Vibrational Characteristics of Linear Space Frames

A digital computer program for computing the modes of frequencies of large arbitrary linear space frames is presented. The computational procedure used deals exclusively with nonzero submatrices of the system mass and stiffness matrices thus avoiding both trivial arithmetic and wasted data storage space. The solution technique is a generalization of the well-known Stodola method of beam vibration analysis. Beginning with an initial approximation of a system mode (computed by the program on the basis of a static loading condition specified in the input data), an equivalent inertia loading acting over the entire structure is evaluated. The static deformation of the structure corresponding to the equivalent inertia loading is computed, providing an improved approximation of the system mode. This procedure is executed repeatedly until convergence is attained. In computing higher modes, a procedure based on orthogonality relations is used to sweep out previously-computed lower modes. Examples are presented of solutions computed by the program, including computer-generated plots of mode shapes.