STABILITY ANALYSIS OF STEADY MOTION USING THE DISPLACEMENT-BASED VARIATIONAL METHOD

A general criterion for checking the stability of the equilibrium state of a system in steady motion is presented. Such a criterion requires that: when being disturbed a change in a system the resistance will certainly occur according to the level of external excitations, the system will remain stable if the generated resistances surpass the effect of applied disturbance. Otherwise, the system becomes unstable. This procedure can be more appropriately termed a displacement-based variational method, as the small displacement changes resulting from the process of disturbance is employed to measure the resistance offered by the system. Based on D’Alembert’s principle, where dynamic problems can be treated in a static way, the proposed method is applicable to the problems of dynamic stability as well. Results of seven illustrative problems are essentially identical to classical solutions, which serves as a strong basis enabling the application of the present method to the problems of stability of steady motion.