Free-free Plate Research Articles

Modelling the Sound of a Golf Ball Impacting a Titanium Plate

A model was developed to predict the sound of a ball impacting a USGA CoR plate, as a first step towards simulating the acoustics of a ball/driver impact. A ball was dropped from 2.5 m onto a free-free plate with the impact sound recorded with a microphone. The experiment was replicated in Ansys/LS-DYNA, with both the exact Boundary Element Method and the Rayleigh method applied to predict the sound. The Rayleigh method predicted lower acoustic pressure than the Boundary Element Method, and was less accurate at predicting relative amplitudes of the frequency spectrum. The models under-predicted decay time, although, increasing mesh density improved agreement with the experiment. Further work should look to improve agreement between model and experiment for decay time, while investigating the effect of impact speed for a range of plate thicknesses.

Theoretical and experimental predictions of the hydroelastic response of a very large floating structure in waves

A prediction method for the hydroelastic behavior of a very large box-shaped flexible structure in regular waves is proposed. The structure considered is representative of such structures as a floating international airport and thus the horizontal dimensions are expected to be as large as several kilometers in both length and width. In the analysis, the structure is divided into a number of substructures and the continuous deformation is approximated by the succession of a discrete displacement of each substructure. The displacement of each component is determined from the equation of motion of a uniform free-free plate representing the substructure, while taking structural constraints into account as an additional restoring force. The hydrodynamic forces on the substructure are determined by enforcing the normal velocity of the flow to be equal to that of the corresponding body surface. Thus, the fluid motion and the body motion interact with each other, which is termed ‘hydroelastic interaction’, requiring the simultaneous solution of the structure and fluid problems.

Experimental investigation of the vibroacoustic behavior of structures for validation purposes

Various test parameters that might affect the accuracy of the vibrational characteristics of thin plates are examined. For the development and validation of acoustical radiation models based on the vibrational characteristics of the structure, the relative influence of these parameters is evaluated and limits are provided. Vibrational and acoustical experimental results on several free-free plates are presented. The influence of excitation source types, mass loading and mass compensation procedures are examined in view of the inherent variability between test specimens.

The dynamics and control of large space structures after the onset of thermal shock

This paper considers the problem of predicting the open and closed loop dynamics of large space structures after the onset of thermal shock. The thermal gradients induced in space structures due to solar radiation heating result in thermal deformations. The temperature gradient time history, the related thermal deflection response, the moments acting on a thermally deflected beam, and the control effort required for different combinations of solar incidence angles and material properties are considered in this investigation. The analysis is performed for structures which are nominally inertially stabilized as well as gravity stabilized. For the case of basic orbiting structural elements, such as a free-free plate (modelled as a beam in-plane), depending on the orientation, and required pointing accuracy, it may be necessary to redesign control algorithms previously developed for models which exclude the thermal shock effects.

Bending and Vibration of Plates of Variable Thickness

The problem of bending and vibration of plates of variable thickness and arbitrary shapes and with mixed boundary conditions was solved by a modified energy method of the Rayleigh-Ritz type. General trial functions of deflection were obtained, one in Cartesian coordinates for rectangular plates and the other in polar coordinates for other shapes. The forced boundary conditions were satisfied approximately by introducing fixity factors which depended upon the prescribed conditions. Central deflections for circular plates subjected to static bending were within 0.2 percent of published results while they were within 1 percent for rectangular plates. The differences of natural frequencies of various rectangular plates were from 0.05 percent for simple, 2.9 percent for clamp, and up to 4.3 percent for free-free plates based on the published values.

Measurements of energy flows in impacts

This paper describes experiments designed to measure the spectrum of the vibratory energy injected into structures by impacts. It is felt that if the techniques prove to be feasible, the information provided might be useful in efforts to reduce the noise generated by impact-preducing machines. Two techniques are described. The first requires measurements of the reverberation time of the impacted structure, and of the energy spectrum of the transient acceleration of the structure in response to the impact, observed at many points on the structure. The second requires only a single impact response measurement, and a single measurement of the steady-state response to a steady-state excitation at the impact point. These experimental methods are tested using the impact of a small steel sphere against a large, thin free-free plate. A simple theoretical expression for the spectrum of the injected energy is available for this case. The experimental results are compared to the theoretical prediction.