ارتعاشات آزاد پنل و پوسته متصل کروی- استوانه‌ای به روش مربعات دیفرانسیلی تعمیم یافته دو بعدی

نوع مقاله : مقاله پژوهشی

نویسندگان

دانشکده مکانیک دانشگاه صنعتی خواجه نصیر الدین طوسی

چکیده

در این پژوهش ارتعاشات آزاد پنل و پوسته‌های ایزوتروپیک متصل به‌هم کروی-استوانه‌ای بررسی شده‌است. پوسته و پنل‌ها به ترتیب از دوران 360 وکمتر از 360 درجه یک منحنی حول محور تقارن مرکزی ایجاد می‌شوند. با استفاده از تئوری تغییر شکل برشی مرتبه اول که اثر تغییر شکل‌های برشی و اینرسی‌های دورانی را به خوبی مدل می‌کند، معادلات استخراج شده‌اند. سپس با فرضیات سینماتیکی دانل و اصل همیلتون معادلات حرکت پنل‌ها استخراج شده‌اند. معادلات با روش مربعات دیفرانسیلی تعمیم یافته در هر دو جهت x,θ و φ,θ که به ترتیب مربوط به بخش‌های استوانه‌ای و کروی هستند گسسته‌سازی شده‌اند. پس از معادل‌سازی مشتق‌های موجود در معادلات با یک بسط چند جمله‌ای با استفاده از روش بیان شده، دستگاه معادلات دیفرانسیلی به معادلات جبری تبدیل می‌شود. در گام بعد فرکانس‌های طبیعی پوسته و پنل‌های ترکیبی کروی ـ استوانه‌ای با شرایط مرزی مختلف بدست‌ آمده‌است و درستی پاسخ‌های استخراج ‌شده با نرم‌افزار آباکوس و مقالات معتبر بررسی شده‌اند. در نهایت اثر پارامتر‌هایی مانند ضخامت، طول بخش استوانه‌ای و شعاع بخش کروی بر روی فرکانس‌های طبیعی مدل مورد نظر بررسی شده‌است.

کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

Free vibration of joined spherical-Cylindrical panel and shells using the 2D GDQ method

نویسندگان [English]

  • nadia motazedian
  • Ali Asghar Jafari
faculty of mechanical engineering of k.n.toosi university of technology
چکیده [English]

In this study, free vibrations of isotropic cylindrical-spherical shell panels connected to each other were investigated. Shells and panels are created by a curve around the central symmetry axis, with a rotation of 360 degrees or less. Equations were extracted using the first-order shear deformation theory, which models the effects of shear deformation and rotational inertia well. Then, assuming Donnell kinematic and Hamilton's principle, the equations of motion for the panels were extracted. The equations were discretized in both x, θ and φ, θ directions, which correspond to cylindrical and spherical sections, respectively, using the extended differential squares method. After equating the derivatives in the equations with a polynomial expansion using the method described, the differential equations were transformed into algebraic equations. In the next step, the natural frequencies of the combined cylindrical-spherical shell panels with different boundary conditions were obtained, and the accuracy of the extracted solutions was verified using Abaqus software and reputable articles. Finally, the effects of parameters such as thickness, length of the cylindrical section, and radius of the spherical section on the natural frequencies of the desired model were investigated.

کلیدواژه‌ها [English]

