تحلیل ارتعاش آزاد ورق ساندویچی ضخیم با هسته متخلخل مدرج اشباع شده با استفاده از تئوری تغییر شکل برشی شبهسه‌بعدی

نوع مقاله : مقاله پژوهشی

نویسندگان

1 دانشگاه شهید اشرفی اصفهانی

2 دانشگاه اصفهان،

چکیده

در این پژوهش به بررسی ارتعاش آزاد ورق ساندویچی مستطیلی ضخیم متشکل از رویه‌های همگن و هسته ناهمگن از جنس مواد متخلخل اشباع شده مدرج تابعی پرداخته ‌شده است. در این هسته متخلخل مدرج تابعی، ویژگی‌های مواد در راستای ضخامت بر اساس تئوری تنش بایوت و دیگر توابع داده شده تغییر می‌کنند. حل مساله بر اساس تئوری تغییر شکل برشی شبه‌سه‌بعدی بنا شده و معادلات حاکم و شرایط مرزی با استفاده از اصل همیلتون استخراج ‌شده‌اند. ورق مورد بررسی دارای شرایط تکیه‌گاهی گیردار- ساده-ساده-گیردار بوده و در مطالعات قبلی از روش ساده ناویر که ورق را در شرایط تکیه گاهی ساده بررسی می‌کند استفاده شده، در صورتی که در تحقیق حاضر از روش مربعات دیفرانسیلی  جهت حل مساله و گسسته‌سازی تحلیل عددی استفاده شده است. از جمله مزایای این روش حل، سادگی روش، کاهش حجم محاسبات نسبت به سایر روش‌های عددی و قابلیت لحاظ شرایط مرزی مختلف است. در این پژوهش ابتدا هم‌گرایی و اعتبارسنجی تحلیل نسبت به نقاط شبکه بیان شده، سپس تأثیر مشخصات هسته ورق ساندویچی مانند ضریب تخلخل، ضخامت، ضریب اسکمپتون، و ضخامت کل ورق و شرایط تکیه‌گاهی مختلف روی فرکانس‌های طبیعی ورق ساندویچی بررسی ‌شده است. به روز بودن تئوری استفاده شده در تحلیل ارتعاش آزاد ورق با هسته متخلخل مدرج تابعی از دیگر مزیت‌های اصلی این پژوهش نسبت به پژوهش‌های اخیر است.

کلیدواژه‌ها

عنوان مقاله [English]

Vibration Analysis of Thick Sandwich Plates with Saturated FG-Porous Core Using Quasi-3D Shear Deformation Theory

نویسندگان [English]

  • Ali Zamani 1
  • Mohammad Ali Rahgozar 2
1
2
چکیده [English]

Free vibration analysis of a rectangular thick sandwich plate consisting of outer homogeneous layers with saturated nonhomogeneous Functionally Graded Porous (FGP) core has been conducted. Material property in this porous core could vary along the plate thickness according to Biot’s stress theory and other related functions. Solution to this problem was based on Quasi-Three-Dimensional shear deformation theory, which results the governing differential equations and the boundary conditions of the plate model. The boundary conditions in the considered plate model were clamped-simple-simple-clamped supports, whereas in the previous studies generally Navier method is used in which simple supports is assumed for all sides of the plate. In the present study, in order to obtain our proposed numerical solution, the differential quadrature method is applied. Among advantages of this method are being simple and straightforward, having reduced computational effort compared to other numerical methods and being capable of accounting for plates with different boundary conditions. Convergence and validation of the results with respect to the grid points were first presented. The effect of different core properties such as porosity, thickness, Skempton’s coefficient, total plate thickness, and different boundary conditions on FGP sandwich plate frequencies were investigated. Application of the latest theory for free vibration analysis of FGP sandwich plates is another main advantage of the presented method compared to other recent studies.

