Analysis of the flexural vibration of a thin-plate box using a combination of finite element analysis and analytical impedances

Many practical built-up thin-plate structures, e.g., a modern car body, are essentially assemblies of numerous thin plates joined at their edges. The plates are so thin that they invariably support the weight of the structure and machinery using their substantial in-plane stiffness. Consequently, vibrational power injected into the structure from sources mounted at these stiff points is controlled by high impedance long-wavelength in-plane waves in the plates. As the long in-plane waves propagate around the structure, they impinge upon the numerous structural joints at which short-wavelength flexural waves are generated in adjoining plates. These flexural waves have much lower impedance than the in-plane waves. Hence, the vibration of thin-plate structures excited at their stiff points develops into a mixture of long in-plane waves and short flexural waves. In a previous paper by the same authors, a numerically efficient finite element analysis which accommodated only the long in-plane waves was used to predict the forced response of a six-sided thin-plate box at the stiff points. This paper takes that finite element analysis and, drawing on theory developed in two additional papers by the same authors, couples analytical impedances to it in order to represent the short flexural waves generated at the structural joints. The parameters needed to define these analytical impedances are identified. The vibration of the impedances are used to calculate estimates of the mean-square flexural vibration of the box sides which compare modestly with laboratory measurements. The method should have merit in predicting the vibration of built-up thin-plate structures in the so-called mid-frequency region where the modal density of the long waves is too low to allow confident application of statistical energy analysis, yet the modal density of the short flexural waves is too high to ;allow efficient finite element analysis. (C) 2002 Academic Press.