Continuous Systems
https://resolver.caltech.edu/CaltechTHESIS:10192015-155737101
Year: 1966
DOI: 10.7907/4K3H-1E57
<p>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.</p>
<p>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.</p>
<p>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. </p>
https://resolver.caltech.edu/CaltechTHESIS:10192015-155737101Response of linear, viscous damped systems to excitations having time-varying frequency
https://resolver.caltech.edu/CaltechTHESIS:09152015-094552278
Year: 1966
DOI: 10.7907/NR49-C405
<p>The response of linear, viscous damped systems to excitations having time-varying frequency is the subject of exact and approximate analyses, which are supplemented by an analog computer study of single degree of freedom system response to excitations having frequencies depending linearly and exponentially on time. </p>
<p>The technique of small perturbations and the methods of stationary phase and saddle-point integration, as well as a novel bounding procedure, are utilized to derive approximate expressions characterizing the system response envelope—particularly near resonances—for the general time-varying excitation frequency.</p>
<p>Descriptive measurements of system resonant behavior recorded during the course of the analog study—maximum response, excitation frequency at which maximum response occurs, and the width of the response peak at the half-power level—are investigated to determine dependence upon natural frequency, damping, and the functional form of the excitation frequency.</p>
<p>The laboratory problem of determining the properties of a physical system from records of its response to excitations of this class is considered, and the transient phenomenon known as “ringing” is treated briefly.</p>
<p>It is shown that system resonant behavior, as portrayed by the above measurements and expressions, is relatively insensitive to the specifics of the excitation frequency-time relation and may be described to good order in terms of parameters combining system properties with the time derivative of excitation frequency evaluated at resonance. </p>
<p>One of these parameters is shown useful for predicting whether or not a given excitation having a time-varying frequency will produce strong or subtle changes in the response envelope of a given system relative to the steady-state response envelope. The parameter is shown, additionally, to be useful for predicting whether or not a particular response record will exhibit the “ringing” phenomenon. </p>
https://resolver.caltech.edu/CaltechTHESIS:09152015-094552278Analytical and Experimental Studies of Random Vibration
https://resolver.caltech.edu/CaltechETD:etd-09202002-101725
Year: 1966
DOI: 10.7907/8wxv-qh07
<p>Analytical and experimental investigations are made of the response of linear systems subject to magnitude-limited Gaussian broadband random excitation. A mathematical analysis for determining the statistical properties of this excitation is developed. Experimental studies on the probabilistic response of linear systems with magnitude-limited input are also presented.</p>
<p>Secondly the peak characteristics of the response of linear systems subject to Gaussian broadband random excitation are investigated. It is shown that the number of peaks per unit time of the response of a single degree of freedom system increases as the frequency bandwidth of the excitation increases. Analytical and experimental techniques are developed to study the peak distribution characteristics of multi-degree of freedom systems and continuous systems. It is found that the normal mode random variables are statistically independent if the system damping is small, and the modal frequencies are sufficiently separated.</p>
<p>Finally the method of Fokker-Planck is used to obtain the statistical properties of the response of a first order Coulomb damped system. The first order probability density function of displacement of this nonlinear system is determined. A simplified method for developing the autocorrelation function, and the power spectral density is discussed and applied to the above problem. The results are further substantiated by experiment. Experimental investigations are also carried out to determine the power spectral density of the response of a second order nonlinear system with Coulomb restoring force to white noise input. The results are compared with those given by Wolaver.</p>https://resolver.caltech.edu/CaltechETD:etd-09202002-101725Analytical and Experimental Studies of Impact Dampers
https://resolver.caltech.edu/CaltechETD:etd-04172003-091816
Year: 1965
DOI: 10.7907/XK0P-R658
A study is made of the general behavior of a single particle impact damper, with the main emphasis on symmetric 2 impacts/cycle motion. The exact solution for this case is derived analytically and its asymptotically stable regions are determined. The stability analysis defines the zones where the modulus of all the eigenvalues of a certain matrix relating conditions after each of two consecutive impacts is less than unity.
Results of the analysis are supplemented and verified by experimental studies with a mechanical model and an analog computer. Additional numerical investigations are made with a digital computer.
It is found that, under practically realizable conditions, impact damping is effective in reducing the vibration amplitude levels resulting from sinusoidal, random, or impulse-like excitation.https://resolver.caltech.edu/CaltechETD:etd-04172003-091816