Periodically stiffened fluid-loaded plates, I: Response to convected harmonic pressure and free wave propagation

In this paper several aspects of the vibration of and sound radiation from an infinite fluid-loaded plate stiffened periodically by line supports are studied. The supports may exert both forces and moments on the plate. First the response to a convected harmonic pressure is found by using Fourier transforms and the response is seen to consist of an infinite set of space harmonics whose amplitudes are found explicitly. Certain infinite sums arise and when fluid loading is neglected these are evaluated analytically. A condition is derived for the propagation of free waves. For the fluid loaded case an acoustically damped "propagating" wave is seen to exist. An expression for the response to a general excitation is derived and from this the acoustic pressure in the far field is determined.