Response of unconstrained layer panels to random excitation at a point

Abstract: ................................................................................................. vii Nomenclature ......................................................................................... xv List of Figures ....................................................................................... xix List of Tables....................................................................................... xxv

Abstract: For theoretical evaluation of the response of a structure under random acoustic excitation a complete understanding is required of the various modes of vibration and the modal damping associated with each mode. In order to evaluate these parameters for plates with unconstrained layer damping treatment, some of the theoretical approaches applicable are used. Experimentally observed modal frequencies and associated loss factors are compared with those estimated by different theories for all edges simply supported and all edges clamped boundaries, after accounting for the damping at supports. The modes of vibration used in the theoretical analysis for these boundaries are compared with those observed in the experiments. These results are made use of in Part II for the evaluation of response under random acoustic excitation.

Abstract: It is well known that thin metal plates used for covering machines and vehicles vibrate as a result of the original vibrations and airborne sounds, and through their own resonances and radiation properties become new noise sources. These disturbing effects can be fought by stiffening the plates or using layers of high internal viscosity on the plates. For practical purposes our research group has carried out a series of measurements in order to examine the effectiveness of vibration damping layers. Generally, we investigated plates of 2×1 m2 which, at the same time, we coated with viscoelastic damping layers of different compounds. The method of investigation was in one case excitation by an electromagnetic transducer driven with constantly varied frequency or with white noise of third-octave bands, and in the other case an impulsive excitation carried out by hitting the plate. The latter method seemed to be more suitable for determining the damping factor as a function of frequency. The frequency dependence was investigated using third-octave band filters. The results showed that the resinous layers made with filler, and smeared evenly over the plate, reduced the bending vibration of the plates by a factor which was a function of frequency. When the damping material was added as a band on the sides of the plates we obtained good results only if the plate was mounted in a frame and the frame was excited. At the same time we investigated the added effect of multi-layered sheets and found the changes to be dependent upon the experimental procedure, and not always significant. Our results were given to the industrial organizations dealing with noise abatement and use will be made of these results in the production of trains and buses.

Abstract: By virtue of the mean‐square calculus, a technique has been developed to determine the covariance and spectral‐density functions for a plate of arbitrary boundary conditions subjected to loadings that are random in space and time Also cross covariance and resulting spectral density functions are found As an illustrative example, the theory developed here is applied to a simply supported plate subjected to both a point load and a line load that is random in time only The solutions are presented in the form of infinite series that converge rapidly