Modeling the acoustic radiation of plates using circular pistons

We propose an equivalent piston model (EPM) for estimating the modal radiation efficiency of complex-shaped plates. In this model, the structure is not discretized into small elementary radiators. Instead, it involves determining the minimum number, size, volume velocity, and position of vibrating pistons that radiate in accordance with the mode shape they emulate, i.e. one piston per lobe within the mode shape, regardless the plate’s shape. For shapes relatively close to rectangles, a specific version of the method is proposed by representing the shape only by two characteristic lengths (EPM-RD), and paving the virtual surface with pistons vibrating at alternate phases along a rectangular grid. The validity of this assumption is evaluated in terms of shape dissymmetry, which can cause residual radiators to appear, and where the dissymmetry can affect the spatial distribution of lobes. With a known spatial distribution mimicking the mode shapes, it is possible to estimate also average values of radiation parameters, such as the average radiation efficiency and time-average mean power. The average radiation efficiency and power follow the Equipartition Theorem and allow the calculation to be performed without cross-terms and using only the modal efficiencies and resonance frequencies. Due to their simplicity and ease of implementation, piston-based equivalent models have great potential for solving radiation problems from flat structures. Any mode shape can be modeled with vibrating pistons and analytical formulations can be easily derived, even for complex geometries. Moreover, with EPM-RD, average values can also be calculated, which provides an estimation of average radiated properties within seconds without requiring any integration or large matrices to be solved.