Abstract
This chapter describes a method of setting up the system matrix by the application of the concept of separate matrices for the stiffnesses and masses of the system. These separate matrices multiplied together yield the system matrix. The chapter also presents the methods of structural vibration analysis. Both the stiffness and flexibility matrices are symmetric, and this property is because of the reciprocal theorem. In most manufacturers' program packages, there is a structural analysis program suitable for finding the stresses and deflections in a framework. Generally this program will not include a facility for determining dynamic behavior of the structure, but it can be used to generate the flexibility matrix from which the system matrix and, hence, the natural frequencies may be determined. Using a typical program supplied by IBM (TRUSS), the procedure will be as follows: (1) supply the framework data for TRUSS in the appropriate form as specified in the program manual; (2) specify loading cases for unit load in the X and Y directions at the position of each mass in turn; and (3) the results of this program are the elements of the flexibility matrix. These are used as input data for a program which calculates the natural frequencies.
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