Complex Eigenvalue Analysis and Nonlinear Transient Vibration of an Axially Moving String With an Attached Travelling Oscillator Under Wind Excitations

Abstract

The eigenvalue analysis and nonlinear dynamics of an axially moving string with an attached traveling oscillator excited by wind loadings are presented in this paper. The couplings in both of mass and stiffness between the string and the oscillator are considered. The Green’s function in an explicit form is obtained by the theorem of Green’s function construction, and the analytical transcendental equation is directly obtained. The maximum variance rate is defined to analyze the coupling strength of the subsystems. It is demonstrated that the first eigenvalue changes significantly when the natural frequency of the oscillator is close to that of the string’s first frequency. The equation of motion of nonlinear transient vibration of the coupled system is obtained by considering aerodynamic loading and geometric nonlinearity of the string. The equation is solved numerically for the transient response of the vibration. The effect of the geometrical nonlinearity due to large deformation and the interaction between the oscillator and the string are also presented.