Solution of the Characteristic Frequency Equations of Levy-type Sandwich Panels with Auxetic Honeycomb Core based on the Improved Reddy’s Third-order Theory

Authors

1 PhD Candidate, Department of Mechanical Engineering, Faculty of Engineering, Islamic Azad University, Arak Branch, Arak, Iran.

2 Assistant Professor, Department of Mechanical Engineering, Faculty of Engineering, Islamic Azad University, Arak Branch, Arak, Iran.

3 Associate Professor/Arak University

4 Professor, Department of Mechanical Engineering, Faculty of Engineering, Islamic Azad University, Arak Branch, Arak, Iran.

5 Assistant Professor, Department of Mechanical Engineering, Faculty of Engineering, Arak Branch, Islamic Azad University, Arak, Iran

Abstract

In this paper, the equations of motion are derived based on the improved third-order shear deformation theory with shear correction factors to investigate the free transverse vibration of rectangular sandwich panels having Levy boundary conditions. Reddy’s third-order theory devote a parabolic distribution for transverse shear stress along the thickness of plate and is suitable for thin to relatively thick single-layer plates. However, for the case of sandwich panels, in Reddy’s theory, the continuity condition of inter-laminar surfaces is not satisfied. This defect is improved by adding shear correction factors only in the energy viewpoint. Sandwich panel consist of isotropic facesheets and an auxetic honeycomb core making from the same facesheet’s material. The effective properties of honeycomb core were derived from the newest revised Gibson model based on Timoshenko beam theory. For validation, some comparison study is carried out to compare the current solution with the results reported in literature and also finite element ANSYS software.The results of validation indicates the important effect of suitable shear correction factors to decrease error percentage. Finally, the effect of boundary conditions, panel thickness to length ratio, core thickness to panel thickness ratio and geometrical parameters of the reentrant hexagon cell on the non-dimensional natural frequencies were investigated and the results were presented in some graphs.