  • Free vibration
  • joined cylindrical-spherical shell
  • joined cylindrical-spherical panel
  • Two-dimensional generalized differential quadratic
  • First-order shear deformation
[1] Shakouri, M., and M. A. Kouchakzadeh, "Free vibration analysis of joined conical shells: analytical and experimental study", Thin-Walled Structures, 2014, Vol.85, pp.350-358.
[2] Sarkheil, Saeed, Mahmoud Saadat Foumani, and Hossein M. Navazi, "Theoretical and experimental analysis of the free vibrations of a shell made of n cone segments joined together", Thin-Walled Structures, 2016, Vol.108, pp.416-427.
[3] Zingoni, Alphose, and Nosakhare Enoma, "Strength and stability of spherical-conical shell assemblies under external hydrostatic pressure", Thin-Walled Structures, 2020, Vol.146, p.106472.
[4] Yang, Yeong-Bin, and Jae-Hoon Kang, "Vibrations of a composite shell of hemiellisoidal-cylindrical shell having variable thickness with and without a top opening", Thin-Walled Structures, 2017, Vol.119, pp.677-686.
[5] Irie, T., G. Yamada, and Y. Muramoto, "Free vibration of joined conical-cylindrical shells", Journal of Sound and Vibration, 1984, Vol.95, no.1, pp.31-39.
[6] Lee, Young-Shin, Myung-Seog Yang, Hyun-Soo Kim, and Jae-Hoon Kim, "A study on the free vibration of the joined cylindrical–spherical shell structures", Computers & Structures, 2002, Vol.80, no.27-30, pp.2405-2414.
[7] Qu, Yegao, Yong Chen, Yifan Chen, Xinhua Long, Hongxing Hua, and Guang Meng, "A domain decomposition method for vibration analysis of conical shells with uniform and stepped thickness", Journal of Vibration and Acoustics, 2013, Vol.135, no.1, p.011014.
[8] Wu, Shi Hao, Ye Gao Qu, Xiu Chang Huang, and Hong Xing Hua, "Free vibration analysis on combined cylindrical-spherical shell", Applied Mechanics and Materials, 2012, Vol.226, pp.3-8.
[9] Yusefzad, Mahdi, and Firouz Bakhtiari Nejad, "A Study on the Free Vibration of the Prestressed Joined Cylindricalspherical Shell Structures", Applied Mechanics and Materials, 2013, Vol.390, pp.207-214.
[10] Wu, Shihao, Yegao Qu, and Hongxing Hua, "Vibrations characteristics of joined cylindrical-spherical shell with elastic-support boundary conditions", Journal of mechanical science and technology, 2013, Vol.27, pp.1265-1272.
[11] Wu, Yongfu, Chen Zhao, Haofeng Liang, Sishi Yao, Jianghong Xue, and Peng Xu, "Free vibration of composite cylindrical shells with orthogonal stiffeners", Journal of Theoretical and Applied Mechanics, 2022, Vol.60.
[12] Su, Zhu, and Guoyong Jin, "Vibration analysis of coupled conical-cylindrical-spherical shells using a Fourier spectral element method", The Journal of the Acoustical Society of America, 2016, Vol.140, no.5, pp.3925-3940.
[13] Lee, Jinhee, "Free vibration analysis of joined spherical-cylindrical shells by matched Fourier-Chebyshev expansions", International Journal of Mechanical Sciences, 2017, Vol.122, pp.53-62.
[14] Xie, Kun, Meixia Chen, and Zuhui Li, "Free and forced vibration analysis of ring-stiffened conical–cylindrical–spherical shells through a semi-analytic method", Journal of Vibration and Acoustics, 2017, Vol.139, no.3, p.031001.
[15] Ko, Soo-Min, and Jae-Hoon Kang, "Vibration of hemispherical-cylindrical-hemispherical shells and complete hollow spherical shells with variable thickness", International Journal of Structural Stability and Dynamics, 2019, Vol.19, no.03, p.1950018.
[16] Pang, Fuzhen, Haichao Li, Jie Cui, Yuan Du, and Cong Gao, "Application of flügge thin shell theory to the solution of free vibration behaviors for spherical-cylindrical-spherical shell: a unified formulation", European journal of mechanics-A/solids, 2019, Vol.74, pp.381-393.
[17] Li, Haichao, Gao Cong, Lei Li, Fuzhen Pang, and Jicai Lang, "A semi analytical solution for free vibration analysis of combined spherical and cylindrical shells with non-uniform thickness based on Ritz method", Thin-Walled Structures, 2019, Vol.145, pp.106443.
[18] He, Qi, Hong-Liang Dai, Qin-Feng Gui, and Jun-Jian Li, "Analysis of vibration characteristics of joined cylindrical-spherical shells", Engineering Structures, 2020, Vol.218, pp.110767.
[19] Pang, Fuzhen, Haichao Li, Hailong Chen, and Yanhe Shan, "Free vibration analysis of combined composite laminated cylindrical and spherical shells with arbitrary boundary conditions", Mechanics of Advanced Materials and Structures, 2021, Vol.28, no.2, pp.182-199.
[20] Bagheri, H., Y. Kiani, and M. R. Eslami, "Free vibration of FGM conical–spherical shells", Thin-Walled Structures, 2021, Vol.160, p.107387.
[21] Wang, Jiaxing, Yan Qing Wang, and Qingdong Chai, "Free vibration analysis of a spinning functionally graded spherical–cylindrical–conical shell with general boundary conditions in a thermal environment", Thin-Walled Structures, 2022, Vol.180, pp.109768.
[22] Gao, Cong, Fuzhen Pang, Jie Cui, Haichao Li, Ming Zhang, and Yuan Du, "Free and forced vibration analysis of uniform and stepped combined conical-cylindrical-spherical shells: A unified formulation", Ocean Engineering, 2022, Vol.260, p.111842.
[23] Sobhani, Emad, Amir R. Masoodi, Ömer Civalek, and Amir Reza Ahmadi-Pari, "Free-damped vibration tangential wave responses of FG-sandwich merged hemispherical-cylindrical shells under effects of artificial springs at merging and boundary conditions", Engineering Structures, 2023, Vol.284, p.115958.
[24] Reddy, Junuthula Narasimha, Theory and analysis of elastic plates and shells, CRC press, 2006.
[25] Shu, Chang, Differential quadrature and its application in engineering, Springer Science & Business Media, 2000.
[26] Tornabene, Francesco, Erasmo Viola, and Daniel J. Inman, "2-D differential quadrature solution for vibration analysis of functionally graded conical, cylindrical shell and annular plate structures", Journal of Sound and Vibration, 2009, Vol.328, no.3, pp.259-290.
[27] Tornabene, Francesco, and Erasmo Viola, "Vibration analysis of spherical structural elements using the GDQ method", Computers & Mathematics with Applications, 2007, Vol.53, no.10, pp.1538-1560.