A METHOD FOR FAST ANALYSIS OF LOW-ORDER FREQUENCIES IN COMPLICATED BEAM-TYPE STRUCTURES BASED ON BEAM THEORY
In modern engineering calculations, we often have to deal with dynamic analysis, or even optimization of dynamic performance for complicated slender structures whose longitudinal dimensions are significantly larger than their transverse ones. Based on a fine FEM model of such complicated structures, constructing an approximate physical model which requires only a small amount of work and can be used to predict the structural dynamic performance and meet the requirements of design, optimization, simulation, and other tasks in the preliminary design stage is still very valuable in many design departments. This paper presents a model reduction method for these structures, which is based on the plane cross-section assumption and displacement interpolation function of beam, and results in a physical reduced model. By using the vibration modal vectors of the reduced model and constructing an initial guess of vibration modes of the original structure, one Rayleigh-Ritz iteration results in a high-accuracy estimate of vibration frequency, which is also compared with the Krylov subspace methods. The examples show the validity of this method.