کلیدواژه‌ها [English]

  • Saturated functionally graded porous (FGP) sandwich plate
  • free vibration
  • Biot’s theory
  • quasi-three-dimensional-shear deformation theory
  • differential quadrature method

مراجع

  1. Khorshidi, K., Fallah, A., and Siahpush, A., “Free Vibrations Analaysis of Functionally Graded Composite Rectangular Nanoplate Based on Nonlocal Exponential Shear Deformation Theory in Thermal Environment”, Scientific and Technology of Composite, Vol. 4(1), pp. 109-120, 2017. (In Persian).
  2. Haji monfared nejad, A., “Application of Differential Quadrature Method on Free Vibration of Clamped Sandwich Composite Plates Resting on Elastic Foundation”, M.Sc. Thesis, Shahid Chamran University, Faculty of Engineering, (In Persian)
  3. Sorush, M., “Investigation of Castellated Sandwich Structures”, M.Sc. Thesis, Azad University in South Branch of Tehran, Faculty of Engineering, 2009. (In Persian).
  4. Mahmudkhani, S., “Vibration Analysis of Viscoelastic Sandwich Plates under the Effects of Nonlinearities and Random Excitations”, D. Thesis, Sharif University of Technology, Aerospace Engineering Faculty, 2013. (In Persian).
  5. Botshekanan dehkordi, M., Rajabi, I., and Nurbakhsh, H., “Low Velocity Impact Analysis of Sandwich Plate with Composite Faces and Temperature Dependent Flexible Core Considering Thermal Effects”, Journal of Mechanic Engineering, Vol. 48. pp. 35-44, 2018. (In Persian).

6.     Malekzade, K., Payegane, Gh., and Kardan, M., “Dynamic Response of Sandwich Panels with Flexible Cores and Elastic Foundation Subjected to Low-Velocity Impact”, Amirkabir Journal of Science & Research (Mechanical Engineering), Vol. 45(2), pp. 27-42, 2013. (In Persian).

