A New Method for Mid- to High-Frequency Vibration Analyses of Beam Structures 2019-01-1535
Vibration analyses of complex flexible structures in mid- to high-frequency regions have important applications in auto, aerospace and ship engineering, as well as high-tech developments. In this paper, a new method is proposed for mid- and high-frequency vibration analysis of flexible beam structures. In this method, the vibration of a multi-body beam structure is modeled by an augmented formulation of the Distributed Transfer Function Method (DTFM). The formulation does not rely on discretization, treats all the beam members and different types of connection and boundary conditions systematically, and does not need to change formulas of calculation when the excitation frequency varies from low to high. Unlike conventional methods, the DTFM-based analysis does not require the knowledge of coupling loss factors and energy transmission coefficients. A highlight of the new method is that it delivers frequency response solutions with detailed local information on displacement, slope, moment and shear force, which otherwise may be difficult to obtain by conventional methods for mid- to high-frequency analyses.
The proposed method is illustrated on two-dimensional Euler-Bernoulli beam frames in numerical simulation. The method is compared with the finite element analysis (FEA), statistical energy analysis (SEA) and energy flow analysis (EFA) and good agreement is seen in all the examples. The new method is numerically efficient and delivers highly accurate solutions in frequency regions from 10^2 to 10^8 Hz, and beyond. The method is readily applicable to mid- to high-frequency analyses of Timoshenko beam structures and three-dimensional beam structures. It is believed that the proposed DTFM is a useful tool for design and optimization of complex structures in engineering applications.
Bingen Yang, Yichi Zhang
University of Southern California
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