Finite Design against Buckling of Structures under Continuous Harmonic Excitation

摘要

This paper focuses on the use of Dunkerly principle and modal analysis to design a multi-mass system against buckling failure. A Functional Energy approach is used to establish the stiffness and mass matrixes of a hypothetical structure under harmonic excitation in order to appropriately determine the dynamic response of a system under buckling failure mode. In order to allow for the use of the Dunkerley principle to form an approximate equation that would allow the approximation of the fundamental natural frequency of the system, the lumped mass formulation of an element is used instead of the consistent mass matrix formulation. The assembly of the global elements stiffnesses and the global lumped mass matrixes enabled evaluation with Dunkerley principle. Finally modal analysis was carried out using matlab codes for eginvalue problems to establish the eigenvalues and eigenvectors that describe the different modes of excitation under different natural frequencies predicted by the eigenvalues. The design depicts an isolated resonance as frequency of excitation which is 157rads/sec differs with 191rad/sec evaluated by Dunkerley and the maximum frequency of 197rad/sec estimated through eigenvalue approach.