Mathematical elasticity. Theory of shells by Jeffrey M. Lemm

By Jeffrey M. Lemm

The target of quantity III is to put down the correct mathematical foundations of the two-dimensional conception of shells. To this finish, it presents, with none recourse to any a priori assumptions of a geometric or mechanical nature, a mathematical justification of two-dimensional nonlinear and linear shell theories, by way of asymptotic equipment, with the thickness because the "small" parameter.

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Zy ....... 4/4L/-'. _~ ,~:' -. ~ c c A b .. -- I:~i ;~ 7 0,0 10 5 10 6 7 10 Re Fig. 2, Strouhal number for circular cylinders versus Reynoldsnumber /3/ 54 H. • ".. , • 'I, I " ' ........ - .... - II ....... - - - _ei. 05 o ,. - - ........ 3, Strouhal number for rectangular cross section versus ratio b/d /3/ The Strouhal number may be influenced by the turbulence intensity of the wind. In a recently finished research work /4/ the effect ofturbulence has been investigated. Fig. 4 shows the result for aT-profile.

5% of the structure s weight. The control drive use an AC servomotor (see fig. 23). H. Hirsch For high rise buildings, there may be cases in which the external wind forces exceed the assumed seismic forces (in regions with seismic activities) in structural design, depending not only on their weight, but also on their shape. Therefore it is important to plan on response wind loads by means of passive control only. Experiments verify that enough vibration effect can be obtained. However, as the subject building has a long natural period, the devices will not commence effective operation until the building has reached astate of considerable dynamic deflection.

SO ! "" -ISO ~ ..................... ,..... j...... 0 -SO J -100 .... , ;.. . ~ .. ~ ... ~ ... :. ~ ...... i .............. ~.... " .. .. ~ ..... ; ............... :. :. ':···· .. ·····················:······1'···· : l ~ j : :: ........... :.... ~ ...... ; ... t.. ~... :.. ~ ................ ~.......... :... ~.... .... ·. ···::r::r··~~~··~:r~:···. ·: .......... ~ ......... ~ ..... ~... ~.. ~ .. ~.? !....... j.... ~ ~ .. H. Hirsch 7. NEW TRENDS IN PASSIVE AND ACTIVE CONTROL Recently new proposals have been reportet relating to passive and active optimum control of wind induced vibrations of slender structures (steeI chimneys) /36/ and tall buildings /33/ /34/ /35/.

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