Radiation efficiency of natural modes of plates with beam stiffeners

In this paper, the radiation efficiency of the natural modes of finite plates with attached beams is considered. Firstly, the scattering of flexural waves, by the beams and the boundaries, in the plate is considered. The reflection and transmission coefficients along with the near-field coefficients of the beam are used to calculate the vibration field of the plate, by taking into account an infinite number of reflections from the boundaries. A wavenumber transform of the vibration velocity field is used to calculate the sound power and the radiation efficiency. The stiffening beams will shift the resonant frequencies of the plate to higher or lower frequencies depending upon the resonant frequency of the beam. This will also affect the radiation efficiency. From numerical evaluation, it is shown that the beam behaves as an added stiffness for frequencies below the resonant frequency of the beam stiffener whereas for frequencies above this frequency the beam behaves as an added mass.