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 by way of recognized 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. specifically, the ebook demonstrates the breadth of present learn job in continuum mechanics. a number of theoretical, computational, and experimental ways are suggested, overlaying finite elasticity, vibration and balance, and mechanical modeling. The assurance displays the level and influence of the examine pursued via Professor Haseganu and her foreign colleagues.

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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. This means that a stiffened shell is heavier than an unstiffened one. In the next sections we compare the vibrations frequencies and the critical pressures for stiffened and unstiffened shells of equal masses.

3 we can see the values 7 for the optimal ultimate X* and uniform Xu springs arrangements. 3. Values of the function ~f(X). 001 If n = 2, then X* = Xu. In the case n > 2 it follows from (44) that «i, for the optimal ultimate arrangement, is greater than for the uniform one since -y(X*) > j(Xu). 4 lists the values of the parameter K±, obtained by means of different methods for a stiffened beam with clamped edges. The approximate values Ki(X*) have been found by formula (44) for the optimal ultimate Sergei B.

The mass of an unstiffened shell is MQ = Gh0, where G = 2irR3pl. We compare too with the fundamental vibration frequency, co\, of an stiffened shell of thickness h < ho and mass Ms = M + Mr=M0, (60) where M = Gh is the mass of the skin (the mass of the shell), Mr is the mass of the reinforcement (the mass of the rings). We consider rings with rectangular cross-sections of width a and height b = ka. In this case Mr = 2irR3pnra2k. Using relations (58) and (59), we obtain V "§ d= h \drl r]>i1*v, y > where BaA „ B= ank3 v " = ^"' w , (62) , It follows from (60) and (62) that , -> ,2 A nrk (1 -d)2B .

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