Finite-difference time-domain analysis of structure-borne sound using a plate model based on the Kirchhoff-Love plate theory

Abstract

A vibroacoustic numerical method employing an implicit finite-difference time-domain (FDTD) method, in which the target architecture is modeled as a composition of two-dimensional plate elements, is proposed in this paper. While structure-borne sound is a difficult phenomenon to predict owing to the complexity of the vibration mechanism on the building structure, wave-based numerical techniques may enable its accurate prediction by virtue of their flexibility from the viewpoint of modeling the object. However, with the current PC performance, prediction for a large-scale problem is still difficult. To solve such a problem, we model the target structure as a composition of plate elements to reduce the simulated field to two dimensions, in contrast to the discretization of the field into three-dimensional solid elements. This results in memorysaving and faster simulation. In this paper, the basic theory of vibroacoustic analysis for a model with plate elements is described, and the results of a case study for a box-type structure are discussed.

Finite-difference time-domain analysis on structure-borne sound transmission characteristics of double-plate structures connected by elastically supported bars

“…The damping characteristics of the bending vibration using Eq. (1) are simulated by setting appropriate values of $ and " [6] for the acrylic planar material.…”

“…To simulate the vibration propagation by FDTD, the elastic wave analysis is available; however threedimensional modelling of the objects by the analysis requires higher computational costs. To reduce the costs, FDTD modelling of the plate-like and/or rod-like structures by using 2-dimensional plate elements [6] and/or 1-dimensional beam elements [7] has been investigated. By using this method, relatively costless vibroacoustic simulation of building structures is possible.…”

Finite-difference time-domain analysis of the vibration characteristics of a beam-plate structure using a dimension-reduced model

“…(25) have a curve that is convex downward. The measured loss factor in our previous paper [21] was modeled by setting appropriate coefficients for n and l. Appropriate pairs of these coefficients were searched for by applying the least squares method. As a result, two pairs of parameters, as shown in Table 1, are obtained for the frequency ranges of 10 to 100 Hz and 100 Hz to 2 kHz.…”

“…Considering the continuity conditions described in Section 2.3, the continuity conditions of Eqs. (21) and (22) are rewritten as follows.…”

“…In addition, these investigations have treated simple structures with single plates, and the applicability of these methods to practical cases, such as real building structures, has not been clarified. In order to simulate the vibration of a real-scaled structure composed of multiple plate-like elements using a time-domain scheme, Asakura et al proposed a vibro-acoustic FDTD simulation method [21][22][23]. In this method, the target structures are modeled as a composition of multiple two-dimensional plate or one-dimensional beam elements, and the characteristics of the vibration and radiated sound can be obtained.…”