Large Deflection Multimode Response of Clamped Rectangular Panels to Acoustic Excitation. Volume 1

Abstract

Abstract : An analytical method is developed for the determine of large deflection multimodal random response of clamped rectangular plates subjected to normal incidence acoustic impingements. The Karman-Herrmann large deflection plate equations are solved by a technique which reduced the fourth order nonlinear partial differential equations to a set of second order nonlinear differential equations with time as the independent variable. The differential equation solution utilizes a Fourier-type series representation of the areas function and out-of-plane reflection. The compatibility equation is solved by direct substitution, and the equilibrium equation is solved through the use of Bubnov-Galerkin method. The acoustic excitation is assumed to be Gaussian. The Krylov-Bogoliuboc-Caughey equivalent linearization method is then employed that the derived set of second order nonlinear differential equations is linearized to an equivalent set of second order linear differential equations. Transformations of coordinates from the generalized displacements to the normal- mode coordinates and an iterative scheme are employed to obtain root-mean-square (RMS) maximum panel deflection, RMS maximum strain and equivalent linear (or nonlinear) frequencies of vibration for clamped rectangular panels at various excitation pressure spectral density (PSD). Convergence of the results is demonstrated by using 4, 6, 10 and 15 terms in the transverse deflection function. Effects of panel length-to-width ratio and damping ratio on panel response are also studied. There are two volumes reporting this research effort; this volume, Volume I, contains the mathematical formulations and numerical results, Volume II gives the computer program codes.