Nonlinear vibration analysis of axially moving strings in thermal environment

Abstract

In this study, nonlinear vibration of axially moving strings in thermal environment is investigated. The vibration haracteristics of the system such as natural frequencies, time domain response and stability states are studied at different temperatures. The velocity of the axial movement is assumed to be constant with minor harmonic variations. It is presumed that the system and the environment are in thermal equilibrium. Using Hamilton’s principle, the system equation of motion, and t[1]he boundary conditions are derived and then solved by applying Multiple Time Scales (MTS) method. The effect of temperature on the vibration characteristics of the system such as linear and nonlinear natural frequencies, stability, and critical speeds is investigated. Considering ideal and non-ideal boundary conditions for the supports, nonlinear vibration of the system is discussed for three different excitation frequencies. The bifurcation diagrams for ideal and non-ideal boundary conditions are presented under the influence of temperature at various speeds.

Keywords

• Axially moving string
• Nonlinear vibration
• Multiple time scales method
• Critical speed