Steady-state and bifurcation analysis of strongly nonlinear dynamical systems /
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| Other Authors: | , , |
| Format: | Thesis Book |
| Language: | English |
| Published: |
1990.
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| Subjects: | |
| Online Access: | ProQuest, Abstract Link to OAKTrust copy |
| Abstract: | The study concerns the steady-state response of strongly nonlinear dynamical systems subjects to periodic forcing excitations. The dynamic behavior of simple mechanical models with a piecewise-smooth nonlinearity is investigated for single degree of freedom (SDOF) systems. For two-dimensional system, a horizontal Jeffcott rotor both with discontinuous and cross coupling stiffness is studied. Finally, response and bifurcation analysis is performed for a simplified rotor model with piecewise-linear support stiffness as an example of multi degree of freedom (MDOF) nonlinear systems. A new HB (Harmonic Balance)/AFT (Alternating Frequency Time) method has been developed to obtain the harmonic and subharmonic responses of strongly nonlinear systems. The method employs an explicit Jacobian form in an iterative procedure which ensures convergence at all parameter values. The new method proved to be a robust and accurate numerical scheme for the analysis SDOF, two-dimensional and MDOF nonlinear systems. For the MDOF systems with piecewise-smooth nonlinearity, an impedance method is applied to reduce the associated nonlinear differential equations to linear algebraic equations involving only the nonlinear coordinates. For the quasi-periodic response, a modified DFT (Discrete Fourier Transform) method is utilized along with an IDFT (Inverse Discrete Fourier Transform). The stability analysis of the determined steady-state motion is carried out using the associated perturbed equations. Floquet multipliers of the associated monodromy matrix are determined using a new discrete HB/AFT method. The hyperbolicity of the monodromy matrix is used to determine the bifurcation types involved, that are: (i) flip, (ii) fold, or (iii) secondary Hopf. For the SDOF system, chaotic motion was found to occur through period doubling. Boundary crisis as well as internal crisis are also found to occur for the SDOF system. For the Jeffcott rotor model with a piecewise nonlinearity, a chaotic whirling motion following a sequence of period doubling is detected. Secondary Hopf bifurcation (invariant tori in Poincare section) occurred due to the presence of the cross coupling terms. |
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| Item Description: | Typescript (photocopy). Vita. "Major subject: Mechanical engineering." |
| Physical Description: | xxii, 215 leaves : illustrations ; 29 cm |
| Bibliography: | Includes bibliographical references. |