روشهای عددی در مهندسی

روشهای عددی در مهندسی

تحلیل ارتعاش آزاد ورق ساندویچی ضخیم با هسته متخلخل مدرج اشباع شده با استفاده از تئوری تغییر شکل برشی شبهسه‌بعدی

نوع مقاله : مقاله پژوهشی

نویسندگان
علی زمانی 1
محمد علی رهگذر 2
1 دانشگاه شهید اشرفی اصفهانی
2 دانشگاه اصفهان،
10.47176/jcme.42.1.9621
چکیده
در این پژوهش به بررسی ارتعاش آزاد ورق ساندویچی مستطیلی ضخیم متشکل از رویه‌های همگن و هسته ناهمگن از جنس مواد متخلخل اشباع شده مدرج تابعی پرداخته ‌شده است. در این هسته متخلخل مدرج تابعی، ویژگی‌های مواد در راستای ضخامت بر اساس تئوری تنش بایوت و دیگر توابع داده شده تغییر می‌کنند. حل مساله بر اساس تئوری تغییر شکل برشی شبه‌سه‌بعدی بنا شده و معادلات حاکم و شرایط مرزی با استفاده از اصل همیلتون استخراج ‌شده‌اند. ورق مورد بررسی دارای شرایط تکیه‌گاهی گیردار- ساده-ساده-گیردار بوده و در مطالعات قبلی از روش ساده ناویر که ورق را در شرایط تکیه گاهی ساده بررسی می‌کند استفاده شده، در صورتی که در تحقیق حاضر از روش مربعات دیفرانسیلی  جهت حل مساله و گسسته‌سازی تحلیل عددی استفاده شده است. از جمله مزایای این روش حل، سادگی روش، کاهش حجم محاسبات نسبت به سایر روش‌های عددی و قابلیت لحاظ شرایط مرزی مختلف است. در این پژوهش ابتدا هم‌گرایی و اعتبارسنجی تحلیل نسبت به نقاط شبکه بیان شده، سپس تأثیر مشخصات هسته ورق ساندویچی مانند ضریب تخلخل، ضخامت، ضریب اسکمپتون، و ضخامت کل ورق و شرایط تکیه‌گاهی مختلف روی فرکانس‌های طبیعی ورق ساندویچی بررسی ‌شده است. به روز بودن تئوری استفاده شده در تحلیل ارتعاش آزاد ورق با هسته متخلخل مدرج تابعی از دیگر مزیت‌های اصلی این پژوهش نسبت به پژوهش‌های اخیر است.
کلیدواژه‌ها
ورق ساندویچی با هسته متخلخل مدرج تابعی اشباع شده
ارتعاش آزاد
تئوری بایوت
تئوری تغییر شکل برشی شبهسه‌بعدی
روش مربعات دیفرانسیلی

عنوان مقاله English

Vibration Analysis of Thick Sandwich Plates with Saturated FG-Porous Core Using Quasi-3D Shear Deformation Theory

نویسندگان English

Ali Zamani 1
Mohammad Ali Rahgozar 2
چکیده English

Free vibration analysis of a rectangular thick sandwich plate consisting of outer homogeneous layers with saturated nonhomogeneous Functionally Graded Porous (FGP) core has been conducted. Material property in this porous core could vary along the plate thickness according to Biot’s stress theory and other related functions. Solution to this problem was based on Quasi-Three-Dimensional shear deformation theory, which results the governing differential equations and the boundary conditions of the plate model. The boundary conditions in the considered plate model were clamped-simple-simple-clamped supports, whereas in the previous studies generally Navier method is used in which simple supports is assumed for all sides of the plate. In the present study, in order to obtain our proposed numerical solution, the differential quadrature method is applied. Among advantages of this method are being simple and straightforward, having reduced computational effort compared to other numerical methods and being capable of accounting for plates with different boundary conditions. Convergence and validation of the results with respect to the grid points were first presented. The effect of different core properties such as porosity, thickness, Skempton’s coefficient, total plate thickness, and different boundary conditions on FGP sandwich plate frequencies were investigated. Application of the latest theory for free vibration analysis of FGP sandwich plates is another main advantage of the presented method compared to other recent studies.

کلیدواژه‌ها English

Saturated functionally graded porous (FGP) sandwich plate
free vibration
Biot’s theory
quasi-three-dimensional-shear deformation theory
differential quadrature method
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