کنترل تغییرشکل دینامیکی قاب‌‌ بتن آرمه تحت بار زلزله با استفاده از لایه پیزوالکتریک

نوع مقاله : مقاله پژوهشی

نویسندگان

1 گروه مهندسی عمران، واحد خمین، دانشگاه آزاد اسلامی، خمین، ایران - گروه مهندسی عمران، واحد جاسب، دانشگاه آزاد اسلامی، جاسب، ایران

2 گروه مهندسی عمران، واحد خمین، دانشگاه آزاد اسلامی، خمین، ایران

چکیده

مواد پیزوالکتریک نوعی از مصالح هوشمند می‌‌باشند که به دلیل خصوصیات فوق‌‌العاده همانند تبدیل انرژی مکانیکی به الکتریکی و بالعکس مورد توجه پژوهشگران زیادی در علوم مهندسی مختلف قرار دارند. امروزه استفاده از این مصالح، برای کنترل تغییر شکل، کاهش نوسان و کنترل فعال سازه ‌‌ها در صنعت ساختمان رو به افزایش می‌‌باشد. در این مقاله، به تعیین و کنترل تغییرشکل دینامیکی یک قاب بتنی یک دهانه با پوشش لایه پیزوالکتریک روی تیر و ستون‌‌ها تحت بار لرزه‌‌ای پرداخته می‌‌شود. به منظور کنترل تغییرشکل دینامیکی قاب بتنی، از یک کنترل‌‌کننده تناسبی- مشتقی استفاده شده است بدین شکل که یک لایه پیزوالکتریک در نقش محرک و یک لایه در نقش سنسور درنظر گرفته می‌‌شود. معادلات حاکم بر اجزا تیر و ستون قاب بتنی با استفاده از تئوری‌‌ برشی مرتبه بالا ، محاسبه روابط انرژی، اعمال اصل همیلتون و در نظر گرفتن ولتاژ اعمالی بر مصالح پیزوالکتریک به دست می‌‌آیند. جهت کوپل کردن معادلات بدست آمده برای تیر و ستون، از شرایط مرزی پیوستگی در نقاط اتصال تیر به ستون ها به یکدیگر استفاده می‌‌شود. به منظور حل عددی معادلات کوپل شده دینامیکی، از روش عددی تفاضلات مربعی استفاده شده است در این روش، معادلات دیفرانسیلی به معادلات جبری تبدیل شده و در نهایت به کمک روش نیومارک، تغییرشکل دینامیکی قاب بتنی بر حسب زمان محاسبه می‌‌گردد. بعد از صحت‌‌سنجی نتایج، اثر پارامترهای مختلفی همچون ولتاژ اعمالی به لایه پیزوالکتریک، کنترل‌‌کننده از نوع پیزوالکتریک، ضخامت لایه پیزوالکتریک و اثرات ترکیبی آنها بر تغییرشکل دینامیکی بررسی شد. در اینجا، مقادیر بهینه پارامترهای کنترل‌‌کننده شامل ضریب تناسب و ضریب مشتق به‌‌ترتیب برابر با 3/824 و 5/812 به‌‌دست آمدند. نتایج نشان می‌‌دهد برای تعداد نقاط شبکه 15، تغییرشکل دینامیکی بدست آمده از روش تفاضلات مربعی همگرا می‌‌شود. همچنین، اگر از یک کنترل‌‌کننده از نوع پیزوالکتریک استفاده شود، دامنه نوساتات تغییرشکل به شدت کاهش یافته و زمان میرایی سیستم کوتاه‌‌تر خواهد شد. به عبارت دیگر استفاده از کنترل‌‌کننده به ترتیب منجر به کاهش 72 و 65 درصدی تغییرشکل دینامیکی جانبی و قائم  قاب می‌‌شود. همچنین مشاهده شد، که تغییرشکل دینامیکی جانبی قاب درحالتی‌‌که فقط ستون‌‌ها لایه پیزوالکتریک دارند کمتر از حالتی است که فقط تیر لایه پیزوالکتریک دارد درحالی‌‌که این موضوع برای خیز دینامیکی قائم قاب بالعکس می‌‌باشد.

کلیدواژه‌ها

موضوعات

عنوان مقاله [English]

Dynamic deflection control of reinforced concrete frame under earthquake load with piezoelectric layer

نویسندگان [English]

  • mahmood Rabani Bidgoli 1
  • masoud kargar 2
  • hamid mazaheri 2
1 Department of Civil Engineering, Jasb branch, Islamic Azad university, Delijan , Iran
2 Department of Civil Engineering, Islamic Azad University, Khomein,Iran
چکیده [English]

Piezoelectric materials are a type of smart materials that are of interest to many researchers in various engineering sciences due to their extraordinary properties such as converting mechanical energy into electrical energy and vice versa. In this article, the determination and control of the dynamic deformation of a one-span concrete frame with a piezoelectric layer coating on beams and columns under seismic load is discussed. In order to control the dynamic deformation of the concrete frame, a proportional-derivative controller has been used in such a way that a piezoelectric layer is considered as an actuator and a layer as a sensor. The governing equations for the beam and column components of concrete frame are obtained by using high-order shear theory, calculating energy relations, applying Hamilton's principle and considering the applied voltage on piezoelectric materials. In order to solve the dynamic coupled equations, the numerical method of differential quadrature method has been used and finally, with the help of Newmark method, the dynamic deformation of the concrete frame is calculated. After validating the results, the effect of various parameters such as voltage applied to the piezoelectric layer, piezoelectric type controller, thickness of the piezoelectric layer on dynamic deformation were investigated. Here, the optimal values of controller parameters, including proportionality coefficient and derivative coefficient, were obtained as 3.824 and 5.812, respectively. The results show that the use of the controller leads to a reduction of 72 and 65 percent of the lateral and vertical dynamic deflection of the frame, respectively.

کلیدواژه‌ها [English]

  • Dynamic deflection
  • concrete frame
  • numerical method
  • piezoelectric controller
  • mathematical modeling

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نشریه مهندسی عمران امیرکبیر
دوره 56، شماره 2
1403
صفحه 229-252

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