Sound Radiation From a Vibrating Dome-Shaped Radiator Surrounded by a Rigid Infinite Baffle

Accurate modeling and analysis of baffled radiators are crucial for understanding their acoustic radiation characteristics, as these models serve as the foundation for evaluating the performance of real-world loudspeakers. This paper focuses on the radiation behavior of a dome-shaped radiator in an infinite baffle. A key theoretical insight is that the far-field sound pressure of a dome radiator can be expressed as a three-dimensional Fourier transform (3D-FT) integral of its surface velocity. Building on this foundation, we derive theoretical expressions for several typical acoustical quantities, including beampattern, directivity factor (DF), specific radiation impedance, and radiated sound power, under the far-field approximation and axisymmetric velocity distribution conditions. Next, we address the null problems observed in the DF of current velocity distributions, which arise due to the complex exponential integral term in the DF's numerator. A detailed analysis is performed to identify and understand the root causes of this issue. As a solution, we design an equalization filter based on the frequency spectral characteristics of an actual vibrating dome to smooth the DF across the entire frequency range. A performance comparison between several typical vibrating velocity distributions and the proposed distribution is presented, with evaluation results demonstrating that the proposed velocity distribution achieves a higher and smoother DF than existing models.