Numerical analysis for the dynamic response of lumped-mass systems subjected to a bilinear resistance function - Huapanichyont, Kitti (1975)
The objective of this paper is to present a procedure to determine the inelastic responses of single-degree of freedom, as well as multi-degree of freedom, structures under one-directional dynamic loading condition. The single-degree of freedom system, in damped and undamped cases, is idealized as a single storey one bay rigid frame which is subjected to horizontal dynamic load at the floor level. The force-displacement behavior of this frame is characterized as bilinearwhich consist of the initial elastic, inelastic and unloading conditions. For the multi degree of freedom system (Undamped), a non-prismatic cantilever beam subjected to distributed load is chosen. This beam is divided into finite elements of equal lengths thus defining the number of lumped masses and loads. The moment-curvature relationship of the beam section at any specified mass point is presented for both initial elastic and inelastic ranges, and also during the unloading condition. The equations of motion for damped and undamped cases of both systems are written by applying the D'Alemberts' principle and presented in scalar form. Finally, the solution of the equations is carried out by using a numerical technique - the B integration method, which was developed by Newmark in 1964. This solution process determined the inelastic responses of the two structures as they are subjected to dynamic loads. The finite different approach is also utilized in the solution of the beam problem. The numerical results derived from the solutions of the two systems are presented in tabular and graphical forms. The responses are examined in accordance with the order of magnitude errors as compared to those obtained by the elastic solution of the same systems using the B - integration method and the rigorous solution.
Thesis (M.S.)--University of the Philippines, Quezon City.
Keywords: Structural stability; Dynamics; Numerical analysis