Natural frequency and bending analysis of heterogeneous polar orthotropic-faced sandwich panels in the existence of in-plane pre-stress

• Autorzy: Alipour M. M. , Shaban M.

Identyfikatory

DOI

10.1007/s43452-020-00105-2

• Języki publikacji: EN

Abstrakty

EN

In this paper, the effects of plane pre-stresses on the free vibration and static analyses of circular and annular sandwich panels are examined based on an accurate formulation, as first time. It is assumed that initially pre-stresses consist of in-plane normal (tensile/compressive) and pure bending stresses. New first-order shear deformation theory together with a layerwise approach for sandwich panel is utilized. The sandwich panels are made up of either orthotropic or heterogeneous polar orthotropic materials. Furthermore, piecewise-defined linear local in-plane displacements are adopted based on zigzag theory. The governing partial differential equations are extracted by implementing principle of minimum total potential energy. A unified analytical solution procedure is developed based on power series method for the analysis of heterogeneous initially stressed annular and circular sandwich panels with arbitrary boundary conditions. The transverse shear stress is precisely calculated by considering three-dimensional theory of elasticity. To validate the proposed formulation, the obtained results are compared with those of finite element method. After numerically demonstrating the accuracy of the method, the effects of different geometrical and material parameters, boundary conditions and in-plane pre-stresses on the free vibration and static behavior of circular and annular sandwich panels are investigated.

Słowa kluczowe

EN

pre-stress; sandwich panel; unified analytical solution; heterogeneous orthotropic facing; natural frequency; bending

PL

naprężenie wstępne; płyta warstwowa; częstotliwość drgań

• Wydawca: Springer ; Wrocław University of Science and Technology
• Czasopismo: Archives of Civil and Mechanical Engineering
• Rocznik: 2020
• Tom: Vol. 20, no. 4
• Strony: 174--197
• Opis fizyczny: Bibliogr. 41 poz., tab., wykr.

Twórcy

autor

Alipour M. M.

• Department of Mechanical Engineering, University of Mazandaran, 47416‑13534 Babolsar, Iran

autor

Shaban M.

• Mechanical Engineering Department, Faculty of Engineering, Bu-Ali Sina University, Hamadan, Iran

