... Parametric instability in a system is caused by periodically varying coefficients in its governing differential equations. While parametric excitation of lumped-parameter systems has been extensively studied, that of distributed-parameter systems has been traditionally analyzed by applying Floquet theory...

... of the vibratory energy of the string within a control volume, and the energy growth mechanism of the string during retraction is elucidated. The solution methods are applied to a moving elevator cable with variable length. An interesting parametric instability phenomenon in a translating string with sinusoidally...