Improved Time‐History Analysis for Structural Dynamics. II: Reduction of Effective Number of Degrees of Freedom

Abstract

A crude analysis of a dynamic system involves very few degrees of freedom. When a more refined model is desired, more degrees of freedom must be introduced. This will increase the number of modes present and result in modes with very high frequencies in the model. The presence of these modes causes severe restriction in the size of time interval that can be used for step‐by‐step dynamic analysis in nonlinear problems. This restriction is removed by a new type of perturbation procedure that generalizes the method of static condensation and can treat relaxation of constraints in addition to variables associated with small masses. The additional degrees of freedom are treated algebraically rather than as true dynamic variables. The method is applied to structures with significant material nonlinearity. The lower‐frequency motions are corrected as a result of the presence of the additional degrees of freedom, but the very high frequency motions are not introduced. Thus, the time interval is selected corresponding to the highest frequency involving only the dynamic variables rather than to the much higher freqencies that would ordinarily be present.