Free vibration Study of simply supported cylindrical laminateds panels with piezoelectric layer

محورهای موضوعی : فصلنامه شبیه سازی و تحلیل تکنولوژی های نوین در مهندسی مکانیک

مصطفی معطری ¹ ( کارشناس ارشد، دانشکده مهندسی مکانیک، دانشگاه آزاد اسلامی واحد همدان، همدان، ایران. )
فرزان براتی ² ( استادیار، دانشکده مهندسی مکانیک، دانشگاه آزاد اسلامی واحد همدان، همدان، ایران. )

تاریخ دریافت : 1394/11/02 تاریخ پذیرش : 1395/02/31 تاریخ انتشار : 1395/08/01

کلید واژه: Free vibration, Piezoelectric, Fourier series, Laminate, Plane strain,

چکیده مقاله :

In the present study, vibration of cylindrical laminates with different layers and angles were studied. In order to actuate and polarize in radial direction, a piezoelectric layer was located at outer surface of composite shell. Laminates were assumed long enough so that plane strain state analysis in 2D can be used properly. In order to satisfy the boundary conditions, variables in terms of Fourier series were obtained. The governing equations reduced to ordinary differential equations at thickness direction and by power series method, the exact solution equations were obtained, unknown coefficient were calculated with rapid convergence. By using the matrix transfer method, vibration response of composite shell were obtained. Finally, results for the first seven modes of natural frequency of multi layer cylindrical shell were obtained. In addition, for both state of one single piezoelectric layer and five layer shell at the end, variable response such as displacement, principal stress and strain were achieved.

چکیده انگلیسی:

  در این پژوهش، به مطالعه و حل دقیق ارتعاشات آزاد پوسته های چندلایه استوانه ای پرداخته شده است. لایه ها از نوع زاویه ای بوده و با زوایای مختلف نسبت به هم قرار گرفته اند. در سطح خارجی پوسته چندلایه استوانه ای، یک لایه پیزوالکتریک قرارگرفته است که به منظور تحریک مناسب در راستای شعاعی قطبیده شده است. پوسته طویل بوده و با فرض کرنش صفحه ای بصورت دوبعدی تحلیل می گردد. متغیرها در هر لایه برای برآورده کردن شرایط مرزی که شامل تکیه گاههای ساده در لبه ها می باشند بر حسب سری های فوریه بسط داده شده اند. معادلات حاکم به معادلات دیفرانسیل معمولی در راستای ضخامت تقلیل پیدا می کنند سپس از روش سری با تابع توانی برای حل این معادلات که منجر به یک پاسخ دقیق و همگرایی سریعتر می شود استفاده می گردد و ضرایب مجهول پاسخ ارتعاشی با روش ماتریس انتقال بدست می آیند. نتایج برای فرکانس طبیعی پوسته چندلایه استوانه ای در هفت مود اول و در دو حالت تک لایه ی پیزوالکتریک و پوسته پنج لایه در انتها و شکل کلی پاسخ متغیرهای نظیر جابجایی، تنش ها و کرنش های اصلی بدست آمده است.

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