Synthesis of linear lumped-parameter systems in which a mode shape is partially prescribed

Abstract

The paper presents a means of synthesizing the inertial elements of a linear lumped-parameter system so that the system will freely vibrate at a prescribed frequency with a mode shape which, although not completely defined, satisfies certain specified requirements. Although the problem cannot normally be solved to give a unique result, it is shown that the solution may be expressed in terms of a linear combination of vectors and associated scalar multipliers, which may assume arbitrary values providing that these lead to non-negative inertial elements. The procedure is illustrated by two numerical examples, the second of which demonstrates a means of extracting mode shape admissibility criteria for systems in which the stiffness matrix is known.