Detonation of hydrogen-oxygen at low temperature and high pressure

Abstract

Table 1 Values of aAT(b/t)\ for appearance of the second mode FIRST MODE Fig 3 Buckling of flat plates under combined stressbuckles into the first mode when the stress in the x direction, which is larger than % the stress in the y direction, reaches the following value:(3)(5) <r x = and the deflection form is w = w 0 sm(7rx/b) so that the unit axial shortening in the buckle mode is d ( i \ fb (dw i = (to) Jo U dx The condition of compatibility in the a; direction gives aAT = <r x B x /E -vv y /E + 8/b (6) Substituting Eqs (3) and (5) in Eq (6) and solving for WQ yieldsThe critical stress condition for the curved plate is calculated by utilizing the following criterion:which was arrived at by adding the buckling stress of the cylinder to that of a square plate The radius R in the previous equation is taken as the constant radius which gives the same deflection as the sine wave,The equation for compatibility in the y direction reduces toSubstituting Eqs (7, 9, and 10) in Eq (8) and setting v = 0 30 yields aAT(6/«) 2 = 1 17£ y 2 + 3 05£ y -0 27 ± [1 36B tf 4 + 7 YIBJ + 1 3&B, 2 -2 lOB^2] 1 / 2 (11)As can be seen from Eq (11), the value of the parameter aAT(6/i) 2 at which the second mode occurs depends, in a rather involved way, on the values of the in-plane restraint param-By I 2 3 1 6 74 19 2 36 6 B x 2 6 33 18 7 36 1 3 5 84 18 2 35 5 eters B x and B y A set of values of aAT(b/t) 2 for various restraints, including completely restrained B x = B y = |1, and lightly framed panels B x = B y = 3, is given in Table_l Concluding RemarksAll the values of a AT (6/0 2 are significantly higher than the value 2 43, which is the lowest value corresponding to initial buckling in the second mode with complete inplane restraint of the heated panel in the y direction The value of B x is of minor importance as long as the panel buckles initially in the first mode In the application of the preceding results it should be noted that the assumptions of simple support and uniform compression may lead to overoptimism where these conditions are not closely approximated References 1 Fung, Y C , "Some recent contributions to panel flutter research/ 7 ATAA J 1, 898-909 (1963) 2 Fralich, R W , "Postbuckling effects on the flutter of simply supported rectangular panels at supersonic speeds," NASA