Use Of Plate Theory Research Articles

Stress and damping of wide cantilever beams under free vibration

Research has shown that the damping of a vibrating structure is highly dependent on its stress function. In this study, the bending stress and damping of wide cantilever beams under free vibration were analyzed using the classical plate and beam theory. The damping stress equation for cantilever beams under free vibration was derived based on the empirical function of unit dissipating energy, whereas the plate bending equation was derived using the double finite integral transform method. The bending stress and damping ratio results from the beam and the plate theory were compared with simulation results from finite element analysis (FEA) for different length-to-width ratios. Results show that the plate theory displayed a good agreement with FEA results in terms of estimated value and trending curve shape when a significantly large number of terms were used. Using a small number of terms resulted in large errors at high length-to-width ratios, but provided sufficient estimates when the length-to-width ratio dropped below four. It was found that the beam theory was only valid for beams with very high length-to-width ratios or square plates. Beyond this ratio, the beam theory recorded a higher error estimate than the plate theory. Overall, the most accurate stress and damping estimations come from the use of plate theory with a very high number of terms.

On the use of plate theory to evaluate the load relaxation in bolted flanged joints subjected to creep

The effect of load relaxation due to creep has a major impact on the tightness of bolted flanged joints. Several leak incidents have been reported in the petrochemical and nuclear power plants related to creep. It is clear that the current flange design code does not address adequately the effect of high temperature on the mechanical and leakage integrities of bolted flange joints used in pairs or with blind cover plates. It is possible to include the creep analysis in the design methodology. This paper outlines an analytical approach based on plate theory used to determine the creep effect of blind cover plates and flanges of a small size on the bolt and subsequently the gasket load relaxation in bolted flanged joints. It details the theoretical procedure to predict the creep effect of those flanges considered as plates. The results from the theoretical model are verified by comparison with 3D finite-element results.