Vibrations  of axially moving continua in presence of obstacle at the supports

• Axially travelling continuous systems have many applications in industries. These can be in the form of a string, beam, etc. Its most widespread uses include belt-pulley drives for power transmission, ropeways, elevators, conveyers, paper holding equipment, thread lines, magnetic tapes, etc.

• Axially traveling continuous systems have many applications in industries, such as threadlines, high-speed magnetic and paper tapes, band saw blades, power transmission using belt pulley drive and chains, as well as pipes that contain flowing fluid. However, the biggest challenge in all these systems is instability, which is responsible for undesired large amplitude vibrations. These undesirable oscillations make it difficult for the entire system to operate smoothly and can reduce its performance and functionality. It is known that there exists a critical speed above which continuum structures might lose stability. This instability, caused by axial speed, might lead to self-excited vibrations. Various mathematical models have been developed to study such types of vibrations, but most of them have ignored the finite size of the obstacle/pulley over which these structures move. Therefore, it is necessary to develop an extensive mathematical model that considers the complexity of the moving boundary and associated wrapping nonlinearity. Vortex induced vibrations of such systems might be an interesting point of investigation. 

Some important observations-

•Harmonic nature of the frequencies and their dependence on the static-wrapped length of the string.

•Time-varying modeshapes.

•Amplitude modulations.

•Reduction in the modulation frequency when the relative size of two curved obstacles approach each other.

•Existence of mode-locked periodic solution with equipartition of energy among the various vibrational modes.