رویکرد حسابان کسری برای خمش ورق ویسکوالاستیک با استفاده از تئوری ورق اصلاح‌شده دو متغیره

نوع مقاله : مقاله پژوهشی

نویسندگان

1 دانشکده مهندسی مکانیک و هوافضا، دانشگاه صنعتی شیراز

2 صنعتی شیراز*مهندسی مکانیک

3 دانشکده ریاضی، دانشگاه صنعتی شیراز

چکیده

در این مقاله رفتار خمشی وابسته به زمان ورق ویسکوالاستیک مستطیلی بر مبنای تئوری ورق اصلاح‌شده دومتغیره و با رویکرد حسابان کسری مورد بررسی قرار می‌گیرد. ورق مورد نظر دارای تکیه‌گاه ساده و تحت بارگذاری گسترده یکنواخت می‌باشد و برای شبیه‌ سازی رفتار ویسکوالاستیک از مدل کسری مرچانت سه پارامتری استفاده می‌شود. با استفاده از تبدیل لاپلاس، معادلات حاکم بر در دامنه زمان به دامنه لاپلاس تبدیل می‌شوند و سپس برای حل این معادلات از روش ناویر استفاده می‌شود. برای بدست‌آوردن پاسخ ورق ویسکوالاستیک از اصل تناظر الاستیک- ویسکوالاستیک استفاده می‌شود به این طریق که پاسخ ورق الاستیک هم‌ارز به مسئله ویسکوالاستیک تعمیم داده می‌شود. نتایج حاصل از این تحقیق، از جمله خیز و کرنش‌های صفحه‌ای و جانبی، با نتایج حاصل از مدل الاستیک و مدل مرچانت استاندارد مقایسه می‌شود که از مقایسه نتایج حاصل با نتایج مراجع می‌توان نتیجه گرفت که روش پیشنهادی از دقت مطلوبی برخوردار است. همچنین به مطالعه تغییرات خیز در راستای ضخامت و تأثیر نسبت منظری ورق بر نتایج نیز پرداخته می‌شود. این پژوهش نشان می‌دهد که مدل کسری پیشنهادشده قابلیت شبیه‌سازی هر دو اثر میرایی و کشسانی دارد که این با طبیعت ساختاری مواد ویسکوالاستیک هماهنگی بیشتری دارد.
 

کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

Fractional calculus approach for bending of viscoelastic plate using two-variable refined plate theory

نویسندگان [English]

  • Elahe Nayebi 1
  • Seyed Jafar Rouzegar 2
  • Mohammad Hosein Heydari 3
1 Department of Mechanical and Aerospace Engineering, Shiraz University of Technology
2 Shiraz University of Technology, Mechanical Engineering Department
3 Department of Mathematics, Shiraz university of Technology, Shiraz, Iran
چکیده [English]

This paper deals with the time-dependent bending behavior of a rectangular viscoelastic plate based on the two-variable refined plate theory using the fractional calculus approach. The plate is fully simply-supported and is subjected to uniformly-distributed loading and the three-parameter merchant model is used for simulation of viscoelastic behavior. The time-domain governing equations are converted into frequency-domain ones using the Laplace transform and then, these equations are solved by the Navier method. The viscoelastic plate response is obtained using the elastic-viscoelastic correspondence principle so that the response of an elastic equivalent problem is extended into the viscoelastic problem. The results of this study, including plate deflection, and in-plane and transverse strains are compared with the results of the elastic model and the standard merchant model where the comparison of obtained results with the reference ones shows that the proposed approach has good accuracy. Also, the variation of deflection through the plate thickness and the effect of aspect ratio on the results are studied. This study shows that the proposed fractional model has the ability to simulation of both elastic and viscose effects simultaneously which is more compatible with the nature of viscoelastic materials.

کلیدواژه‌ها [English]

  • fractional calculus
  • Linear viscoelasticity
  • Refined plate theory
  • Plate bending
  • Laplace transform
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