تحلیل ارتعاشات دامنه بزرگ تیرهای متخلخل مدرج هدفمند دوجهته با مقطع باریک شونده روی بستر الاستیک با استفاده از یک تئوری برشی مرتبه بالا

نوع مقاله : مقاله پژوهشی

نویسندگان

1 دانشکده مهندسی مکانیک، واحد شیراز، دانشگاه آزاد اسلامی، شیراز، ایران

2 دانشکده مهندسی مکانیک و انرژی، دانشگاه تگزاس شمالی، تگزاس شمالی، آمریکا

چکیده

این مقاله تحلیل ارتعاشات دامنه بزرگ تیرهای متخلخل مدرج هدفمند دو جهته در شرایط مرزی مختلف را با استفاده از نظریه تغییر شکل برشی مرتبه سوم و تانسور گرین و غیر خطی بودن هندسی ون کارمن بررسی می‌کند. خواص مواد این تیرها با توجه به قانون توانی و نمایی در دو جهت تغییر می‌کند. معادلات حرکت و شرایط مرزی مرتبط با استفاده از اصل همیلتون به‌دست آمده است. برای حل سیستم معادلات، روش ترکیبی مربعات دیفرانسیلی تعمیم یافته همراه با یک روش تکرار عددی مستقیم ایجاد شده است. پس از اثبات همگرایی این روش، از نتایج استخراج شده از یک مطالعه قبلی بر اساس نظریه برشی تیموشنکو برای اعتبار سنجی نتایج استفاده می‌شود. سپس تأثیر شاخص‌های گرادیان مواد در دو جهت، نسبت دامنه فرکانس، ضریب تخلخل، اثر باریک شوندگی مقطع، پارامترهای بستر برشی و الاستیک و شرایط مرزی مختلف بر فرکانس‌های دامنه بزرگ تیرهای مدرج هدفمند مورد بررسی قرار می‌گیرد. نتایج نشان می‌دهد که رفتار فرکانس‌های غیر خطی بی بعد با افزایش ضرایب بستر و ضریب باریک شوندگی افزایش یافته و افزایش در ضریب تخلخل و گرادیان ماده در دو جهت، سبب کاهش در فرکانس‌های غیر خطی می‌شود، این نتایج در طراحی بهینه تیرهای دو جهته تأثیر گذار بوده و در روش‌های پیش‌بینی و کشف مودهای شکست این تیرها بسیار مؤثر است.

کلیدواژه‌ها

موضوعات

عنوان مقاله [English]

Large-Amplitude Frequency Analysis of Bi-directional Functionally Graded with Non-Uniform Porous Beams using a Higher Order Shear Deformation Theory

نویسندگان [English]

  • mohammadamin forghani 1
  • Yousef Bazargan lari 1
  • parham Zahedinejhad 2
  • Kazemzadeh-parsi Mohammad-Javad 1
1 Department of Mechanical Engineering,Shiraz Branch, Islamic Azad University, Shiraz, Iran
2 Department of Mechanical Engineering, University of North Texas, North Texas, USA
چکیده [English]

This Paper deals with the large amplitude frequency behavior of porous bi-directional functionally graded beams subjected to various boundary conditions which are simply supported, clamped-simply supported, clamped-clamped, and clamped-free utilizing Reddy third-order shear deformation theory and Green’s tensor together with the Von Karman geometric nonlinearity. The material properties of the beam change according to power and exponential law in both directions. The equations of motion and associated boundary conditions are derived by means of Hamilton’s principle. A generalized differential quadrature method in conjunction with a direct numerical iteration method is selected to solve the system of equations. Demonstrating the convergence of this method, the verification is performed by using extracted results from a previous study based on the Timoshenko beam theory. The results of extensive studies are provided to understand the influences of the different gradient indexes, vibration amplitude ratio, porosity coefficient, Tapered ratio, shear and elastic foundation parameters, and boundary conditions on the Large amplitude vibration frequencies of the bi-directional functionally graded beams. The results reveal that non-linear frequencies increase with the rise of elastic foundation and tapered coefficients and the soar of porosities and material gradients in two directions causes a sharp decrease in non-dimensional frequencies. The results of this study, while carefully examining the frequencies of variable cross-sectional functionally graded beams, are effective in the optimal design of bi-directional beams and are very effective in predicting and detecting failure modes of these beams.

کلیدواژه‌ها [English]

  • Large-amplitude vibration
  • Bi-directional functionally graded beam
  • Porous
  • Variable cross section
  • Third order shear deformation theory

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نشریه مهندسی مکانیک امیرکبیر
دوره 54، شماره 8
آبان 1401
صفحه 1761-1788

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