Effect of axial forces on the free vibration characteristics of discrete-membered structures

This work has been devoted to study the effect ofthe axial force in the plane-framed structures, modifyingthe structural stiffness matrix, by the use of stabilityfunctions to include the axial effects, and a study ofthese effects on the vibration characteristics of theplane-framed structures using the lumped mass matrix.The axial effect was formed separately from thestructure stiffness matrix as an independent matrix calledthe geometric stiffness matrix. To include the axialeffect in the structure stiffness matrix, the stabilityfunction (~) was first introduced by Livesley (8), andtables for its values for compressive forces were publishedby Maj id (9).The effect of axial forces in vibration of framedstructures was studied by Nowacki (11), developed andintroduced in matrix form by Clough and Penzien (2), butit is doubtful that it has seen much practical use todate, because of its complication and· long calculation.In this work the above methods were compared by theuse of discrete-parameter finite-element for plane framedstructures, and a comparison was carried out by usingthe stability function (9) instead of the geometricstiffness matrix.