Free Vibrations of Pre-Twisted Plates : Fundamental Theory : Vibration, Control Engineering, Engineering for Industry

The derivation of fundamental equations needed to investigate the free vibrations of thin pre-twisted plates is presented in this paper. Firstly, the strain-displacement relationships are derived by employing assumptions of the thin shell theory, and their simplified forms are proposed for plates having relatively large length-to-width ratios. Next, the principle of virtual work for the free vibration of the thin pre-twisted plates is formulated. The equation derived will be used to analyze the free vibrations of the thin pre-twisted plates by the Rayleigh-Ritz procedure