Plates (Engineering)--Vibration

An energy method for predicting the natural frequency and loss
factor for square plates with partial and complete coatings is
developed. Both simply-supported and edge-fixed bonndary conditions
are considered. An impulse testing technique is used to
provide an experimental verification of the analysis for the case
of an edge-fixed square plate. The analytical and experimental
results are in close agreement, and indicate that partial coatings
can provide effective damping treatments.

The feasibility of using structural modification techniques to determine the effect of added viscoelastic damping treatments on the modal properties of a distinct eigenvalue system and a degenerate system is investigated. Linear perturbation equations for the changes introduced into the system eigenproperties are derived and applied to several examples involving the flexural vibration of beams and square plates with varying degrees of damping treatment. Both large and small perturbations are considered. An FEM code has been developed to compute the dynamic system parameters which are subsequently used in an iterative method to determine the modal properties. The perturbation approach described can accommodate temperature and frequency-dependent material properties, and the procedures involved are illustrated in the examples considered. Results obtained for these examples are compared with those available from closed form or finite element solutions, or from experiments. Excellent agreement of the results of the present method with those of other contemporary methods demonstrates the validity, overall accuracy, efficiency and convergence rate of this technique. The perturbation approach appears to be particularly well suited for systems with temperature and frequency dependent material properties, and for design situations where a number of damping configurations must be investigated.

The total vibrational power flow in connected plate structures is investigated using an analytical "Power Flow" approach. The effects of shear and rotary inertia on the flexural wave transmission and the influence of in-plane wave generation at structural discontinuities are included in the analytical model. In formulating a Power Flow model, the structure is divided into substructures whose responses may be determined analytically to obtain expressions for the input and transfer mobilities of the substructures. For the case of plate-type structures joined along a line, the mobilities are functions of both frequency and space. The power transmission between the individual plate substructures is then written as a function of these mobility expressions. The structure of concern in this dissertation consists of two plates connected in an L-configuration. In obtaining the expressions for the mobilities, the vibrational response of the individual plates is determined by solving the appropriate equations of motion. In this study the antisymmetric (flexural) motion is described using Mindlin's (1951) thick plate approximation to the three-dimensional equations of motion. The applicability of this thick plate formulation is limited to frequencies below the frequency of the first antisymmetric mode of thickness-shear vibration of the plate. The symmetric (in-plane) motion of the plates is described using the generalized theory of plane stress which neglects the direct coupling of the in-plane motion with the thickness vibration modes, and is therefore valid only for frequencies which are lower than the frequency of the first mode of pure thickness vibration of the plate. The results for the power transmission in the L-plate obtained using the Power Flow formulation are verified at high frequencies by comparison with the results obtained using the Statistical Energy Analysis (SEA) technique. The SEA formulation for the L-plate is based on Mindlin's equations for flexural motion and the theory of generalized plane stress for in-plane vibration. The results of the Power Flow formulation are verified at low frequencies by the results obtained using a Finite Element model of the L-shaped plate.