Direct superposition of Wilson trial functions by computerized symbolic algebra

Abstract

Method of direct superposition of trial vectors, proposed by Wilson, is elucidated for the vibration analysis of systems, possessing damping, by the computerized symbolic algebra. The essence of the method is using a specific set of trial functions (Wilson trial functions) derived in a special manner from the appropriate static solution, rather than performing a mode superposition analysis by the exact eigenvectors of the system. Immediate advantage of the method is that the static solution, to which a dynamic solution should tend for the vanishing excitation frequency, is obtained automatically, by using a single vector, whereas within the exact eigenvectors, infinite number of eigenvectors are involved to obtain a static solution. A specific example is numerically evaluated and it is clearly demonstrated that the superposition of the Wilson trial functions yields extremely accurate results with fewer vectors than using the conventional set of trial functions, utilized within the Rayleigh-Ritz method.