Linear and nonlinear analysis of a clamped plate subjected to air-blast loading

This study presents an elastic linear and nonlinear analysis of a fully clamped thin plate subjected to air-blast loading. The dynamic equations of motion for the plate are derived based on the classical thin plate theory and the von Karman geometric nonlinear theory. The geometry and the loading of the problem considered is symmetric about the mid-point of the plate and, therefore, the four-mode displacement function is assumed. The Galerkin method is used to formulate a set of four differential equations of motion for both linear and nonlinear analysis. The Friedlander distribution is modified to incorporate the dynamic interactions between the blast wave front and the plate's surface. The numerical integration of the blast load over the area of a small element of the plate is carried out by the Gaussian quadrature. The linear and nonlinear equations of motion are solved numerically using the fourth-order Runge-Kutta method. The displacement time-histories of the plates subjected to the blast load obtained by the proposed model agree well with the existing experimental and finite-element analysis results. The numerical investigation of the dynamic interactions between the wave front and the plate's surface shows that the peak pressure calculated from the modified Friedlander model depends on the radial distance-to-plate's dimension ratio but the maximum impulse does not. Since the acceleration response of the plate subjected to blast load depends on the peak pressure, this modified Friedlander model should be used in the analysis for all radial distance-to-plate's dimension ratio. On the other hand, if the displacement response of the plate is of interest, the Friedlander model may be used because the displacement response of the plate depends only on the maximum impulse. The effect that the plate's aspect ratio, the plate's surface area and the charge location has on the response of the plate subjected to air blast loadings is also studied. It is found that a square plate is the weakest configuration among all of the rectangular shapes. For a square plate, the flexibility of the plate increases when the plate's area increases. However, when the plate's dimension is larger than 900 mm x 900 mm in linear analysis or 1000 mm x 1000 mm in nonlinear analysis, the flexibility of the plate decreases for the loading considered. The charge location does not have significant effect on the maximum displacement of the plate.