تحليل كمانش و ارتعاشات آزاد پنل استوانه‌اي تقويت شده با توزيع‌هاي مختلف نانو لوله‌هاي كربني بر بستر الاستيك

Buckling and free vibration analysis of cylindrical panel reinforced by various distributions of CNTs on elastic foundation

كمانش و ارتعاشات پنل استونه‌اي تقويت شده با توزيع‌هاي مختلف نانو لوله‌هاي كربني براي دو حالت يكنواخت و مدرج تابعي مورد بررسي قرار مي‌گيرد. معادلات ديفرانسيل حاكم بر پنل استوانه‌اي بر اساس تئوري تغيير شكل برشي مرتبه اول با استفاده از روش انرژي به‌دست مي‌آيد. همچنين از قانون اختلاط، براي تعيين خواص پوسته استوانه‌اي استفاده مي‌شود. مي‌توان نتيجه گرفت كه با انتخاب مناسب توزيع نانو لوله كربني و كسر حجمي سفتي سازه افزايش يافته و در نتيجه بار كمانش بحراني و فركانسهاي طبيعي پنل استوانه‌اي افزايش مي‌يابد. لذا اين نكته در طراحي بهينه سازه‌ها در مقياس نانو حائز اهميت مي‌باشد.

In this paper, buckling and free vibration analysis of cylindrical panel reinforced by various distributions of carbon nanotubes (CNTs) on elastic foundation for two cases including uniform distributed (UD) and functionally graded (FG) is studied. Based on the first order shear deformation theory (FSDT), the equilibrium equations of cylindrical panel reinforced by CNTs are derived using energy method and Hamilton’s principle. Then, using Navier’s type solution, the governing equations of equilibrium for cylindrical panel reinforced by various distributions of CNTs are solved. Using the mixture rule, the material properties of cylindrical panel reinforced by CNTs are estimated. In this study, the effects of volume fraction, various distributions of CNTs, elastic foundation parameters on the critical buckling load and natural frequency of cylindrical panel reinforced with CNTs are investigated. The obtained results of this research indicate that the trend of increasing natural frequency leads to increase in the percentage of CNTs and elastic modulus parameters which the maximum natural frequency occurs for FG-X case. Also increasing the percentage of CNTs and elastic modulus parameters leads to increase the critical buckling load which the maximum and minimum values of this load take place for FG-X and FG-O, respectively. On the other hands, it can conclude that with suitable selecting of CNTs distributions and volume fraction, the stiffness of structures increases and then the critical buckling load and natural frequencies enhance. Thus this point is noticeable to design the optimum of structures at nanoscale.