Pressure instrumentation in explosive forming : the non-linear transient displacement of a circular plate

Abstract

The use of explosive forming for small production runs has been considered suitable for New Zealand manufacturing. A literature review of the explosive forming process establishes the need for instrumentation that enables the loading of the workpiece to be determined, particularly that associated with the workpiece/energy transfer medium interaction. Because of the magnitude of the initial shock wave the development of a pressure transducer based upon the non-linear deflection of a circular clamped plate or plate/dielectric foundation is considered. A modal analysis of the linear response of a clamped plate or plate/foundation system with viscous damping and subject to a transient loading is derived. The Winkler and Pasternak models were used to represent the foundation behaviour. To determine the non-linear response of both a rigidly fixed edge and a simply supported immovable edge plate for similar conditions to those applied to the modal analysis a numerical program is developed. The spatial domain is modelled by central finite differences with a time element method giving a resultant recurrence scheme which is used in the time domain. An analysis of the effect of viscous damping on the stability of a range of three point schemes is derived for a single degree of freedom system and the results presented. For a range transient loads a strong correlation was obtained between the linear deflection results determined from numerical program and the modal analysis. The dynamic non-linear deflection of the plate and plate/foundation system is presented for step loads and a transient exponentially decaying load.