Free Vibration Investigations of Rotating FG Beams Resting on Elastic Foundation with Initial Geometrical Imperfection in Thermal Environments

<div>The first nondimensional frequency of the cantilever FGM beam on the initial imperfect parameter <svg height="9.25202pt" id="M137" style="vertical-align:-3.29111pt" version="1.1" viewbox="-0.0498162 -5.96091 10.0307 9.25202" width="10.0307pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M384 393C384 425 346 448 294 448C244 448 200 431 150 399C75 351 23 271 23 176C23 90 52 45 132 19C150 13 166 9 195 2C245 -10 260 -27 260 -55C260 -92 234 -127 218 -145L237 -159C271 -137 333 -93 333 -18C333 43 283 62 228 74C199 80 186 84 172 89C116 109 101 150 101 210C101 318 164 400 241 400C276 400 301 390 327 356C334 347 338 343 346 345C367 349 384 374 384 393Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,4.966,3.132)"><path d="M245 635C92 635 37 457 37 312C37 149 91 -12 244 -12C395 -12 449 166 449 312C449 469 395 635 245 635ZM243 598C332 598 358 454 358 312C358 173 334 26 245 26C158 26 128 174 128 313S152 598 243 598Z"></path></g></svg> and the temperature.</div>

Mathematical Problems in Engineering

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Figure 13

Figure 13: Free Vibration Investigations of Rotating FG Beams Resting on Elastic Foundation with Initial Geometrical Imperfection in Thermal Environments 

Figure 13 | Free Vibration Investigations of Rotating FG Beams Resting on Elastic Foundation with Initial Geometrical Imperfection in Thermal Environments 