مجله علمی صوت و ارتعاش

مجله علمی صوت و ارتعاش

تحلیل ارتعاشات پوسته مخروطی متخلخل چرخان با بکارگیری روش مربعات دیفرانسیل تعمیم یافته دو بعدی

نوع مقاله : مقاله پژوهشی

نویسندگان
علی اصغر جعفری
سید امیرمسعود تکمیلی
دانشکده مهندسی مکانیک، دانشگاه صنعتی خواجه نصیرالدین طوسی، تهران، ایران
چکیده
در این پژوهش، رفتار پوسته‌ی مخروطی چرخان متشکل از ماده‌ی هدفمند متخلخل مورد مطالعه قرار گرفته است. معادلات حاکم بر پوسته‌ی مخروطی نسبتاً ضخیم با استفاده از تئوری تغییر شکل برشی مرتبه‌ی اول استخراج شده‌اند. در این معادلات، اثرات نیروی گریز از مرکز ناشی از دوران پوسته نیز در نظر گرفته شده که منجر به ایجاد انرژی کرنشی حاصل از کشش حلقه‌ای در معادلات حاکم می‌شود. معادلات دیفرانسیل جزئی با به‌کارگیری روش مربعات دیفرانسیل تعمیم ‌یافته‌ی دو بعدی به دستگاه معادلات جبری تبدیل شده و سپس با حل مسئله‌ی مقدار ویژه، فرکانس طبیعی سیستم به‌دست آمده است. پس از اطمینان از صحت مدل ریاضی ارائه‌ شده، تأثیر پارامترهای مختلفی از قبیل سرعت دوران، شرایط مرزی، ماده‌ی متخلخل و زاویه‌ ی نیم ‌رأس مخروط بر فرکانس ‌های طبیعی پیشرو و پسرو بررسی شده است. بر اساس نتایج به‌ دست ‌آمده، افزایش پارامتر متخلخل موجب کاهش فرکانس طبیعی می‌شود. همچنین، با افزایش سرعت دورانی، مقادیر فرکانس طبیعی افزایش می‌یابد.
کلیدواژه‌ها
ارتعاشات آزاد
پوسته مخروطی چرخان
ماده متخلخل درجه‌بندی شده
مربعات دیفرانسیل تعمیم یافته دو بعدی
تئوری تغییر شکل برشی مرتبه اول
موضوعات

عنوان مقاله English

Vibration Analysis of Rotating Porous Conical Shells Using the Two-Dimensional Generalized Differential Quadrature Method

نویسندگان English

Ali Asghar Jafari
Seyed Amirmasoud Takmili
Faculty of Mechanical Engineering, K. N. Toosi University of Technology, Tehran, Iran
چکیده English

This study investigates the vibrational behavior of a rotating conical shell composed of a functionally graded porous material. The governing equations for a relatively thick conical shell are derived based on the first-order shear deformation theory. These equations incorporate the effects of centrifugal forces induced by the shell's rotation, which result in an initial hoop tension strain energy. The partial differential equations are discretized into a set of algebraic equations using the two-dimensional generalized differential quadrature (2D-GDQ) method. The natural frequencies of the system are subsequently obtained by solving the resulting eigenvalue problem.



Following the validation of the proposed mathematical model, the influence of various parameters—including rotational speed, boundary conditions, porosity material, and the cone's semi-vertex angle—on the forward and backward natural frequencies is examined. The results indicate that an increase in the porosity parameter leads to a reduction in the natural frequency. Conversely, the natural frequency values are found to increase with higher rotational speeds.

کلیدواژه‌ها English

Free Vibrations
Rotating Conical Shell
Functionally Graded Porous Material
Two-Dimensional Generalized Differential Quadrature (2D-GDQ)
First-Order Shear Deformation Theory (FSDT)
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