Active Control of Sound Radiation Pressure

This paper is concerned with the problem of suppressing the acoustic radiation pressure generated by a structure vibrating in air. The approach is to control the vibration of the modes of the structure most responsible for the radiation pressure. This control is carried out by active means, i. e., by feedback control. As a numerical example, the problem of active control of the far-field radiation pressure generated by the vibration of a simply-supported rectangular elastic plate is considered. The influence on the control effectiveness of various design parameters, such as the number of controlled modes, the choice of controlled modes, the number of actuators and the location of the actuators, is investigated. The conclusion is that, depending on the magnitude of the excitation frequency, satisfactory control can be achieved by using a sufficient number of actuators and by controlling a relatively large number of modes.

Shear Buckling of Simply-Supported Rectangular Elastic Plate

The equation for the buckling of a homogeneous elastic plate is well known For a simply-supported rectangular plate without shear (Nxy=0), the critical loads are usually found by substituting into equation (1) and determining the loads at which nontrivial solutions exist. In the presence of shear, however, the difficulty with the above approach is that the shear term would involve cosines instead of sines.

Influence of Large Amplitudes on Free Flexural Vibrations of Rectangular Elastic Plates

In a recent paper (1) a set of plate equations was derived, which governs motions with small elongations and shears, but moderately large rotations, valid for an isotropic material obeying Hooke’s law. The resulting theory, which may be considered the dynamic analog of the von Karman plate theory, is applied presently to the study of free vibrations of a rectangular, elastic plate with hinged, immovable edges. The nonlinear equations are solved approximately by employing a perturbation procedure and also the principle of conservation of energy directly. The influence of large amplitudes on the period of free vibration and on the maximum normal stress is established. The free vibrations of a beam are studied as a special case and the resulting period compared with a previous investigation.