By N. J. Hoff (auth.), Miklós Hetényi, Walter G. Vincenti (eds.)

This quantity includes the complaints of the 12th overseas Congress of utilized Mechanics, held at Stanford college on August 26 to 31, 1968. The Congress was once prepared by means of the foreign Union of Theoretical and utilized Mechanics; contributors of the IUTAM Congress Committee and Bureau are indexed below Congress association. The contributors of the Stanford Organizing Committee, which was once liable for the designated association of the Congress, also are given, as are the names of the sponsors and the economic and academic firms that contributed so generously to the monetary help of the assembly. these attending the Congress got here from 32 nations and totaled 1337 individuals, plus better halves and kids. an inventory of the registered individuals is integrated within the quantity. The technical periods of the Congress comprised 4 normal Lectures and 281 contributed papers, the latter being provided in teams of 5 simultaneous periods. the ultimate collection of the contributed papers used to be made at the foundation of abstracts by means of a world Papers dedicate tee of IUTAM consülting of G. ok. BATCHELOR, E. BECKER, N. J. HOFF, and W. T. KOlTER.

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**Additional info for Applied Mechanics: Proceedings of the Twelfth International Congress of Applied Mechanics, Stanford University, August 26–31, 1968**

**Example text**

We are very grateful to Mr. BOZICH and to an the students who took care of these jobs and of many other chores. A former graduate student of ours, SAM McINTOSH, who is now Assistant Professor, contributed many good ideas and, in particular, was in charge of everything connected with transportation. The projection and sound effects were in the hands of JIM CLOUD and I think we should say "thank you" to him because he has done a good job. The man who was in charge of an the technical services is KEVIN FORSBERG who donated bis time even though he is not even connected with Stanford University.

4 -1 2 et si l'on adopte ,y x2 = t 213 (3l - x) on obtient et les coefficients sont bien dans l'ordre: n2 T = 2,467 42 17 = 2,471 5 '2 2,500). = Un exemple interessant de comparaison entre 180 methode de RAYLEIGH et celle de TIMOest celui de l'etude des conditions' critiques de 180 poutre encastree a sa base, dans le cas Oll l'on tient compte de l'effet du poids propre de 180 poutre. Soit Q = ql ce poids propre (nous supposerons EI et q constants). En designant par 'Yj = 'Yj(~) l'equation de 180 ligne elastique entre les abscisses x et l, le moment flechissant est SHENKO M I = PU - y) + Jq('Yj - y) d~ x ce qui donne l'equation differentielle Ely" = que l'on peut deriver suivant Ely'" PU - I y) + Jq('Yj x + (P + Q - - y) d~ qx) y' = o.

0 0 Considerons alors le polynome du seeond degre 1 II(A) = I JEIy"2dx o 2,1 JY'2dx + I ,1 2J(j;/)2 dx 0 0 ou ,1 est une indeterminee et ou y est une deformation virtuelle arbitraire que l'on exprime par la serie 00 on obtient aisement I 00 II(,1) =2;aZ(Pk - ,1)2JUk 1 -;;/k)"- dx 0 0 expression definie positive, qui ne s'annule que lorsque tous les ak sont nuls sauf uno Le discriminant de II(,1) est donc negatif ou nul: I I Jy'2 dx JEIy"2 dx ZO - y)2 d [ (j EI x < ~l Jy'2 dx 0 Ö et l'egalite n'a lieu, avec la valeur P k , que pour Y = akYk' La meme representation d'une deformation virtuelle compatible per met de calculer le quotient de TIMOSHENKO (ou celui de RAYLEIGH): 1 Jy'2 dx o I J(j o ;/)2 1 ~a% J (A ;/k)2 dx dx 1 0 formule qui montre que le rapport de TIMOSHENKO est le barycentre des valeurs spectrales PI> ...