تحليل ارتعاشات آزاد صفحات مشبك هدفمند FGM در محيط‌هاي حرارتي

Free Vibration analysis of Functionally Graded Lattice Plates in Thermal Envirnoment

در پژوهش حاضر دو روش تحليلي و عددي براي مطالعه و بررسي ارتعاشات آزاد ورق‌هاي مشبك هدفمند در محيط‌هاي حرارتي بكار گرفته شده است. در روش تحليلي، خواص ورق هدفمند به‌صورت تابعي از دما تعريف شده و براي در نظر گرفتن خواص ورق مشبك از ماتريس سفتي تعريف شده بر اساس نظريۀ وسيليو استفاده شده است. معادلات تعادل حاكم، بر اساس نظريه تغيير شكل برشي مرتبه اول كه شامل مؤلفه‌هاي جابجايي و دوراني مي‌باشد، به‌دست آمده و با فرض شرايط مرزي چهار طرف گيردار به روش انرژي حل شده است. با حل مسأله مقدار ويژه، رفتار ارتعاشي سازه در محيط حرارتي (با حضور تنش حرارتي) تعيين شده است. نتايج تحليلي و عددي با نتايج آثار گذشته مورد مقايسه و صحت ‌سنجي قرار گرفته است. در زمينه ارتعاشات آزاد ورق مشبك هدفمند در محيط حرارتي مطالعات پارامتري مختلفي از جمله تغيير اندازه ريب‌ها، فاصله ريب‌ها و ... جهت پيش‌بيني رفتار سازه صورت گرفته است.

In the present study, two analytical and numerical methods have been used for studying and testing of Functionally Graded Lattice plates in thermal environments. In the analytical method, the properties of the Functionally Graded plates are defined as a function of temperature, and to take account of the properties of Lattice Plates, the stiffness matrix defined by V.V. Vasiliev is used. The governing equilibrium equations are obtained based on the first order shear deformation theory, which includes displacement and rotational components, and is solved by assuming the boundary conditions that are fully clamped by the energy method. By solving the problem of a special value, the vibrational behavior of the structure in a thermal environment (with the presence of thermal stress) is determined. Analytical and numerical results have been compared and verified with the results of previous works. In the field of free vibration, a Functionally Graded Lattice plate in a thermal environment has been used to study various parameters such as changing the size of the ribs, the distance between the ribs and ... for predicting structural behavior. The results show that when the temperature rises, the normal frequency in the Functionally Graded Lattice plate decreases with the decrease of the width of the ribs and the increase in the distance between the ribs. The use of a purposeful grid plate as a ceramic core reinforcement increases the natural frequency by up to 50%, which in a thermal environment with a rise in temperature, the natural frequency drop is about 3%, while in the FGM plate, this reduction is about 11%. The results also show that the Functionally Graded Lattice plate and the use of the core of the sandwich structure increases the strength and resistance to heat.