تحلیل کمانش میکروتیر دو پیونده براساس مدل ردی – لوینسون با استفاده از روش تربیع دیفرانسیلی

نوع مقاله: مقاله علمی پژوهشی

نویسندگان

1 مهندسی مکانیک، مکانیک جامدات، دانشگاه جامع امام حسین (ع)، تهران، ایران

2 دانشگاه جامع امام حسین (ع)، تهران، ایران

چکیده

در این مقاله، کمانش خطی میکرو تیر دو پیونده بر اساس مدل ردی – لوینسون بررسی شده است. این سیستم شامل یک میکروتیر ایزوتروپ و یک میکروتیر کامپوزیتی با خاصیت الاستیک، الکتریکی و مغناطیسی می‌باشد. این تیرها توسط فنرهای الاستیک که با دو مدل وینکلر و پاسترناک شبیه سازی شده‌اند به یکدیگر متصل گردیده‌اند. برای اطمینان از صحت نتایج بدست آمده، نتایج کار حاضر با نتایج محققان دیگر مقایسه و مشاهده می‌گردد که تطابق بسیار خوبی بین نتایج وجود دارد. با افزایش ثوابت وینکلر و پاسترناک بار کمانش در راستای نسبت ضخامت به پارامتر مقیاس طول، افزایش می‌یابد.

کلیدواژه‌ها

موضوعات


 

[1]   Mindlin, R.D.,  and Tiersten, H.F., "Effects of Couple-stresses in Linear Elasticity", Archive for Rational Mechanics and Analysis, Vol. 11, pp. 415-448, (1962).

 

[2]    Yang, A.C.M., Chong, D.C.C., and Tong, P., "Couple Stress Based Strain Gradient Theory for Elasticity", International Journal of Solids and Structures, Vol. 39, pp. 2731-2743, (2002).

 

[3]   Mindlin, R.D., "Second Gradient of Strain and Surface-tension in Linear Elasticity", International Journal of Solids and Structures, Vol. 1, pp. 417-438, (1965).

 

[4]   Lam, D.C.C., ang F. Y., Chong A.C.M., Wang J., and Tong P., "Experiments and Theory in Strain Gradient Elasticity", Journal of Mechanics Physics of Solids, Vol. 51, pp. 1477-1508, (2003).

[5]   Şimşek, M., Kocatürk, T., and Akbaş, S. D., "Static Bending of a Functionally Graded Microscale Timoshenko Beam Based on the Modified Couple Stress Theory", Composite Structures, Vol. 95, pp. 740-747, (2013).

 

[6]   Arefi, M., and Zenkour, A. M., "Vibration and Bending Analyses of Magneto–electro–thermo-elastic Sandwich Microplates Resting on Viscoelastic Foundation", Applied Physics A, pp. 123-550, (2017).

 

[7]   Ansari, R., and Sahmani, S., "Bending Behavior and Buckling of Nanobeams Including Surface Stress Effects Corresponding to Different Beam Theories", Composite Structures, Vol. 49, pp. 1244-1255, (2011).

 

[8]   Ansari, R., Gholami, R., Faghih Shojaei, M., Mohammadi, V., and Sahmani, S., "Size-dependent Bending, Buckling and Free Vibration of Functionally Graded Timoshenko Microbeams Based on the Most General Strain Gradient Theory", Composite Structures, Vol. 100, pp. 385-397, (2013).

 

[9]    Eltaher, M. A., Emam Samir, A., and Mahmoud, F. F.," Static and Stability Analysis of Nonlocal Functionally Graded Nanobeams", Int. J. Composite Structures, Vol. 96, pp. 82-88, (2013).

 

[10]  Mohammadimehr, M., and Mahmudian-Najafabadi, M., "Bending and Free Vibration Analysis of Nonlocal Functionally Graded Nanocomposite Timoshenko Beam Model Rreinforced by SWBNNT Based on Modified Coupled Stress Theory", Department of Solid Mechanics, University of Kashan, Iran, (2013).

 

[11]  Arefi, M., and Zenkour, A. M., "Size-dependent Electro-elastic Analysis of a Sandwich Microbeam Based on Higher-order Sinusoidal Shear Deformation Theory and Strain gradient Theory", J. Intelligent Material Systems and Structures, Vol. 29, pp. 1394-1406, (2017).

 

[12]   Thai, H.T., "A Nonlocal Beam Theory for Bending, Buckling, and Vibration of Nanobeams ", Int. J. Engineering Science, Vol. 52, pp. 56-64, (2012).

 

[13]    Li, Y.S., Feng, W.J., and Cai, Z.Y., "Bending and Free Vibration of Functionally Graded Piezoelectric Beam Based on Modified Strain Gradient Theory", Composite Structures, Vol. 115, pp. 41-50, (2014).

 

[14]    Şimşek, M., and Reddy, J. N., "A Unified Higher Order Beam Theory for Buckling of a          Functionally Graded Microbeam Embedded in Elastic Medium using Modified Couple Stress Theory", Composite Structures, Vol. 101, pp. 47-58,  (2013).

