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

By David J Steigmann, Remi Vaillancourt, Ardeshir Guran

The contributions during this quantity are written through famous experts within the fields of mechanics, fabrics modeling and research. They comprehensively deal with the center concerns and current the newest advancements in those and comparable parts. particularly, the e-book demonstrates the breadth of present examine job in continuum mechanics. various theoretical, computational, and experimental methods are pronounced, masking finite elasticity, vibration and balance, and mechanical modeling. The insurance displays the level and effect of the study pursued by way of Professor Haseganu and her foreign colleagues.

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Extra resources for Advances in mechanics of solids: in memory of Prof. E.M. Haseganu

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L \ t 0 Fig. 9. x[ n/ xf g» X \ j x% i First vibration mode of a beam stiffened by n r hinges for X = Xr. e. X* = Xr. The root arrangement Xr depends only on the boundary conditions. The optimal ring arrangement in case c » 1 depends mainly on the boundary conditions, because X° ~ X* = Xr for the large values of stiffness c. 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.

The root arrangement Xr depends only on the boundary conditions. The optimal ring arrangement in case c » 1 depends mainly on the boundary conditions, because X° ~ X* = Xr for the large values of stiffness c. 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.

It follows from (36) and (38) that n_1 d4u — - = cnv0[l - J2 5(£ - j)}. i=i Integrating this equation gives (v 77/1 - 7 p - = cnvQ[£ - j - c3(s)], j < £ < j + 1. After the homogenization, the last + i equation takes the form r 1 C3 = j (f-jR=2. and, after another integration followed by homogenization, we get u4(s,0 = cnv0{(£~j)2(i-j - l ) 2 - 1/720], j < £ < j + 1. Substituting (34) into (32) and equating the coefficients of n~ 4 , we obtain the equation of the next approximation. The homogenization of this equation yields d4V4 dsA „ ' CUV4 c2n2 720 ^^Tv0 = ^0^4 + K4V0.

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