By Ardeshir Guran;Andrei L. Smirnov;David J. Steigmann

The contributions during this quantity are written via famous experts within the fields of mechanics, fabrics modeling and research. They comprehensively deal with the middle concerns and current the most recent advancements in those and comparable components. particularly, the publication demonstrates the breadth of present learn job in continuum mechanics. a number of theoretical, computational, and experimental ways are pronounced, overlaying finite elasticity, vibration and balance, and mechanical modeling. The assurance displays the level and impression of the study pursued by way of Professor Haseganu and her overseas colleagues.

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Additional resources for Advances in Mechanics of Solids: In Memory of Professor E. M. Haseganu (Series on Stability, Vibration and Control of Systems)

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We will see below that the effective stiffness is optimal from some point of view; therefore the case c 3> 1 is of interest in engineering. Carrying out a similar calculation for the buckling problem, we obtain that Ai(0) < Ai(rj) < 2Ai(0), Ai(0) ~ 4£ 6 7r/(3 1 / 4 0. The effective stiffness 77^ in the buckling problem is the root of the equation A 1 (77)=2A 1 (0). 7. Optimal Rings Arrangement In the general case, the minimal positive root ct\ of Eq. (24) depends on the spring stiffness, c, and the set, X = (x\, X2, • • •, xUr), of coordinates of Buckling, Vibrations and Optimal Design of Ring-Stiffened Shells 29 the springs.

Substituting d = d*; into (63) we obtain the optimal values of a and 77, V*v={l{d^2B- a*v = y/(l-dl)/A, Hence, the effective stiffness 77* is at the same time the optimal stiffness ensuring the maximal value of the fundamental frequency. It follows from (64) that, for n > l , d:~g1/3^n-5/3! / : ( n ) ^ M : ) l/2^ n l/6. Therefore, the fundamental vibration frequency of a stiffened shell increases with n for large n. The following approximate expression for d* d:^g 1 / 3 (l-^ 1 / 3 ), ««1 (66) is derived by means of an asymptotic method (see [Bauer et al.

93w0 w3(s) = < u 3 ( s ) > = < - ^ - 3 - > = 0 . A further integration followed by a homogenization gives d2wo f \ n -g-f- = v2{s) = 0, dw ° f \ —— =v1(s) n = 0, 1 c\ f \ two(s,0 =«o(s). Buckling, Vibrations and Optimal Design of Ring-Stiffened Shells 33 After the homogenization of the second equation in (36) we get -—- + cnv0 = (38) K0V0. Equation (38) describes the vibrations of a simply supported beam on an elastic base (see Fig. 10). „ « l\i i i i l\ Fig. 10. Homogenization > Stiffened beam and beam upon an elastic base.

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