TAILIEUCHUNG - MODELLING OF MECHANICAL SYSTEM VOLUME 2 Episode 10

Tham khảo tài liệu 'modelling of mechanical system volume 2 episode 10', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 338 Structural elements Figure . Mode shape n 4 m 1 Here the plate is found to buckle according to the first mode n m 1. It corresponds to the critical temperature increase 1 nh 2 Aớc c 6a 1 v L Figure refers to a steel plate L 1m. The natural frequency of the 1 1 mode is plotted versus AỚ together with the variation of the critical temperature increase as a function of the plate thickness. Modal density and forced vibrations near resonance Of course the formula also holds in the particular case of unstressed plates. The point here is to investigate a few consequences of the n m dependency of the natural frequencies which is governed by the coefficient X 2 mn Ly It is easy to check that it can take similar values for several pairs of mode indices. This is illustrated in Figure where all the natural frequencies are plotted for m and n varying from 1 to 10. The results refer to a steel square plate L 1m h 2 mm. It clearly shows that the plate can vibrate according to several flexure modes whose natural frequencies are very close to each other. So if a plate is excited by a nearly resonant force even if the excitation spectrum is Plates out-of-plane motion 339 Figure . Thermal buckling of a square steel plate Figure . Natural frequencies of the flexure modes of a square plate 340 Structural elements limited to a fairly narrow frequency range the plate response is not restricted to a single resonant mode but is made up of a linear superposition of all the nearly resonant modes whose frequencies lie within the frequency range of the excitation signal. Furthermore the coefficients entering in the superposition are very sensitive to small defects in the plate geometry support conditions and material. As a consequence the experimental determination of the modal properties of plates is often a difficult task. On the other hand the multi modal response can explain the complexity of the figures obtained by Chladni already evoked in .

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