Dynamics of Frames with Nonuniform Elastic Members

Fundamental and higher characteristic values and characteristic vectors of frameworks with elastic or rigid members are obtained by an approximation of a dynamic structural matrix. The approximate method is derived based on the direct iteration procedure, and the reduced dynamic matrix. The dynamic structural matrix is composed of the product of the dynamic mass matrix and the mass flexibility matrix which is formulated from the structural configurations, and the elastic properties of the divided segments of the constituent nonuniform members. A computer program and numerical examples are provided of which eigenfunctions are tabulated and plotted. Significant differences or frequencies of the same structure with various considerations of rigid-body analysis versus elastic analysis, rigid-joint versus pin-connected joints are shown.