Vibration analysis for framed structures using the finite-difference time-domain method based on the Bernoulli-Euler beam theory

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A vibration analysis method for structure-borne sound transmission in framed structures using an implicit finite-difference time-domain (FDTD) method is proposed in this paper. The prediction of structure-borne sound is difficult owing to the complexity of the vibration mechanism in building structures. As a powerful means of analyzing structure-borne sound, wave-based numerical techniques have the potential to solve the problem accurately by virtue of their flexibility from the viewpoint of modeling the object. For this reason, we model the target structure as a composition of beam elements and calculate the characteristics of the wave propagation using the FDTD method. Using the beam model, we can decrease the dimension of the simulated field to one dimension, compared with the situation that the field is discretized by three-dimensional solid elements. This results in a reduction of the computational cost. In this paper, the basic theory of the calculation method for a model with beam elements is described and the results of a case study of a multilayered frame structure are discussed.

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