Prediction for architectural structure-borne sound by the finite-difference time-domain method

Abstract

Herein the possibility of the FDTD method, which considers longitudinal and shear waves and two types of damping terms, is investigated as a new prediction method for architectural structureborne sound. Equations of motion and Hooke's laws of three-dimensional elastic bodies are directly discretized with a difference scheme of the leap-flog algorithm. Using these formulations, vibrationmode transformations at the junctions of building frames can be considered without special handling. This method seems to be especially effective for providing both visible and audible predictions because time responses can be obtained directly. First, the formulations and the stability condition are discussed. Next, a parallel computing algorithm to efficiently perform the FDTD calculation is introduced. Finally, the predicted results are compared to the measured data from the viewpoints of energy decay and frequency characteristics. From these comparisons, it is confirmed that the predicted results and the measured data are in good agreement if the appropriate damping terms are employed.

Finite-difference time-domain method for heterogeneous orthotropic media with damping

“…Hence, this section focuses on two boundaries: a fixed boundary and a free boundary. Although our previous work [12] defined fixed and free boundaries at the plane that includes the reference points of normal stress, the boundaries in the present study are defined at the plane that includes the reference points of normal velocity to the boundary surface.…”

“…The authors have investigated the possibility of employing the vibroacoustic FDTD method, which considers longitudinal and shear waves as well as two types of damping, to predict architectural structure-borne sound [12]. One of the two types of damping is proportional only to the velocity and the other is proportional to the secondorder space derivative of the velocity and the strain velocity.…”

“…2, the formulation for heterogeneous orthotropic media is derived, including basic equations, averaging of material parameters, boundary conditions, and the stability condition. Procedures for discretization and excitation are omitted because they are the same as in our preceding work [12]. In Sect.…”

Finite-difference time-domain analysis of structure-borne sound using a plate model

“…In order to predict such transmission characteristics of vibration, prediction methods using wavebased numerical analysis have been proposed [1][2][3]. Toyoda and Takahashi [1] proposed 3-dimensional elastic wave analysis for structure-borne sound by the finite-difference time-domain (FDTD) method.…”

“…In order to predict such transmission characteristics of vibration, prediction methods using wavebased numerical analysis have been proposed [1][2][3]. Toyoda and Takahashi [1] proposed 3-dimensional elastic wave analysis for structure-borne sound by the finite-difference time-domain (FDTD) method. In this method, the target building structures are spatially discretized by 3-dimensional meshes in the x, y, and z directions, and accurate modeling of the vibration field is possible.…”