Aperiodic response and bifurcation of dynamic systems with strong local nonlinearities /
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| Other Authors: | , , |
| Format: | Thesis Book |
| Language: | English |
| Published: |
1992.
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| Subjects: | |
| Online Access: | Link to OAKTrust copy |
| Abstract: | A study o f the steady state, quasi-periodic response of strongly nonlinear dynamical systems is carried out. The dynamic behavior of simple mechanical models under quasi-periodic or periodic excitations is investigated for single degree of freedom (SDOF) systems. For a two dimensional system, a horizontal Jeffcott rotor both with discontinuous and cross coupling stiffness is studied using a new modified fixed point algorithm. The modified fixed point algorithm (FPA) is introduced to obtain quasi-periodic solutions, generated through a Hopf bifurcation, of strongly nonlinear systems. The method employs an analytical Jacobian form in an iterative procedure so that the convergence to the solutions is considerably improved compared to the conventional fixed point algorithm, in which a numerical difference scheme is utilized to compute elements of the Jacobian matrix. Circle mapping is employed to estimate the winding (or rotation) numbers of determined quasi-periodic solutions. Using modern dynamical systems theory, a complex mode-locking dynamic behavior o f a modified nonlinear Jeffcott rotor is identified. A new HB (Harmonic Balance)/TFC (Time Varying Fourier Coefficients) method has been developed to obtain quasi-periodic solutions of the nonlinear systems under quasi-periodic excitation. The new method proved to be a robust and accurate numerical scheme for the analysis of multi-periodically forced nonlinear systems. The HB/TFC method is modified in order to determine quasi-periodic solutions of periodically forced nonlinear systems. The method can be considered as a generalization of the Van der Pol or averaging type approximate methods, and leads to much better approximation to the solutions sought. In addition, the HB/TFC method provides for constructing Poincare flows for the solution so that the winding number o f a quasi-periodic response can be estimated efficiently. |
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| Item Description: | Typescript (photocopy). Vita. "Major subject: Mechanical Engineering." |
| Physical Description: | xxi, 174 leaves : illustrations ; 29 cm |
| Bibliography: | Includes bibliographical references. |