Drgania Ram Przestrzennych z Elementów Cienkościennych o Profilu Otwartym - J. Rutecki (Engineering Transactions, 1959)
The system of differential equations of vibration of a thin-walled bar with open cross-section loaded in any manner is integrated by separation, assuming that the bar is symmetric in relation to two mutually perpendicular axes. The values of the edge functions are introduced as principal parameters. Next, vibration of a thin-walled bar with open cross-section and loaded by generalized forces is analyzed, the amplitudes being determined in every plane. The torsional amplitudes are also considered. At the same time, the amplitudes of bending moments, transverse forces, bimoments and bending-twisting moments are determined. After a detailed analysis of vibration of the bar in various cases of necessary for the method of strains are load, equations derived. This method is used in the present paper for the purpose of calculating the vibration of bars. In the final a system stage, the dynamic reactions are obtained and the vibration of a spatial frame is considered, considerations being confined to a single numerical example concerning symmetric vibration of a frame in relation to the y-axis, the warping at the nodal points of the frame being disregarded.