Mechanics |
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2006, No. 2
S.A. Lychev, S.V. Saleev
CLOSED SOLUTION OF BOUNDARY VALUE PROBLEM FOR RECTANGULAR PLATE FIXED ON BOUNDARY5
The closed solution of boundary value problem for rectangular plate fixed on boundary is obtained. Typically the solutions of the problem can be obtained by the Rayleigh–Ritz energy method. This method in general gives infinite system of the linear algebraic equations, which is to be solved only numerically. The obtained solution is of the form of expansion based on complete sets of functions satisfying prescribed boundary conditions and special to relation of orthogonality, generated by functional of potential energy of system. The proposed method leads to diagonal infinite system of the linear algebraic equations while the expansion coefficients can be found independently.
G.P. Cherepanov
ON THE COLLAPSE OF THE WORLD TRADE CENTER IN NEW YORK ON SEPT. 11, 2001
The generally-accepted explanation of the collapse of the World Trade Center towers on September 11, 2001 is based on the speculative “theory” of progressive buckling of bearing columns at the speed of free fall triggered by creep buckling of the columns of the floor subject to the conflagration from the spilled fuel, and by dynamic impact of the upper structure. In the present paper it is shown that this official “theory” is wrong because it is built on false assumptions and incorrect calculations. The “theory” cannot explain the free fall, explosion sound, and pulverization of the buildings as well as other facts of this event. The simultaneous collapse of the neighboring 47-story tower directly contradicts to the “theory” . It is shown that, consistent with all known facts of the matter, the scenario of all collapses was this: (i) heating of bearing columns in the ”hot” spot caused high compressive thermal stresses in these columns, (ii) these stresses combined with internal stresses gered a fracture wave, and (iii) the fracture wave disintegrated the entire building by invisible cracks for less than 0.1 s producing the sound of explosion and providing the conditions necessary for free fall of steel fragments and dust clouds of tiny fragments of glass, marble and concrete. The theory of fracture waves, see Appendix 1, supports this scenario. The official “theory” is cited in Appendix 2.
L.I. Fridman, Ę.S. Morgachev
Unsteady oscillation dynamic analysis for plates strained according to the Timoshenko hypothesis is given in random curvilinear orthogonal planimetric coordinates. Analysis is developed by series according to characteristic modes on the basis of devised orthogonality conditions. It remains valid at any combination of the following conditions at plate contour: free edge, hinge support and anchorage. Numerical results for a free annular plate under impulsive loading are presented.