David J Steigmann, Remi Vaillancourt, Ardeshir Guran's Advances in mechanics of solids: in memory of Prof. E.M. PDF

By David J Steigmann, Remi Vaillancourt, Ardeshir Guran

ISBN-10: 9812568670

ISBN-13: 9789812568670

The contributions during this quantity are written by means of famous experts within the fields of mechanics, fabrics modeling and research. They comprehensively deal with the middle concerns and current the newest advancements in those and similar parts. particularly, the booklet demonstrates the breadth of present study job in continuum mechanics. various theoretical, computational, and experimental techniques are suggested, protecting finite elasticity, vibration and balance, and mechanical modeling. The assurance displays the level and impression of the learn pursued by means of Professor Haseganu and her foreign colleagues.

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Additional info for Advances in mechanics of solids: in memory of Prof. E.M. Haseganu

Example text

Here rn = znjz\ ~ (2n + l ) / 3 . Using formulas (47) we obtain the following approximate values of the effective stiffness for the vibrations and buckling ^(n)~7-1(^-l), %*(n)^7-1(^/3-l). 5 we can see the values rfv and rf^ of the effective stiffness for various n. 5. Values of r/* and rj*. 179 for a shell with simply supported edges. 6, r] >rfb. e. the fundamental vibration frequency and the critical pressure of a stiffened shell are higher than of an unstiffened one. All formulas are derived under the assumption that Ms = M0 + Mr, where Ms is the mass of the stiffened shell, MQ is the mass of the unstiffened shell, and Mr is the mass of the rings.

6 . For n > 6 the error of formula (66) is less t h a n 5%. 7 one can see the values of d*, a*, and f* for the same stiffened shell. T h e optimal parameter for freely supported (FS) and clamped (CL) shells are given in the left and right columns, respectively. 7. Optimal values of the parameters. 28 a For the shells under consideration, the ratio f* = LOI/WQ increases with nr. 5 times higher t h a n the fundamental frequency LJQ for an unstiffened shell of the same mass. It follows from (60) t h a t d*v = M*/M*3, where M * and M* are the optimal masses of the skin and the whole stiffened shell, respectively.

8. Homogenization In this section we consider the uniform arrangement Xu of the rings on a freely supported cylindrical shell. This arrangement is often used in industrial applications and is the subject of theoretical considerations. On the other hand, the uniform arrangement is close to the optimal one if the edges of the shell are freely supported and c > 1. If the number nr of springs is large and the stiffness of each spring c is small, one can use the homogenization method (see [Babushka (1976)]3, [Sanchez-Palencia (1980)] n ) for the approximate evaluation of the eigenvalues a\.

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Advances in mechanics of solids: in memory of Prof. E.M. Haseganu by David J Steigmann, Remi Vaillancourt, Ardeshir Guran

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