Dynamic modeling of linear beam-like structures using the Equivalent Beam Stiffness method Part I: Development and benchmarking

Abstract

Analysts of beam-like structures are perennially challenged by complex geometries which are not readily translated into beam element models. The Equivalent Beam Stiffness method, or simply EBS, is presented as an extension to and improvement upon the technique of Thomas and Littlewood in which the effective stiffness diameter profile of a freely suspended rotor was estimated by applying the Euler-Bernoulli beam equation to the measured first lateral bending mode shape. The result was a set of new diameters which replaced those determined from drawings. Based upon the more generally applicable Timoshenko form, the EBS method accounts for transverse inertia and shear deformation effects, the latter requiring an a priori estimate of the equivalent stiffness diameter. Additional improvement is provided by using a continuous description of the mass and inertia properties, rather than the lumped-mass representation used previously, and an analytical approach to the extraction procedure. This allows the bending stiffness to be determined throughout the structure, while other methods to the inverse beam dynamics problem, mostly optimisation-based, determine discrete values. The effects of measurement errors are examined and it is shown the EBS method provides reasonable extractions in the presence of noise levels akin to careful modal test data. The successful application of the technique to two full-scale turbine shafts will be discussed in Part II.