Layerwise Theory for Free Vibration and Panel Flutter Analysis of VSCL Plates using IGA

Dabouee, Mehdi; Khalafi, Vahid; Zarei, Hamidreza

doi:10.22034/jsst.2025.1588

Layerwise Theory for Free Vibration and Panel Flutter Analysis of VSCL Plates using IGA

Document Type : Original Research Paper

Authors

Mehdi Dabouee

Vahid Khalafi

Hamidreza Zarei

Department of Aerospace Engineering, Shahid Sattari Aeronautical University of Science and Technology, Tehran, Iran

10.22034/jsst.2025.1588

Abstract

This research examines the free vibration and panel flutter of composite laminates with curvilinear fibers. It employs the isogeometric analysis (IGA) framework along with layerwise theory. The growing utilization of composite structures in the aerospace and mechanical industries has led to the increasing popularity of variable-stiffness composite laminate (VSCL). These laminates with curvilinear fibers are designed to achieve customized mechanical properties and improve design efficiency. To achieve greater accuracy than equivalent single-layer theories (ESL) and improved computational efficiency compared to 3D elasticity models, a layerwise theory based on Ferreira's formulation was adopted. This approach uses the kinematic assumptions of first-order shear deformation theory (FSDT) to define the displacement field within each layer. Subsequently, the governing equations for free vibration and panel flutter are obtained from the Hamilton principle, utilizing first-order piston theory to model aerodynamic pressure. The geometric domain is discretized using the isogeometric analysis method, in which the cubic NURBS basis functions used for the exact geometric modeling are simultaneously employed as the approximation functions in the finite element formulation. Numerical results are obtained by solving the eigenvalue problem. A parametric study was performed to investigate the impact of several factors, including layup configuration, thickness ratios, fiber curvature, and boundary conditions of the VSCL plates. The findings demonstrate strong alignment with previous research, confirming the proposed formulation's accuracy and effectiveness.

Keywords

Free Vibration

Panel Flutter

Variable-Stiffness Composites

Isogeometric Analysis

Layerwise Theory

Subjects

Aerospace Engineering

Article Title Persian

تئوری لایروایز برای تحلیل ارتعاشات آزاد و پنل فلاتر چندلایه‌های کامپوزیتی با سفتی متغیر به روش حل عددی آیزوژئومتریک

Authors Persian

مهدی دابویی

وحید خلفی

حمیدرضا زارعی

دانشجوی دکترا، دانشکده مهندسی هوافضا- دانشگاه علوم و فنون هوایی شهید ستاری- تهران- ایران

Abstract Persian

در این پژوهش تحلیل ارتعاشات آزاد و پنل فلاتر چندلایه‎های کامپوزیتی دارای الیاف منحنی‌شکل با رویکرد حل عددی آیزوژئومتریک با استفاده از تئوری لایروایز ارائه می‌گردد. با توجه به کاربرد گسترده سازه‌های ساخته‌شده از مواد مرکب در صنایع هوافضا و مکانیک، از ورق‌های کامپوزیتی با سفتی متغیر به‌منظور کنترل خواص مکانیکی مطلوب و طراحی کارآمدتر استفاده گردید. به‌منظور افزایش دقت پاسخ نسبت به تئوری تک‌لایه‌ی معادل و نیز افزایش سرعت محاسباتی نسبت به مدل الاستیسیته سه‌بعدی، از تئوری لایروایز فریرا به همراه فرضیات تئوری برش مرتبه اول برای فرض میدان جابجایی بهره گرفته شده است. در ادامه، با استفاده از روش انرژی و اصل کار مجازی و با فرض تئوری پیستون مرتبه اول برای شبیه‌سازی فشار آیرودینامیک، معادلات حاکم برای ارتعاشات آزاد و پنل فلاتر ورق استخراج گردید. گسسته‌سازی هندسه با روش حل عددی آیزوژئومتریک صورت پذیرفت که در آن از توابع پایه نربز مکعبی که برای مدل‌کردن دقیق هندسه بکار می‌رود، همزمان به عنوان تابع تقریب در فرمولبندی اجزای محدود نیز استفاده شده است. نتایج عددی از حل مساله مقدار ویژه بدست آمد و پارامترهای مختلفی از جمله نوع چیدمان، میزان انحنای الیاف، شرایط مرزی و نسبت‌های ابعادی در صفحات کامپوزیتی با الیاف منحنی ارائه گردیده است. مقایسه نتایج به‌دست‌آمده با نتایج دیگر پژوهش‌ها انطباق خوبی دارد و دقت و کارایی فرمولبندی ارائه‌شده را نشان می‌دهد.

Keywords Persian

ارتعاشات آزاد

پنل فلاتر

کامپوزیت‌های سفتی متغیر

روش آیزوژئومتریک

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