ABSTRACT
Theoretically, mode superposition is an effective method of obtaining the free or forced vibration response of a continuous system of finite extent. In practice, several difficulties may arise in the application of the method. First, it may not be possible to determine the mode shapes and frequencies of the continuous system being analyzed. This is particularly so for systems of complex geometry, or/and nonuniform properties. Second, the mode superposition response is obtained in the form of an infinite series, and although the series usually converges quite rapidly when the displacement response is being calculated, convergence may be quite slow for other parameters of interest, such as for example, the bending moment and shear force in a beam undergoing transverse vibrations, and axial force in a bar undergoing axial vibrations. In such a case, many more terms of the series must be included in the computations to obtain reasonable accuracy.
