Int. J. Impact Engng Vol. 6, No. 3, pp. 225-240, 1987 0734-743X/87 $3.00+0.00 Printed in Great Britain © 1987 PergamonJournals Ltd. DYNAMIC PLASTIC FAILURE OF A FREE-FREE BEAM NORMAN JONES* and TOMASZ WIERZBICKIt *Department of Mechanical Engineering, The University of Liverpool, P.O. Box 147, Liverpool L69 3BX, U.K. and tDepartment of Ocean Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, U.S.A. (Received 6 March 1987; and in revised form 4 May 1987) Summary--A simple theoretical procedure is presented for the analysis of a free-free beam which is made from a rigid-perfectly plastic material and subjected to a dynamic pressure pulse. Exact theoretical solutions are presented for a uniform beam under a triangular pressure load and a step beam subjected to uniform pressure pulse. In one case, it was observed that only 25 ~o of the external energy was converted into plastic work for an ideal impulse. The remaining 75 ~ of the energy caused a rigid-body acceleration of the beam. It is concluded that it is more difficult to break a free-free beam, as found in space, than a supported beam. The article concludes with a simplified study of the dynamic failure of an idealized aerospace vehicle. f~(x) A(t) gl(x) I m mo ml m2 p(x, t) Po Pc t teq W X Z D Ep ET ER I L L1, L2 M Mo N Q R R1 R2 T Vo Wo w, X(x) ~c K tl 0 Of Oc NOTATION dimensionless function of spatial pressure variation dimensionless function of temporal pressure variation dimensionless mass distribution length of one bay in the space shuttle mass per unit length reference mass mass per unit length of the central segment of a step beam mass per unit length of the end segment of a step beam transverse pressure (per unit length of a beam) amplitude of the pressure pulse critical pressure to form a hinge time equivalent thickness of the stiffened shell transverse deflection of a beam axial co-ordinate distance along a beam measured from the mass centre diameter of a cylindrical shell total energy dissipated at the plastic hinge total external work kinetic energy of rigid-body motion impulse, also second moment of inertia half-length of the beam segment lengths of a step beam in Fig. 5 bending moment fully plastic bending moment (critical bending moment to initiate failure) axial force shear force radius of a cylindrical shell energy ratio Ep/ET energy ratio ER/ET duration of the bending response initial velocity amplitude of the translational motion amplitude of the rotational motion shape of the bending mode critical fracture strain beam curvature dimensionless pressure amplitude Po/P¢ hinge rotation final rotation angle critical rotation to fracture 225