Title page for ETD etd-10132005-152546


Type of Document Dissertation
Author Abou-Rayan, Ashraf M.
URN etd-10132005-152546
Title Deterministic and stochastic responses of nonlinear systems
Degree PhD
Department Engineering Mechanics
Advisory Committee
Advisor Name Title
Nayfeh, Ali H. Committee Chair
Besieris, Ioannis M. Committee Member
Heller, Robert A. Committee Member
Mook, Dean T. Committee Member
Singh, Mahendra P. Committee Member
Keywords
  • Random vibration.
  • Nonlinear oscillators.
  • Resonant vibration.
Date of Defense 1991-12-03
Availability restricted
Abstract

This dissertation is concerned with the responses of nonlinear systems to both deterministic and stochastic excitations.

For a single-degree-of-freedom system, the response of a simply-supported buckled beam to parametric excitations is investigated. Two types of excitations are examined: deterministic and random. For the nonlinear response to a harmonic axial load, the method of multiple scales is used to determine to second order the amplitude-and phase-modulation equations. Floquet theory is used to analyze the stability of periodic responses. The perturbation results are verified by integrating the governing equation using both digital and analog computers. For small excitation amplitudes, the analytical results are in good agreement with the numerical solutions. The large-amplitude responses are investigated by using simulations on a digital computer and are compared with results obtained using an analog computer. For the stochastic response to a wide-band random excitation, the Gaussian and non-Gaussian closure schemes are used to determine the response statistics. The results are compared with those obtained from real-time analysis (analog-computer simulation). The normality assumption is examined. A comparison between the responses to deterministic and random excitations is presented.

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