Dynamics of Frames With Axial Constraints

Abstract

The number of degrees of freedom for the dynamic analysis of plane and space frames may be considerably reduced by introducing axial constraints. Determination of the rank and basis of the constraint matrix by Gauss‐Jordan elimination with pivoting leads to automatic selection of the best set of dependent and independent joint translations. Then a transformation of the equations of motion to generalized coordinates produces a reduced set of equations that may be solved for the dynamic response of the independent joint translations. This technique can be applied in conjunction with the elimination of joint rotations, thereby accomplishing a double reduction without significant loss of accuracy. The procedure described has been programmed on a digital computer for both plane and space frames, with automatic identification of redundant constraints.