علوم و فناوری کامپوزیت

تحلیل ارتعاش آزاد الکترومکانیکی نانو ورق مستطیلی مرکب پیزوالکتریک با استفاده از تئوری های تغییر شکل برشی اصلاح شده

نوع مقاله : مقاله پژوهشی

نویسندگان

1 استادیار، مهندسی مکانیک، دانشگاه اراک، اراک، ایران

2 کارشناس ارشد، مهندسی مکانیک، دانشگاه اراک، اراک، ایران

چکیده

هدف این مقاله مطالعه ارتعاش آزاد نانو ورق مستطیلی مرکب پیزوالکتریک تحت بار الکترومکانیکی شامل نیروی محوری و ولتاژ خارجی بر اساس تئوری‌های تغییر شکل برشی اصلاح شده نمایی و مثلثاتی به همراه تئوری الاستیسیته غیرمحلی و شرایط مرزی چهار طرف تکیه‌گاه ساده است. در تئوری غیرمحلی تنش در هر نقطه تابعی از کرنش در تمامی نقاط محیط می‌باشد. این تئوری اهمیت بسزایی در ساختارهای با ابعاد میکرو و نانو دارد. درتئوری تغییرشکل برشی اصلاح شده نمایی و تئوری تغییر شکل برشی اصلاح شده مثلثاتی، توابع نمایی و مثلثاتی در راستای ضخامت، جهت در نظر گرفتن تاثیرات تغییر شکل برشی عرضی و اینرسی دورانی بکار رفته است. از تئوری الاستیسیته غیرمحلی جهت در نظر گرفتن پارامتر مقیاس طول کوچک نانو ورق مستطیلی مرکب پیزوالکتریک استفاده شده است. نانو ورق مرکب پیزوالکتریک مورد مطالعه در این تحلیل ورق مستطیلی ساخته شده از ماده مرکب پیزوالکتریک PZT 4 متشکل از ترکیبات بلوری سرب، زیرکونیم و تیتانیم جهت دست‌یابی به خواص فلز- سرامیک و همچنین خاصیت پیزوالکتریک می‌باشد. با بکارگیری اصل همیلتون معادلات دیفرانسیل حاکم بر ارتعاش نانو ورق مستطیلی مرکب پیزوالکتریک به‌دست آمده و برای به‌دست آوردن پاسخ فرکانسی از حل دقیق ناویر استفاده شده است. در نهایت تأثیر پارامتر مقیاس نانو، نیروهای محوری، ولتاژ خارجی و نسبت‌های هندسی روی فرکانس‌‌های طبیعی بی‌‌بعد شش مد ارتعاشی اول نانو ورق مستطیلی مرکب پیزوالکتریک مورد بحث و بررسی قرار گرفته است.

کلیدواژه‌ها

موضوعات

عنوان مقاله [English]

Electro-Mechanical free vibrations analysis of composite rectangular piezoelectric nanoplate using modified shear deformation theories

نویسندگان [English]

  • Korosh Khorshidi 1
  • Ali Siahpush 2
  • Abolfazl Fallah 2

1 1- Department of Mechanical Engineering, University of Arak, Arak, Iran

2 1- Department of Mechanical Engineering, University of Arak, Arak, Iran

چکیده [English]

The aim of this paper is to study the free vibration of composite rectangular piezoelectric nanoplate subjected to an electro-mechanical loading includes a biaxial force and an external voltage based on exponential shear deformation theory and trigonometric shear deformation theory in conjunction with the nonlocal elasticity theory under the simply supported boundary condition. The nonlocal theory states that stress at a point is a function of strains at all points in the continuum. The nonlocal elasticity theory becomes significant for small length scale in micro and nanostructures. In exponential shear deformation theory andtrigonometric shear deformation theory, exponential and trigonometric functions are used in terms of thickness coordinate to include the effect of transverse shear deformation and rotary inertia. Nonlocal elasticity theory is employed to investigate effect of small scale on natural frequency of composite rectangular piezoelectric nanoplate. It is assumed that the composite rectangular piezoelectric nanoplate made of PZT 4 composite piezoelectric material includes crystal compounds of Pb, Zr and Ti to achieve metal-ceramic and piezoelectric properties. The governingdifferential equations of the vibration of the composite rectangular piezoelectric nanoplate are derived by using the Hamilton’s principle, which are then solved by using the Navier method to obtain the natural frequencies of the composite rectangular piezoelectric nanoplate. The detailed parametric study is conducted to discuss the influences of the nonlocal parameter, biaxial force external electric voltage and geometrical ratios on the first six nondimensional frequencies of the composite rectangular piezoelectric nanoplate

کلیدواژه‌ها [English]

  • Composite piezoelectric nanoplate
  • Free vibration
  • Nonlocal
  • Exponential and Trigonometric Shear Deformation
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علوم و فناوری کامپوزیت
دوره 4، شماره 2
تابستان 96
شهریور 1396
صفحه 151-160
فایل ها
هم رسانی
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