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あぁかがさざただなはばぱまやゃらわゎんいぃきぎしじちぢにひびぴみりうぅくぐすずつづっぬふぶぷむゆゅるえぇけげせぜてでねへべぺめれおぉこごそぞとどのほぼぽもよょろを

アァカサザタダナハバパマヤャラワヮンイィキギシジチヂニヒビピミリウゥクグスズツヅッヌフブプムユュルエェケゲセゼテデヘベペメレオォコゴソゾトドノホボポモヨョロヲ ―

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Α Β Γ Δ Ε Ζ Η Θ Ι Κ Λ Μ Ν Ξ Ο Π Ρ Σ Τ Υ Φ Χ Ψ Ω α β γ δ ε ζ η θ ι κ λ μ ν ξ ο π ρ σ τ υ φ χ ψ ω

á à Á À é è É È ç Ç ê

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± × ÷ ≠ ≤ ≥ ∞ ∴ ♂ ♀ ∠ ⊥ ⌒ ∂ ∇ ≡ ≒ ≪ ≫ √ ∽ ∝ ∵ ∫ ∬ ∈ ∋ ⊆ ⊇ ⊂ ⊃ ∪ ∩ ∧ ∨ ￢ ⇒ ⇔ ∀ ∃ ∮ ∑ ∏ ＋－＜＝＞

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1
Vibration analysis of submerged thin FGM cylindrical shells

Muhammad Nawaz Naeem,Madiha Gamkhar,Shahid Hussain Arshad,Abdul Ghafar Shah 대한기계학회 2013 JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY Vol.27 No.3
This study gives a brief work on vibration characteristics of cylindrical shells submerged in an incompressible fluid. The shell is presumed to be structured from functionally graded material. The effect of the fluid is introduced by using the acoustic wave equation. Love’s first order thin shell theory is utilized in the shell dynamical equations. The problem is framed by combining shell dynamical equations with the acoustic wave equation. Fluid-loaded terms are associated with Hankel function of second kind. Wave propagation approach is employed to solve the shell problem. Some comparisons of numerical results are performed for the natural frequencies of simply supported-simply supported, clamped-clamped and clamped-simply supported boundary conditions of isotropic as well as functionally graded cylindrical shells to check the validity of the present approach. The influence of fluid on the submerged functionally graded cylindrical shells is noticed to be very pronounced.