تحلیل ارتعاشات آزاد و اجباری نانوورق مستطیلی ویسکوالاستیک کلوین-ویت با استفاده از تئوری کوپل تنش اصلاح شده

نوع مقاله : مقاله پژوهشی

نویسندگان

1 گروه مکانیک،دانشکده مهندسی، دانشگاه زنجان، زنجان، ایران

2 دانشیار گروه مهندسی مکانیک معاون پژوهشی دانشکده مهندسی دانشگاه زنجان

3 دانشگاه فنی و مهندسی بوئین زهرا، قزوین، ایران

چکیده

در این مقاله ارتعاشات آزاد و اجباری نانوورق ویسکواالستیک واقع بر بستر ویسکواالستیک پاسترناک، مورد بررسی قرار خواهد گرفت. با توجه به عدم توانایی تئوریهای کالسیک االستیسته در توصیف سازه هایی با ابعاد نانو، در این پژوهش از تئوری غیرکالسیک کوپل تنش اصالح شده برای بیان اثر اندازه بهره گرفته شده است. در این پژوهش با استفاده از روش نیمه تحلیلی گالرکین، ارتعاشات آزاد نانوورق برای شش شرط تکیه گاهی متفاوت، بحث شده است؛ همچنین ارتعاشات اجباری نانوورق مستطیلی ویسکواالستیک با استفاده از روش ناویر برای شرط تکیه گاهی ساده مورد مطالعه واقع می شود. در بخش تحلیل نتایج تاثیر پارامترهایی مانند ضریب ویسکواالستیک سازهای نانوورق، پارامتر مقیاس طول ماده و ضریب االستیک خطی بستر بر روی فرکانس طبیعی، ماکزیمم خیز دینامیکی، اختالف فاز و پدیده تشدید ارائه شده است. با توجه به نتایج حاصل شده مشخص شد که در نظر گرفتن پارامتر مقیاس طول ماده منجر به افزایش سفتی و فرکانس طبیعی نانوورق می شود؛ همچنین در نظر گرفتن پارامتر مقیاس طول ماده منجر به رخ دادن پدیده تشدید در فرکانسهای تحریک باالتر و کاهش اختالف فازخواهد شد. وجود ضرایب االستیک خطی و برشی بستر، منجر به رخ دادن پدیده تشدید در فرکانسهای تحریک پایین می شود..

کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

Free and Forced Vibration Analysis of Kelvin-Voigt Viscoelastic Nanoplate by Using Modified Couple Stress Theory

نویسندگان [English]

  • saber salehi 1
  • Omid Rahmani 2
  • S. Amirhosein Hoseini 3
1 Department of Mechanical Engineering, University of Zanjan, Zanjan, Iran
2 University of Zanjan
3 Buein Zahra Technical University, Buein Zahra, Qazvin, Iran
چکیده [English]

With the development of nanotechnology in the industrial applications and engineering sciences, analysis of the behavior of nanostructures has become important. In recent years, expansion and using of non-classical theories to predict the behavior of nanostracture materials has attracted the attention of researchers. In this paper, free and forced vibration of viscoelastic nanoplate on the Pasternak viscoelastic foundation will be studied. In this study, due to the inability of classical theories to describe the behavior of nano-dimensional structures, the non-classical modified couple stress theory has been used for express the size effect. By using the Galerkin semi-analytic method, free vibrations analysis for six different boundary conditions are discussed; also, forced vibration of rectangular viscoelastic nanoplate is studied by using the Navier method for simply supported boundary condition. Kelvin-Voigt model is used to simulate the behavior of viscoelastic nanoplate. In the results analysis section, the effect of small-scale factor, structural viscoelastic coefficient, linear elastic coefficient of foundation, external damping coefficient of foundation and shear coefficient of foundation on the natural frequency, maximum dynamic deflection and resonance phenomenon are presented.

کلیدواژه‌ها [English]

