Plates (Engineering)--Vibration

An energy method is presented for predicting the natural frequencies,
radiation loss factor and system loss factor of simply supported
rectangular plates under fluid loading. Both bare plates and plates
with complete damping treatments are considered. Results obtained
using the method developed are compared with two other theories.
The agreement is generally good. The study points out the need for
detailed analyses of plate vibration patterns and their associated
radiation output under various plate boundary conditions. There also
exists a need for carefully conducted experimental work to verify
the applicability of the current theory.

A mobility power flow approach is used to study the response of an infinitely-long cylindrical shell with an internal plate discontinuity. The shell is excited by either a ring radial force or by a plane acoustic wave. The junction between the shell and the internal plate is assumed to be radially pinned such that in-plane waves of the plate can be neglected. The junction forces are expressed in terms of the mobility functions of the plate and the shell. From knowledge of the junction forces and velocities, the power input, the power flow from the shell to the plate, the shell response and the radiated far-field scattered pressure are determined for the circumferential mode n = 0. The results show how the energy propagates from one structure to the other, and present a very clear picture of the characteristics of the scattering pattern from the junction forces.

An analytical and experimental investigation of the flow of vibrational power in a thin, L-shaped, finite plate structure subjected to mechanical and acoustic excitation is presented. In the analytical approach, mobility functions are used to determine the structural intensity vectors at various locations on the plate structure. Simulation results of intensity vectors estimated using three different measurement schemes are compared. The experimentally measured intensity vectors, for the case of mechanical excitation, using a four accelerometer array, are presented. They are found to match well with the results from the corresponding simulation. Similar results are obtained for the case of acoustic excitation of the L-shaped plate. The general pattern of the structural intensity vectors is found to be in agreement with the expected results.

The dynamic response of plate structures composed of rigidly connected thin plates subjected to point loads is studied. The finite strip method combined with a new approach for analyzing periodic structures is utilized to obtain substantial reduction in computational efforts. Each strip with various boundary conditions is treated as a waveguide capable of transmitting different wave motions. Wave scattering matrices are defined to characterize wave motions at boundaries, intersection of plates and where type of wave guides are changed. The results obtained from the application of the approach on various plate configurations are presented and discussed.

The interaction between vibrating structures and fluids can have a profound influence upon the natural frequencies of the structure's vibration. This study examines one specific structure; a thin circular plate with the rarely studied free edge condition. It starts by considering a completely free plate in a vacuum and then, using receptance matching, utilises this result to determine the effects, on the natural frequencies, of a centrally located driving rod. Then, using the same technique, a result for the drive admittance of the fluid loaded plate is adapted to predict the natural frequencies of the same structure when subjected to significant fluid loading. All these results are then compared to those obtained from experiments.

An analytical investigation based on the Power Flow Method is presented for the prediction of vibrational Power Flow in simple connected structures subjected to various forms of distributed excitations. The principle of the power flow method consists of dividing the global structure into a series of substructures which can be analyzed independently and then coupled through the boundary conditions. Power flow expressions are derived for an L-shaped plate structure, subjected to any form of distributed mechanical excitation or excited by an acoustic plane wave. In the latter case air loading is considered to have a significant effect on the power input to the structure. Fluid-structure interaction considerations lead to the derivation of a corrected mode shape for the normal velocity, and the determination of the scattered pressure components in the expressions for the Power Flow.

An experimental investigation to determine the effectiveness
of partial constrained layer damping treatments for a
clamped rectangular plate is described. The impulse testing
technique was used with a Hewlett Packard '5423A structural
Dynamics Analyzer' to determine modal parameters of
the first five flexural modes. The results obtained are
compared with theoretical results and they are in agreement.
The results indicate that partial constrained layer damping
treatments, if properly used, can be more effective than
complete treatments.

A theoretical analysis for predicting the system loss factors and
natural frequencies of rectangular plates with complete and partial
constrained-layer damping treatments has been presented. This analysis
is based upon an energy approach to the free vibration of plates.
Results predicted were compared with those from experiments. Satisfactory
agreement has been reached. Both the theoretical and the
experimental results presented in this thesis indicate clearly that
partial constrained-layer damping treatments can provide effective, or
even superior, amounts of damping, and that their use can lead to
significant savings in material costs and weight.

An energy method for predicting the natural frequencies and loss factors
of Rectangular Plates with Complete Constrained-Layer Damping Treatments
has been presented. Results obtained using the method developed were
compared with those of two former theories. The agreement between the
current theory and these two theories was generally good. There is a
serious need for carefully conducted experimental work to verify the
applicability of the current theory and of the various other laminated
plate theories in existence. It is believed that the method of analysis
presented can be extended to handle plates with partial constrainedlayer
damping treatments.

A method of analysis is presented to determine the natural
frequencies and loss factors of a plate covered with viscoelastic
coating, using experimentally obtained mode shapes.
The mode shapes for a square plate clamped on all edges are
determined using an HP 5423 A Structural Dynamics Analyzer.
A computer program, based on the method of analysis, is
developed to determine the natural frequencies and loss
factors of a rectangular plate covered with viscoelastic
material, and clamped on all edges. It was found that,
for a fully coated plate, and for a mesh with twenty-five
mesh points, the error in the fundamental frequency was
approximately 5 percent. A comparison between the mode
shapes for the bare plate and for the fully coated plate
revealed no significant difference. It was also found
that increasing the number of measurement points would
not significantly improve the results.