Grice, R.M. and Pinnington, R.J.
Vibration analysis of a thin-plate box using a finite element model which accommodates only in-plane motion
Journal of Sound and Vibration, 232, (2), . (doi:10.1006/jsvi.1999.2748).
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Many practical built-up structures, e.g., the modern car body, are essentially assemblies of numerous thin plates joined at many edges. The plates are often so thin that they cannot support appreciable loads out of plane. In the case of a car, the body can only support the static loads of either the vehicle or the engine using the substantial in-plane stiffness of the plates. During operation of the vehicle, the dynamic loads applied to the body by the engine and suspension also act in-plane so that the vibrational power injected into the body is controlled by the in-plane properties. The paper argues that under such conditions, the vibrational response of the structure must be dominated by the mobility of long wavelength in-plane waves. To investigate this hypothesis, a six-sided thin-plate box excited by a force at a stiff point where two sides meet is chosen as the test structure. A finite element model of the box is constructed from membrane elements which accommodate only in-plane response. Predictions of the input and transfer frequency response of the box are compared with laboratory measurements with favourable agreement. The finite element model is advantageous because it has relatively few degrees of freedom making it computationally attractive, yet remains valid over very broad frequency ranges. It could therefore be used during the preliminary stages of the design of a practical thin-plate built-up structure.
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