Vibrations of Rectangular Frame Works

Abstract

The free vibrations of rectangular frame works in two groups of mode moving perpendicular and coplanar to its own plane are studied by the Lagrangian-minimizing-method. In the former group, flexural and torsional deformations must be considered, and in the latter, flexural and extensional ones must be. The frequency equations for both groups of vibration are derived explicitly, and numerical results of nondimensional frequencies in some special cases are demonstrated in graphs. The natural fact that the center of gravity of the frame in free vibration does not move is certified analytically.