Bibliografia

• [1] Brunelle EJ, Robertson SR. Vibrations of an initially stressed trick plate. J Sound Vib. 1976;45(3):405–16.
• [2] Chonan S. Random vibration of an initially stressed thick plate on an elastic foundation. J Sound Vib. 1980;71(1):117–27.
• [3] Yang I-H. Generic buckling and bending behavior of initially stressed antisymmetric cross-ply thick laminates. J Compos Mater. Jul. 1989;23(7):651–72.
• [4] Nayar SL, Raju KK, Rao GV. Axisymmetric free vibrations of moderately thick annular plates with initial stresses. J Sound Vib. 1994;178(4):501–11.
• [5] Chen L-W, Doong J-L. Large amplitude vibration of an initially stressed moderately thick plate. J Sound Vib. 1983;89(4):499–508.
• [6] Chen L-W, Doong J-L. Vibrations of an initially stressed transversely isotropic circular thick plate. Int J Mech Sci. 1984;26(4):253–63.
• [7] Chen C-S, Cheng W-S, Chien R-D, Doong J-L. Large amplitude vibration of an initially stressed cross ply laminated plates. Apel Acoust. 2002;63(9):939–56.
• [8] Yang IH, Shieh JA. Vibrational behavior of an initially stressed orthotropic circular Mindlin plate. J Sound Vib.1988;123(1):145–56.
• [9] Chen C-S, Fung C-P. Large-amplitude vibration of an initially stressed plate on elastic foundations. Comput Struct. 2004;82(9):689–701.
• [10] Chen C-S, Fung C-P. Non-linear vibration of initially stressed hybrid composite plates. J Sound Vib. 2004;274(3):1013–29.
• [11] Chen C, Fung C, Chien R. Nonlinear vibration of orthotropic plates with initial stresses on a two-parameter elastic foundation. J Reinf Plast Compos. Feb. 2006;25(3):283–301.
• [12] Chen C-S, Fung C-P, Yu S-Y. The investigation on the vibration and stability of functionally graded plates. J Reinf Plast Compos. Apr. 2008;27(13):1435–47.
• [13] Chen C-S. Investigation on the vibration and stability of hybrid composite plates. J Reinf Plast Compos. Nov. 2005;24(16):1747–58.
• [14] Doong J-L, Chen T-J, Chen L-W. Vibration and stability of an initially stressed laminated plate based on a higher-order deformation theory. Compos Struct. 1987;7(4):285–309.
• [15] Chen C-S, Hsu C-Y, Tzou GJ. Vibration and stability of functionally graded plates based on a higher-order deformation theory. J Reinf Plast Compos. Jun. 2008;28(10):1215–34.
• [16] Nayak AK, Shenoi RA, Moy SSJ. Dynamic response of composite sandwich plates subjected to initial stresses. Compos Part A Appl Sci Manuf. 2006;37(8):1189–205.
• [17] Malekzadeh K, Khalili MR, Jafari A, Mittal RK. Dynamic response of in-plane pre-stressed sandwich panels with a viscoelastic flexible core and different boundary conditions. J Campos Mater. 2006;40(16):1449–69.
• [18] Malekzadeh P, Farajpour A. Axisymmetric free and forced vibrations of initially stressed circular nanoplates embedded in an elastic medium. Acta Mech. 2012;223(11):2311–30.
• [19] Khalili SMR, Hosseini M, Malekzadeh Fard K, Forooghy SH. Static indentation response of an in-plane prestressed composite sandwich plate subjected to a rigid blunted indenter. Eur. J. Mech. A/Solids. 2013;38:59–69.
• [20] Pichal R, Machacek J. Buckling and post-buckling of prestressed stainless steel stayed columns. Eng Struct Technol. 2017;9(2):63–9.
• [21] Rahmani O. On the flexural vibration of pre-stressed nanobeams based on a nonlocal theory. Acta Phys Pol, A. 2014;125(2):532–3.
• [22] Li J. 2087. Effect of pre-stress on natural vibration frequency of the continuous steel beam based on Hilbert-Huang transform. J Vibroeng. 2016;18(5):2818–27.
• [23] Wu K, Wadee MA, Gardner L. Interactive buckling in prestressed stayed beam-columns. Int J Mech Sci. 2020;174:105479.
• [24] Wang HM, Wei YK. Effect of material nonhomogeneity on the mechanical behaviors of a thick-walled functionally graded sandwich cylindrical structure. Results Phys. 2012;2:118–22.
• [25] Sobhani Aragh B, Hedayati H, Borzabadi Farahani E, Hedayati M. A novel 2-D six-parameter power-law distribution for free vibration and vibrational displacements of two-dimensional functionally graded fiber-reinforced curved panels. Eur. J. Mech. A/Solids. 2011;30(6):865–83.
• [26] Nie GJ, Zhong Z, Chen S. Analytical solution for a functionally graded beam with arbitrary graded material properties. Campos Part B Eng. 2013;44(1):274–82.
• [27] Shariyat M, Asemi K. Three-dimensional non-linear elasticitybased 3D cubic B-spline finite element shear buckling analysis of rectangular orthotropic FGM plates surrounded by elastic foundations. Compos Part B Eng. 2014;56:934–47.
• [28] Thai H, Nguyen T, Vo TP, Lee J. Analysis of functionally graded sandwich plates using a new fi rst-order shear deformation theory. Eur J Mech / A Solids. 2014;45:211–25.
• [29] Fazzolari FA, Carrera E. Coupled thermoelastic effect in free vibration analysis of anisotropic multilayered plates and FGM plates by using a variable-kinematics Ritz formulation. Eur J Mech A/Solids. 2014;44:157–74.
• [30] Alibeigloo A, Alizadeh M. Static and free vibration analyses of functionally graded sandwich plates using state space differentia quadrature method. Eur J Mech A/Solids. 2015;54:252–66.
• [31] Pandey S, Pradyumna S. Free vibration of functionally graded sandwich plates in thermal environment using a layerwise theory. Eur J Mech A/Solids. 2015;51:55–66.
• [32] Sofiyev AH. Large amplitude vibration of FGM orthotropic cylindrical shells interacting with the nonlinear Winkler elastic foundation. Compos Part B Eng. 2016;98:141–50.
• [33] Sofiyev AH. Nonlinear free vibration of shear deformable orthotropic functionally graded cylindrical shells. Compos Struct. 2016;142:35–44.
• [34] Nie GJ, Batra RC. Static deformations of functionally graded polar-orthotropic cylinders with elliptical inner and circular outer surfaces. Compos Sci Technol. 2010;70(3):450–7.
• [35] Mirsalehi M, Azhari M, Amoushahi H. Buckling and free vibration of the FGM thin micro-plate based on the modified strain gradient theory and the spline finite strip method. Eur J Mech A/Solids. 2017;61:1–13.
• [36] Shariyat M, Alipour MM. A power series solution for vibration and complex modal stress analyses of variable thickness viscoelastic two-directional FGM circular plates on elastic foundations. Appl Math Model. 2013;37(5):3063–76.
• [37] Alipour MM, Shariyat M. An elasticity-equilibrium-based zigzag theory for axisymmetric bending and stress analysis of the functionally graded circular sandwich plates, using a Maclaurin-type series solution. Eur J Mech A/Solids. 2012;34:78–101.
• [38] Alipour MM. A novel economical analytical method for bending and stress analysis of functionally graded sandwich circular plates with general elastic edge conditions, subjected to various loads. Compos Part B Eng. 2016;95:48–63.
• [39] Alipour MM. Effects of elastically restrained edges on FG sandwich annular plates by using a novel solution procedure based on layerwise formulation. Arch Civ Mech Eng. 2016;16(4):678–94.
• [40] Alipour MM. Transient forced vibration response analysis of heterogeneous sandwich circular plates under viscoelastic boundary support. Arch Civ Mech Eng. 2018;18(1):12–311.
• [41] Akbarov SD, Cilli A, Yahnioglu N. Influence of prestress on the natural frequency of a fluid-filled FGM sphere. Emerg Mater Res.2019;8(4):663–7.

Uwagi

PL

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021)