  1. Abotorabi, M., “Free and Forced Vibration Analysis of Thick Straight and Curved Sandwich Beams with a Core Made of Saturated Porous Materials”, M.Sc. Thesis, Sahid Ashrafi Esfahani University, Faculty of Engineering, 2019. (In Persian).
  2. Sadeghi Goghari, M., “Buckling Analysis of Porous Sector Plates with Piezoelectric Layers”, M.Sc. Thesis, Shahid Bahonar University of Kerman, Faculty of Engineering, 2016. (In Persian)
  3. Khoddami Maraghi, Z., “Vibration and Instability of Sandwich Plates with Nano-Fiber Reinforced Composite and Magnetostrictive Face Sheets”, D. Thesis, Kashan University, Mechanical Engineering Faculty, 2015. (In Persian).
  4. Malekzadeh, K., Khalili, M. R., and Mittal, R. K., “Local and Global Damped Vibrations of Plates with a Viscoelastic Soft Flexible Core: An Improved High-order Approach”, Journal of Sandwich Structures and Materials, Vol.7, pp.431–456, 2005.
  5. Zhong, H., and Gu, C., “Buckling of Symmetrical Cross-ply Composite Rectangular Plates under A Linearly Varying In-Plane Load”, Composite Structures, Vol. 80, pp. 42-48, 2007.
  6. Khorshidi, K., and Farhadi, S., “Free Vibration Analysis of a Laminated Composite Rectangular Plate in Contact with a Bounded Fluid”, Composite Structures, Vol. 104(45), pp. 176-186, 2013.
  7. Malekzadeh, , “Three-Dimensional Free Vibration Analysis of Thick Functionally Graded Plates on Elastic Foundations”, Composite Structures, Vol. 89, pp. 367-373, 2009.
  8. Emami Hoseinabadi, A., Dehghan Tarzjani, H., Rastegari, R., and Khedmati Bazkiaie, A, H., “Analysis of Free Vibrations of a Functional Graded Plate on Pasternak Elastic Substrate with Three Types of Asymmetric Boundary Conditions Using Differential Quadrature Element Method”, Journal of Applied Science Studies in Engineering, Vol. 1(1), pp. 47-55, 2015. (In Persian).
  9. Pormoayed, A., Malekzade Fard, K., and Shahravi, M., “Buckling and Vibration Analysis of a Thick Cylindrical Sandwich Panel with Flexible Core Using an Improved Higher-Order Theory”, Journal of Mechanical Engineering, 3(17), pp. 227-238, 2017. (In Persian).
  10. Nguyan, H. X., Nguyan, T. N., Abdel-wahab, M., Bordas, S., Nguyan-xuan, H., and Vo, T. P., “A Refined Quasi-3D Isogeometric Analysis for Functionally Graded Microplates Based on the Modified Couple Stress Theory”, Computer Methods in Applied Mechanics and Engineering, Vol. 313, pp. 904-940, 2017.
  11. Thai, H. T., and Kim, S. E., “A Simple Quasi-3D Sinusoidal Shear Deformation Theory for Functionally Graded Plates”, Composite Structures, 99, pp. 172-180, 2013.
  12. Shahsavari, D., Shahsavari, M., Li, L., and Karami, B., “A Novel Quasi-3D Hyperbolic Theory For Free Vibration of FG Plates with Resting on Winkler/Pasternak/Kerr Foundation”, Aerospace Science and Technology, Vol. 72, pp. 134-139, 2018.
  13. Gao, K., Gao, W., Wu, B., and Song, C., “Nonlinear Primary Resonance of Functionally Graded Porous Cylindrical Shells Using the Method of Multiple Scales”, Thin Walled Structures, Vol. 125, pp. 281-293, 2018.
  14. Zenkour, A. M., “A Quasi-3D Refined Theory for Functionally Graded Single-Layered and Sandwich Plates with Porosities”, Composite Structures, 201, pp. 38-48, 2018.
  15. Ghumare, S. M., and Sayyad, A. S., “A New Quasi-3D Model for Functionally Graded Plates”, Journal of Applied and Computational Mechanics, Vol. 5(2), pp. 367-380, 2019.
  16. Chen, D., Yang J., and Kitipornchai, S., “Free and Forced Vibrations of Shear Deformable Functionally Graded Porous Beams”, J. Mech. Sci, Vol. 108, pp. 14–22, 2016.
  17. Biot, M. A., “General Theory of Three‐Dimensional Consolidation”, Journal of Applied Physics, 12(2), pp. 155-164, 1941.
  18. Biot M. A., “Theory of Buckling of a Porous Slab and its Thermoelastic Analogy”, Appl. Mech, Vol. 31(2), pp. 194–198, 1964.
  19. Detournay, E., and Cheng, A., Fundamentals of Poroelasticity, Pergamon Press, 1993.
  20. Arshid, E., and Khorshidvand, A. R., “Free Vibration Analysis of Saturated Porous FG Circular Plates Integrated with Piezoelectric Actuators Via Differential Quadrature Method”, Journal of Thin-Walled Structures, Vol. 125, pp. 220-233, 2018.
  21. Afshari, H., “Differential Quadrature Method in Mechanical Engineering Problems”, Poyesh Andishe Publication, Isfahan, (In Persian).
  22. Rao S. S., Mechanical Vibrations, Prentice Hall, 2010.
  23. Bellman, R., and Casti, J., “Differential Quadrature and Long-Term Integration”, Journal of Mathematical Analysis and Applications, Vol. 34, pp. 235-238, 1971.
  24. Bellman, R., Kashef, B., and Casti, J., “Differential Quadrature A Technique for The Rapid Solution of Nonlinear Partial Differential Equations”, Journal of Computational Physics, Vol. 10, pp. 40-52, 1972.
  25. Afshari, H., and Irani Rahaghi, M., “Whirling Analysis of Multi-Span Multi-Stepped Rotating Shafts”, Journal of the Brazilian Society of Mechanical Sciences and Engineering, 40, 424, 2017.
  26. Bert, C. W., and Malik, M., “Differential Quadrature Method in Computational Mechanics: A Review”, Applied Mechanics Reviews, Vol. 49(1), pp. 1-28, 1996.
  27. Du, H., M. Lim., and R. Lin., “Application of Generalized Differential Quadrature ­Method to Structural Problems”, International Journal for Numerical Methods in Engineering, Vol. 37(11), pp. 1881-1896, 1994.
  28. Hebali, H., Tounsi, A., Houari, M. S. M., Bessaim, M., and Bedia, E. A .A., “New Quasi-3D Hyperbolic Shear Deformation Theory for the Static and Free Vibration Analysis of Functionally Graded Plates”, Eng. Mech, Vol. 140, pp. 374-383, 2014.

Reddy, J. N., and Phan, N. D, “Stability and Vibration of Isotropic, Orthotropic and Laminated Plates According to A Higher-Order Shear Deformation Theory”, Journal of Sound and Vibration, Vol. 98(2), pp. 157-170, 1985. 

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