Abstract
Finite difference time domain (FDTD) models are developed to solve the vibroacoustic problem of a thin elastic plate undergoing point force excitation and radiating into an acoustic cavity. Vibroacoustic modelling using FDTD can be computationally expensive because structure-borne sound wavespeeds are relatively high and a fine spatial resolution is often required. In this paper a scaling approach is proposed and validated to overcome this problem through modifications to the geometry and physical properties. This allows much larger time steps to be used in the model which significantly reduces the computation time. Additional reductions in computation time are achieved by introducing an alternative approach to model the boundaries between the air and the solid media. Experimental validation is carried out using a thin metal plate inside a small reverberant room. The agreement between FDTD and measurements confirms the validity of both approaches as well as the FDTD implementation of a thin plate as a three-dimensional solid that can support multiple wave types. Below the lowest room mode, there are large spatial variations in the sound field within the cavity due to the radiating plate; this indicates the importance of having a validated FDTD model for low-frequency vibroacoustic problems.
Highlights
Prediction of low-frequency sound fields inside cavities with airborne sources is well-suited to finite difference time domain (FDTD) models
The FDTD model of the experimental situation uses a scaling factor of s 1⁄4 6 for which the computation time was reduced by using the scaling approach
After accounting for the total number of calculation cells and the time step used in the scaled model, the computation time was reduced by a factor of %170 compared to the original model
Summary
Prediction of low-frequency sound fields inside cavities with airborne sources is well-suited to finite difference time domain (FDTD) models (e.g., see Refs. 1 and 2). This paper concerns FDTD modelling of the interaction between the vibration field of a pointexcited thin elastic plate and the resulting sound field at low frequencies inside an acoustic cavity. Running such a model can be problematic because the general FDTD formulation that uses a uniform FDTD grid requires a large number of calculation cells and small time steps. A scaling approach is introduced to improve computational efficiency for explicit methods that are limited by the Courant condition (but avoids the need for sub-gridding schemes) This approach is valid for vibroacoustic problems where the structural response is dominated by bending wave motion.
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