 

[15]  Mohammadabadi M., and Daneshmehr A. R., "Size Dependent Buckling Analysis of   Microbeams Based on Modified Couple Stress Theory with High Order Theories and General Boundary Conditions", Int. J. Engineering Science, Vol. 74, pp. 1-14, (2014).

 

[16]  Akgöz B., and Civalek Ö., "A New Trigonometric Beam Model for Buckling of Strain Gradient Microbeams", Int. J. Mechanical Sciences, Vol. 81, pp. 88-94, (2014).

 

[17]    Ebrahimi F., and Salari E., "Thermal Buckling and Free Vibration Analysis of Size Dependent Timoshenko FG Nanobeams in Thermal Environments", Int. J. Composite Structures, Vol. 128, pp. 363-380, (2015).

[18]    Arefi, M., Kiani, M., and Zenkour, A. M.,  " Size-dependent Free Vibration Analysis of a Three-layered Exponentially Graded Nano-/micro-plate with Piezomagnetic Face Sheets Resting on Pasternak’s Foundation Via MCST", J. Sandwich Structures and Materials, 1099636217734279, (2017).

 

[19]    Mohammadabadi, M., Daneshmehr, A. R., and Homayounfard, M., "Size-dependent Thermal Buckling Analysis of Micro Composite Laminated Beams using Modified Couple Stress Theory", Int. J. Engineering Science, Vol. 92, pp. 47-62, (2015).

 

[20]    Li, Y.S., Feng, W.J., and Cai, Z.Y., "Bending and Free Vibration of Functionally Graded Piezoelectric Beam Based on Modified Strain Gradient Theory", Composite Structures, Vol. 115, pp. 41-50, (2014).

 

[21]    Levinson, M., "A New Rectangular Beam Theory", J. Sound and Vibration, Vol. 74, pp. 81–87, (1981).

 

[22]    Reddy, J.N., "A Simple Higher-order Theory for Laminated Composite Plates", J. Applied Mechanics, Vol. 51, pp. 745–752, (1984).

 

[23]    Wang, B., Liu, M., Zhao, J., and Zhou, Sh., "A Size-dependent Reddy–Levinson Beam Model Based on a Strain Gradient Elasticity Theory", Meccanica, Vol. 49, pp. 1427-1441, (2014).

 

[24]    Lam, D.D.C., Yang, F., Chong, A.C.M., Wang, J., and Tong, P.," Experiments and Theory in Strain Gradient Elasticity", J. of the Mechanics and Physics of Solids, Vol. 51, pp. 1477–1508, (2003).

 

[25]    Mohammadimehr M., Rousta Navi, B., and Ghorbanpour Arani, A., "Free Vibration of Viscoelastic Double-bonded Polymeric Nanocomposite Plates Reinforced by FG-SWCNTs using MSGT, Sinusoidal Shear Deformation Theory and Meshless Method", Composite Structure, Vol. 131, pp. 654-671, (2015).

 

[26]    Liu, Y., Han, Q., Li, C., Liu, X., and Wu, B., "Guided Wave Propagation and Mode Differentiation in the Layered Magneto-electro-elastic Hollow Cylinder", Composite Structure, Vol. 132, pp. 558–566, (2015).

 

[27]    Akgöz, B., and Civalek, Ö., "A Size-dependent Shear Deformation Beam Model Based on the Strain Gradient Elasticity Theory", Int. J. Engineering Science, Vol. 70, pp. 1-14, (2013).

 

[28]    Li, Y.S., Cai, Z.Y., and Shi, S.Y., "Buckling and Free Vibration of Magneto-electro-elastic Nanoplate Based on Nonlocal Theory", Composite Structure, Vol. 111, pp. 522–529, (2014).

 

[29]    Ansari, R., Gholami, R., and Rouhi, H., "Size-dependent Nonlinear Forced Vibration Analysis of Magneto-electro-thermo-elastic Timoshenko Nanobeams Based upon the Nonlocal Elasticity Theory", Composite Structure, Vol. 126 pp. 216–226, (2015).

 

[30]    Ghorbanpour Arani, A., Atabakhshian, V., Loghman, A., Shajari, A.R., and Amir, S., "Nonlinear Vibration of Embedded SWBNNTs Based on Nonlocal Timoshenko Beam Theory using DQ Method", Phisyca. B, Vol. 407, pp. 2549-2555, (2012).

 

[31]    Murmu, T., and Pradhan, S.C., "Buckling Analysis of a Single-walled Carbon Nanotube Embedded in an Elastic Medium Based on Nonlocal Elasticity and Timoshenko Beam Theory and using DQM", Phisyca E, Vol. 41, pp. 1232-1239, (2009).

 

[32]    Ansari, R., Gholami, R., Faghih Shojaei, M., Mohammadi, V., and Sahmani, S., ''Size-dependent Bending, Buckling and Free Vibration of Functionally Graded Timoshenko Micro Beams Based on the most General Strain Gradient Theory'', Composite Structure, Vol. 100 pp. 385–397, (2013).