Unstable Vibration of Continuous Systems Subjected to Random Parametric Excitation

Abstract

The vibrational behavior of continuous systems such as beams, plates and circular cylindrical shells subjected to random parametric excitations is examined mainly from the viewpoint of possibility of unstable phenomena. The vibrational responses of those continuous systems are analyzed by means of simulation method using random sample functions of trigonometric series generated by random numbers. It turned out that unstable phenomena occur even for the cases in which random parametric excitation inputs have the fairly wide-band power spectra whose dominant frequencies deviate from, for example, the twice of the natural frequencies of continuous sytems. Besides, for such continuous systems as plates or shells which have the high frequency distribution density, unstable vibrations are generated concurrently in multi-vibrational modes. Finally, the experiment was carried out for a simply-supported beam subjected to the narrow-band random parametric excitation and it was ascertained that unstable vibrations really occur, and further the unstable figure domain made by the simulation analysis showed fairly good agreement with the experimental results.