Accurate Reduction of Stiffness and Mass Matrices for Vibration Analysis and a Rationale for Selecting Master Degrees of Freedom

A method is described which permits the reduction of stiffness and mass matrices on to selected degrees of freedom, while accurately retaining, up to a certain cut-off frequency, the dynamic characteristics of the original matrices. The validity of the method is demonstrated by obtaining identical results, for the reduction of a simple system, with those derived from a rigorous solution. An interpolation equation is also developed which allows the eigenvector components on the eliminated degrees of freedom to be determined accurately from the ‘master’ components. Some guidelines are provided for the optimal selection of the ‘master’ degrees of freedom and a procedure defined for progressively improving the initial selection, prior to undertaking the eigenvalue analysis.