An Analysis of the Forced Periodic Motion of a Non-linear Non-conservative One-degree of Freedom Oscillator |
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Contents
Introduction | 7 |
Description of System to be Studied | 15 |
Symmetric Vibration Between xx and x +x | 19 |
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A₁ amplitude of vibration Appendix approximate Fourier series approximate solution assumed assumption 20 B₁ boundary conditions CORN CORNELL UNIV differential equation displacement x(t E-parameters E₁ E₂ equation 18 equation 26 equation 34 equations A.42 equations of motion Equivalent Linearization EZRA CORNELL F₂ force-displacement diagram Fourier coefficients Fourier series expansion function given by equation Hooke's Law hysteresis loop independent of amplitude K₂ Kronecker Delta loop is given material spring method of equivalent non-linear stress-strain notation obtained odd function parameters partial differential equations perturbed motion q sin Ø ratio x/q resonance curves resonant frequency Section shown in Figure simple harmonic oscillator SN₂ Solution of Equation solved specific energy loss ß² stress and strain stress-strain law symmetric vibration thesis UNIVERSITY CORNELL values vibrating system visco-elastic x)-direction the slope