  • Forced vibration؛ Resonance phenomenon
  • Modified couple stress theory
  • Semi analytical Galerkin method
[1] S. Pradhan, J. Phadikar, Nonlocal elasticity theory for vibration of nanoplates, Journal of Sound and Vibration, 325(1-2) (2009) 206-223.
[2] M. Şimşek, Dynamic analysis of an embedded microbeam carrying a moving microparticle based on the modified couple stress theory, International Journal of Engineering Science, 48(12) (2010) 1721-1732.
[3] H. Ma, X.-L. Gao, J. Reddy, A non-classical Mindlin plate model based on a modified couple stress theory, Acta mechanica, 220(1-4) (2011) 217-235.
[4] S. Pouresmaeeli, S. Fazelzadeh, E. Ghavanloo, Exact solution for nonlocal vibration of double-orthotropic nanoplates embedded in elastic medium, Composites Part B: Engineering, 43(8) (2012) 3384-3390.
[5] L.-L. Ke, Y.-S. Wang, J. Yang, S. Kitipornchai, Free vibration of size-dependent Mindlin microplates based on the modified couple stress theory, Journal of Sound and Vibration, 331(1) (2012) 94-106.
[6] A.G. Arani, R. Kolahchi, H. Vossough, Buckling analysis and smart control of SLGS using elastically coupled PVDF nanoplate based on the nonlocal Mindlin plate theory, Physica B: Condensed Matter, 407(22) (2012) 4458-4465.
[7] A. Bakhsheshy, K.Khorshidi, Free vibration of functionally graded rectangular nanoplates in thermal environment based on the modified couple stress theory, ModaresMechanical Engineering, 14(15)(2015,323-330. (In Persian)
[8]S. O. Dezyani, R. A. Jafari-Talookolaei,M. Abedi, H. Afrasiab, Vibration analysis of a microplate in contact with a fluid based on the modified couple stress theory,Modares Mechanical Engineering, 17(2),(2017),47-57.(In Persion)
[9] G. A.Varzandian, S. Ziaei. Analytical Solution of Non-Linear Free Vibration of Thin Rectangular Plates with Various Boundary Conditions Based on Non-Local Theory. Amirkabir Journal of Mechanical Engineering, 48(4),(2017), 331–346.(In Persion)
[10] M. Ghadiri, H. Safarpour, Free Vibration Analysis of a Functionally Graded Cylindrical Nanoshell Surrounded by Elastic Foundation Based on the Modified Couple Stress Theory, Amirkabir Journal of  Mechanical Engineering, 49(4) (2018) 721-730.(In Persion)
[11] R. Ansari Khalkhali, A. Norouzzadeh, R. Gholami, Forced vibration analysis of conveying fluid carbon nanotube resting on elastic foundation based on modified couple stress theory, Modares Mechanical Engineering,15(3), (2015),27-34. (In Persian)
[12] B. Akgöz, Ö. Civalek, Free vibration analysis for single-layered graphene sheets in an elastic matrix via modified couple stress theory, in:  Materials & Design, 2012, pp. 164-171.
[13] T. Aksencer, M. Aydogdu, Forced transverse vibration of nanoplates using nonlocal elasticity, Physica E: Low-dimensional Systems and Nanostructures, 44(7-8) (2012) 1752-1759.
[14] Y. Lei, S. Adhikari, M. Friswell, Vibration of nonlocal Kelvin–Voigt viscoelastic damped Timoshenko beams, International Journal of Engineering Science, 66 (2013) 1-13.
[15] S. Sahmani, R. Ansari, On the free vibration response of functionally graded higher-order shear deformable microplates based on the strain gradient elasticity theory, Composite Structures, 95 (2013) 430-442.
[16] M. Kiasat, H. Zamani, M. Aghdam, On the transient response of viscoelastic beams and plates on viscoelastic medium, International Journal of Mechanical Sciences, 83 (2014) 133-145.
[17] A.W. Leissa, Vibration of plates, OHIO STATE UNIV COLUMBUS, 1969.
[18] H. Zamani, M. Bodaghi, M. Aghdam, M. Salehi, Accurate damping analysis of viscoelastic composite beams and plates on suppressive foundation, Journal of Composite Materials, 49(18) (2015) 2187-2202.
[19] M.R. Nami, M. Janghorban, Resonance behavior of FG rectangular micro/nano plate based on nonlocal elasticity theory and strain gradient theory with one gradient constant, Composite Structures, 111 (2014) 349-353.
[20] M. Mohammadimehr, B.R. Navi, A.G. Arani, Free vibration of viscoelastic double-bonded polymeric nanocomposite plates reinforced by FG-SWCNTs using MSGT, sinusoidal shear deformation theory and meshless method, Composite Structures, 131 (2015) 654-671.
[21] S.H. Hashemi, H. Mehrabani, A. Ahmadi-Savadkoohi, Forced vibration of nanoplate on viscoelastic substrate with consideration of structural damping: an analytical solution, Composite Structures, 133 (2015) 8-15.
[22] M. Arefi, A.M. Zenkour, Nonlocal electro-thermo-mechanical analysis of a sandwich nanoplate containing a Kelvin–Voigt viscoelastic nanoplate and two piezoelectric layers, Acta Mechanica, 228(2) (2017) 475-493. 
[23]A.G. Arani, E. Haghparast, H.B. Zarei, Nonlocal vibration of axially moving graphene sheet resting on orthotropic visco-Pasternak foundation under longitudinal magnetic field, Physica B: Condensed Matter, 495 (2016) 35-49.
[24] S. Pouresmaeeli, E. Ghavanloo, S. Fazelzadeh, Vibration analysis of viscoelastic orthotropic nanoplates resting on viscoelastic medium, Composite Structures, 96 (2013) 405-410.
[25] J. Liu, Y. Zhang, L. Fan, Nonlocal vibration and biaxial buckling of double-viscoelastic-FGM-nanoplate system with viscoelastic Pasternak medium in between, Physics letters A, 381(14) (2017) 1228-1235.
[26] A.G. Arani, M. Jalaei, Transient behavior of an orthotropic graphene sheet resting on orthotropic visco-Pasternak foundation, International Journal of Engineering Science, 103 (2016) 97-113.
[27] A. Jamalpoor, A. Ahmadi-Savadkoohi, M. Hosseini, S. Hosseini-Hashemi, Free vibration and biaxial buckling analysis of double magneto-electro-elastic nanoplate-systems coupled by a visco-Pasternak medium via nonlocal elasticity theory, European Journal of Mechanics-A/Solids, 63 (2017) 84-98.