Plane and Circular Motion of a String

Uniform stability of damped nonlinear vibrations of an elastic string

“…The phenomenon was first observed by Hunton as reported by Harrison [9]. The reference to other subsequent experiments can be found in the book by Nayfeh and Mook [14].…”

Steady-state whirling motions of thin filaments

“…The classical theory of the finite motion of the thin rods was developed by Kirchhoff about 150 years ago, presented in detail by Love (1927), and recently reviewed by Dill (1992). While there are a large number of investigations dealing with the motion of perfectly flexible strings (for example, Carrier, 1945;Harrison, 1948;Oplinger, 1960;Murthy and Ramakrishna, 1965;Narasimha, 1968;Miles, 1984;O'Reilly and Holmes, 1992;Nayfeh et al, 1995;Lin and Ravi-Chandar, 2006), relatively little work has been done on the motion of filaments with non-negligible bending stiffness. Tabor (1997a,b,c, 2000) studied the nonlinear dynamics of the filaments based on the Kirchhoff's rod equations in a series of papers: they studied the stability of various stationary solutions, such as planar ring and straight rod, subject to twisting perturbations.…”

Energy Decay Rate for the Kelvin-Voigt Type Wave Equation With Balakrishnan-Taylor Damping and Acoustic Boundary

“…The analytical studies in the area of stabilization of distributed parameter system is currently of interest in view of application to vibration control of various structural elements. The phenomenon was first observed by Hunton as reported by Harrison [9]. The nonlinear model like (1.1) for transverse vibrations was originally derived by Kirchhoff [8].…”