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Description of System to be Studied
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amplitude decrement amplitude of vibration amplitude xQ Appendix approximate solution assumption 20 boundary conditions constant continuum model Cornell University defined displacement x(t driving force energy loss given equation 18 equation 26 equation 3U equation A.18 equation A.l equations 100 equations describing equations of motion equivalent linear force-displacement diagram Fourier coefficients Fourier series expansion fundamental harmonic given by equation gives the equations Heuristic Model hysteresis loop independent of amplitude intermediate stops internal friction Isotropic Kronecker Delta loop is given magnitude mass material spring Method of Equivalent notation odd function parameters partial differential equations relating the stress resonance curves resonant frequency right hand side second approximation Section series A.38 shown in Figure simple harmonic oscillator Solution of Equation solution x(0 solved specific energy loss stress and strain Substituting the assumptions symmetric vibration thesis trigonometric identities values vibrating system vibration of amplitude vibration xq written x)-direction the slope