Method of images for the harmonic response of beams and rectangular plates

✍ Scribed by R. Gunda; S.M. Vijayakar; R. Singh

• Publisher: Elsevier Science
• Year: 1995
• Tongue: English
• Weight: 763 KB
• Volume: 185
• Category: Article
• ISSN: 0022-460X
• DOI: 10.1006/jsvi.1995.0418

✦ Synopsis

The feasibility of calculating the narrow band harmonic response of thin plates and beams by using the method of images or the ray tracing technique is examined. The fundamental solution of an infinite plate is employed, in conjunction with appropriately placed images, to obtain the dynamic compliance spectra of simply supported rectangular plates over a wide range of frequencies. Predictions yielded by the method of images are in excellent agreement with the normal mode expansion technique. Simply supported beams are analyzed first by considering the fundamental solution of an infinite beam, and second as a case of a narrow plate with simply supported and roller boundary conditions. Both approaches match well with the closed form solutions and with measurements conducted on two beams. Several issues including convergence characteristics and high frequency behavior are discussed.