Abstract    In this paper, the modified couple stress theory is used to study vibration analysis of functionally graded rectangular micro-plates. Considering classical and first order plate theories, the couple governing equations of motion are obtained by using the Hamilton’s principle. Considering an assumed mode method, the accurate size dependent natural frequencies are established for simply supported functionally graded rectangular micro-plates. To show the accuracy of the formulations, present results in specific cases are compared with available results in literature and a good agreement is seen. It is found that the natural frequency parameter of micro-plates will decrease as thickness-length ratio increases especially for lower length scale values. The effects of length scale, functionally graded parameter and plate theories on natural frequencies of functionally graded micro-plates are discussed in details.

Keywords    Vibration, Micro-plate, Functionally graded, Modified couple stress theory

چکیده    در اين مقاله با استفاده از تئوري اصلاح شده تنش کوپلي، ارتعاشات آزاد ميکرو ورق­هاي مستطيلي هدفمند تابعي مورد مطالعه قرار مي­گيرد. با در نظر گرفتن تئوري­هاي کلاسيک و مرتبه اول ورق، معادلات حرکت با استفاده از اصل هميلتون بدست مي­آيد. فرکانس­هاي طبيعي ميکرو ورق­هاي هدفمند تابعي با استفاده از روش مد فرضي براي شرايط مرزي تکيه­گاه ساده تعيين مي­گردند. جهت بررسي صحت نتايج، نتايج کنوني در حالت­هاي خاص با نتايج موجود در تحقيقات ديگر مقايسه شده است و دقت مناسبي مشاهده گرديد. با بررسي نتايج مشاهده مي­شود که با کاهش نسبت اثر مقياس اندازه به ضخامت ورق، پارامتر فرکانس طبيعي ميکرو ورق­ها به­خصوص براي مقادير کوچک مقياس اندازه افزايش مي­يابد. اثرات پارامتر مقياس کوچک، پارامتر تابع هدفمند و تئوري­هاي ورق بر روي فرکانس طبيعي ميکرو ورق هاي هدفمند تابعي نشان داده شده است.

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