Development of a non-Gaussian closure scheme for dynamic systems involving non-linear inertia

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Title: Development of a non-Gaussian closure scheme for dynamic systems involving non-linear inertia
Author: Soundararajan, Aravamudhan
Abstract: The main objective of this investigation is to develop a non -Gaussian closure scheme adapted for the analysis of random response statistics of nonlinear dynamic systems which are subjected to parametric random excitations . The scheme is based on the asymptotic expansion of the non -Gaussian probability density . The technique is found to have two main advantages . The first is that it resolves an observed contradiction of results obtained by other techniques . The second is that it explores new response characteristics not predicted by other methods . The scheme is applied to a number of dynamic systems possessing single and two degrees -of -freedom and various types of nonlinearities . Numerical solutions are obtained and their validity is examined according to certain criteria based on the preservation of moment properties and Schwarz's inequality . Higher order terms are considered to examine the convergence of the Edgeworth expansion . It is found that the inclusion of the third and fourth order semi -invariants is adequate for the series convergence . The response of nonlinear single degree -of -freedom systems exhibits the occurrence of a jump in the response statistics at a certain excitation level which is mainly governed by the system linear damping factor . This new feature may be attributed to the fact that the non -Gaussian closure more adequately models the nonlinearity , and thus results in characteristics that are similar to those of deterministic nonlinear systems . The method is also used to determine the random response of an elevated water tower subjected to a random ground motion . The tower is represented by a two -degree -of -freedom system with cubic nonlinear coupling . In the neighborhood of the internal resonance condition r= w2 /w1 =1 /3 , where w1 and w2 are the normal mode frequencies of the system , the nonlinear modal interaction takes the form of energy exchange between the two modes . Unlike the Gaussian solution , the non -Gaussian closure solution is found to achieve a strictly stationary response in the time domain . The response mean squares are presented as functions of the internal resonance detuning parameter r = 1 /3 + 0 (e ) , where £ is a small parameter , for various system parameters . Unbounded response mean squares are found to take place at regions above and below certain values of the internal resonance r=l /3 . For regions well remote from the exact internal tuning the system exhibits the features of the linear response .
URI: http : / /hdl .handle .net /2346 /17024
Date: 1985-12

Citation

Development of a non-Gaussian closure scheme for dynamic systems involving non-linear inertia. Doctoral dissertation, Texas Tech University. Available electronically from http : / /hdl .handle .net /2346 /17024 .

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