Keywords

References

[1] Peters ST (1998) Composite material handbook. 2nd edn. C&H, London.
[2] Bitzer T (1997) Honeycomb technology. 1st edn. C&H, London.
[3] Gibson LJ, Ashby MF, Schajer GS, Robertson       CI (1982) The mechanics of two-dimensional cellular materials. Proc R Soc London, Ser. A 382: 25-42.
[4] Evans KE, Nkansah MA, Hutchinson IJ, Rogers SC (1991) Molecular network design. Nature 353(6340): 124.
[5] Lakers R (1991) Deformation mechanisms in negative Poisson’s ratio materials: Structural aspects. J Mater Sci 26(9): 2287-2292.
[6] Yang ZC, Deng QT (2011) Mechanical property and application of materials and structures with negative Poisson’s ratio. Adv Mech 41(3): 335-350.
[7] Sun Y, Pugno Nm (2013) In plane stiffness of multifunctional hierarchical honeycombs with negative Poisson’s ratio sub-structures. Compos Struct 106: 681-689.
[8] Gibson LJ, Ashby MF (1999) Cellular solids: Structure and properties. CUP, Cambridge.
[9] Malek S, Gibson LJ (2015) Effective elastic properties of periodic hexagonal honeycombs. Mech Mater 91: 226-240.
[10] غزنوی اسگوئی آ، شرعیات م (1398) تحلیل تنش و جابجایی ورق‌های ساندویچی ضخیم دارای هسته آگزتیک تغییر‌شکل‌پذیر به‌کمک تئوری عمومی-محلی مرتبه سه بهبود یافته. مجله مکانیک سازه‌ها و شاره‌ها 122-109 :(2)9.
[11] Kirchhoff G (1850) Uber das Gleichgewicht und die Bewegung einer elastischen Scheibe. J Reine Angew Math 40: 51-88.
[12] Kirchhoff G (1850) Uber die Schwingungen einer kreisförmigen elastischen Scheibe. Ann Phys 157(10): 258-264.
]13 [قدیریان ح، قضاوی م، خورشیدی ک (1395) تحلیل ارتعاشات و پایداری ورق‌های مرکب چند‌لایه تحت      اثر رطوبت و دما. مجله مکانیک سازه‌ها و شاره‌ها        166-155 :(2)6.
[14] Reissner E (1945) The effect of transverse shear deformation on the bending of elastic plates. J Appl Mech A69-A77.
[15] Mindlin RD (1951) Influence of rotary inertia and shear on flexural motions of isotropic elastic plates. J Appl Mech 18: 31-38.
[16] خورشیدی ک، عنصری‌نژاد س (1395) تحلیل دقیق ارتعاش آزاد ورق‌های قطاعی کوپل شده با لایه پیزو‌الکتریک با بکارگیری تئوری تغییر‌شکل برشی مرتبه اول. مجله مکانیک سازه‌ها و شاره‌ها 138-125 :(4)6.
[17] خورشیدی کوروش، بلالی محمد، قدیمی علی‌اصغر (1394) کنترل ارتعاشات اجباری ورق مستطیلی لایه‌ای مرکب مستقر بر بستر خطی. مهندسی مکانیک مدرس 104-95 :(9)15.
[18] Reddy JN (2003) Mechanics of laminated composite plates and shells: theory and analysis. 2nd edn. CRC press, Boca Raton, Florida.
[19] Khorshidi K, Karimi M (2019) Analytical modeling for vibrating piezoelectric nanoplates in interaction with inviscid fluid using various modified plate theories. Ocean Eng 181: 267-280.
[20] خورشیدی ک، قاسمی م، فلاح ا (1397) تحلیل کمانش میکرو‌صفحه مستطیلی تابعی مدرج بر اساس تئوری تغییر‌شکل برشی نمایی با بکارگیری تئوری تنش کوپل اصلاح شده. مجله مکانیک سازه‌ها و شاره‌ها       196-179:(4)8.
[21] Khorshidi K, Fallah A (2017) Analytical approach for thermo-electro-mechanical vibration of piezoelectric nanoplates resting on elastic foundations based on nonlocal theory. Mech. Adv. Compos. Struct. 6(2): 117-129.
[22] Khorshidi K, Karimi M (2019) Free vibration analysis of size-dependent, functionally graded, rectangular nano/micro-plates based on modified nonlinear couple stress shear deformation plate theories. Mech. Adv. Compos. Struct. 4(2): 127-137.
[23] خورشیدی ک، بخششی ع، قدیریان ح (1395)   بررسی تأثیرات محیط حرارتی بر ارتعاشات آزاد         ورق مستطیلی از جنس مواد تابعی مدرج دو‌بعدی   مستقر بر بستر پسترناک. مجله مکانیک سازه‌ها و شاره‌ها              147-137 :(3)6.
[24] Huang N (1994) Influence of shear correction factors in the higher order shear deformation laminated shell theory. Int J Solids Struct 31(9): 1263-1277.
[25] Di K, Mao XB (2016) Free flexural vibration of honeycomb sandwich plate with negative Poisson’s ratio simply supported on opposite edges. Acta Mat Compos Sin 33(4): 910-920.
[26] Hosseini-Hashemi Sh, Arsanjani M (2005) Exact characteristic equations for some of classical boundary conditions of vibrating moderately thick rectangular plates. Int J Solids Struct 42(3-4): 819-853.
[27] Hosseini-Hashemi Sh, Fadaee M, Taher HRD (2011) Exact solutions for free flexural vibration of Levy-type rectangular thick plates via third-order shear deformation plate theory. Appl Math Model 35(2): 708-727.
[28] Raville ME, Ueng CES (1967) Determination of natural frequencies of vibration of a sandwich plate. Appl Exp Mech 7(11): 490-493.
[29] Rao MK, Desai YM (2004) Analytical solutions for vibrations of laminated and sandwich plates using mixed theory. Compos Struct 63(3-4): 361-373.
Journal of Solid and Fluid Mechanics
Volume 11, Issue 1
March and April 2021
Pages 291-310

Files

Share

How to cite

Statistics