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

ISBN-10: 9812568670

ISBN-13: 9789812568670

ISBN-10: 9812773169

ISBN-13: 9789812773166

The contributions during this quantity are written by way of recognized experts within the fields of mechanics, fabrics modeling and research. They comprehensively handle the middle matters and current the newest advancements in those and comparable components. particularly, the booklet demonstrates the breadth of present study task in continuum mechanics. various theoretical, computational, and experimental ways are pronounced, protecting finite elasticity, vibration and balance, and mechanical modeling. The insurance displays the level and effect of the study pursued by means of Professor Haseganu and her overseas colleagues.

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

Sample text

The asymmetric arrangement of the string x\ ^ 1/2 have been analyzed in [Sharypov (1997)]15. Unlike the case of a symmetric string, when x\ = 1/2, in the asymmetric case Eq. (24) does not split into two simple equations. Let Cfc = 2ctk/l, where 0 < a\ < «2 < • • • are the positive roots of Eq. (24). It is shown in [Sharypov (1997)]15 that Zl > Cl, *2 < C2 (26) for all values of c > 0. The roots £i and £2 are plotted as functions of c for x\ = 1/4 in the right part of Fig. 5. e. \ of Eq. (24) attains its maximum at the symmetric string position x\ =1/2.

4): d4w 4, ,„ = 0, Q• W - where a4 = m4\M - e8m8, for vibrations ^ **-«•»-«, for buckling. 1, M = { " ' ,2 -{ TO , ^ It follows from Eq. (7) that A 8 +8 e™TO4 ) I-. ) are the eigenvalues for which the boundary value problem for Eq. (6) has non-trivial solutions. The problem of extracting two main boundary conditions for Eq. (6) out of four boundary conditions on the shell edges is discussed in detail in [Tovstik and Smirnov (2001)]14. The boundary conditions for Eq. (6) in the case of freely supported shell edges (FS) have the form d w w = ——r = 0 for x = 0, x = I.

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. The solutions of Eq. (38) which satisfy the first of the boundary conditions (37) are WQU = sinfc7rs, «ofc = {kn)4 + en, fc = l , 2 , . . (39) We seek the unknown function W4 in the form w 4 (s,£) =v4{s) +u4(s,f), where < UA > = 0.

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Advances in Mechanics of Solids: In Memory of Professor E. M. Haseganu (Series on Stability, Vibration and Control of Systems) by Ardeshir Guran;Andrei L. Smirnov;David J. Steigmann

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