تحلیل فرکانس‌های طبیعی تیر تیموشنکو مخروطی چرخان از جنس مواد تابعی با لایه محرک پیزوالکتریک

نوع مقاله : گرایش دینامیک، ارتعاشات و کنترل

نویسندگان

1 نویسنده مسئول: استادیار، دانشکده مهندسی مکانیک، دانشگاه آزاد اسلامی، واحد الیگودرز، الیگودرز، ایران

2 استاد، دانشکده فنی و مهندسی، دانشگاه جامع امام حسین(ع)، تهران، ایران

چکیده

در این پژوهش، ارتعاشات آزاد تیر تیموشنکو مخروطی چرخان با لایه محرک پیزوالکتریک موردمطالعه قرار گرفته است. جنس تیر از مواد تابعی
FGM (Functionally Graded Materials) در راستای ضخامت و شرط مرزی یکسر گیردار متصل به هاب در نظر گرفته شده است. تحلیل بر اساس تئوری تغییر شکل برشی مرتبه اول انجام شده است. در ابتدا، انرژی کل سیستم شامل انرژی پتانسیل و جنبشی تیر و لایه پیزوالکتریک محاسبه شده و سپس با بهره‌گیری از‌ روش ریلی- ریتز مبتنی بر کمینه‌سازی انرژی کل سیستم، فرکانس‌های طبیعی سیستم استخراج شده است. در ادامه پس از اعتبارسنجی نتایج حاصل از طریق مقایسه با نتایج سایر محققان، تأثیر پارامترهای هندسی مختلف از قبیل ضخامت و پهنای تیر، شیب مخروط تیر، طول تیر، سرعت دورانی و همچنین ولتاژ پیزوالکتریک بر فرکانس طبیعی مطالعه شده است. نتایج نشان دادند که با افزایش سرعت زاویه‌ای تیر، فرکانس طبیعی افزایش می‌یابد به‌طوری‌که با بیشتر شدن سرعت افزایش، فرکانس طبیعی با شیب تندتری افزایش می‌یابد.

کلیدواژه‌ها


عنوان مقاله [English]

Natural Frequencies Analysis of a Rotating Tapered Timoshenko Beam Made of Functionally Graded Material with Actuated Piezoelectric Layer

نویسندگان [English]

  • Shahrouz Yousefzadeh 1
  • Mohammadmehdi Doostdar 2
1 Corresponding author: Assistant Professor, Faculty of Mechanical Engineering, Aligudarz Branch, Islamic Azad University, Aligudarz, Iran
2 Professor, Faculty of Engineering, Imam Hossein University, Tehran, Iran
چکیده [English]

In this research, the free vibration of rotating tapered Timoshenko beam with piezoelectric layer has been studied. It is assumed that the beam is made of Functionally Graded Materials (FGM) through the thickness direction and the boundary condition is a cantilever attached to the hub. The first-order shear deformation theory has been used to drive governing equations. At first, the total energy of the system such as potential and kinetic energies for the beam and piezoelectric layer has been derived, and then the natural frequencies of the beam have been determined by the Ritz approach based on minimizing the total system energy. After verifying the results by comparing them with other research, the effects of some parameters such as hub radius, rotational speed, taper ratios, rotary inertia, material gradient, piezoelectric voltage, and beam thickness on the natural frequencies of the tapered Timoshenko beam have been studied in detail. The results showed that with increasing the angular velocity of the beam, the natural frequency increases so that as the increasing velocity increases, the natural frequency increases with a steeper slope.

کلیدواژه‌ها [English]

  • Rotating tapered beam
  • functionally graded material
  • natural frequency
  • piezoelectric layer
  • First order shear deformation theory

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دوره 18، شماره 2 - شماره پیاپی 68
شماره پیاپی 68، فصلنامه تابستان
مرداد 1401
صفحه 143-156
  • تاریخ دریافت: 01 بهمن 1400
  • تاریخ بازنگری: 30 بهمن 1400
  • تاریخ پذیرش: 07 تیر 1401
  • تاریخ انتشار: 01 مرداد 1401