Exact free vibration analysis of sector plates coupled with piezoelectric layers using first-order shear deformation plate theory

Authors

Abstract

In this study, free vibration analysis of isotropic sector plates coupled with piezoelectric layers based on first-order shear deformation theory has been analyzed. Governing differential equations of the dynamic behavior of free vibration of isotropic sector plates coupled with piezoelectric layers are derived using Hamilton's principle and the electrostatic Maxwell equations. The Coupled governing differential equations of the vibrating composite plate are solved by applying the method of separation of variables and auxiliary potential functions. The presented analytical exact solution in this paper is validated with available data in the literature. Using numerical results the effect of opening angle of sector plate , the host thickness to radius ratios , inner to outer radius ratios , the ratio of thickness of the piezoelectric layer respect to thickness of the host plate and different boundary conditions on the natural frequencies of the vibrating sector plates coupled with piezoelectric layers are obtained. Also impact, manner and conditions of each parameter on the natural frequencies areconsidered and discussed.

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[1] Ding H, Xu R, Chi Y, Chen W (1999) Free axisymmetric vibration of transversely isotropic piezoelectric circular plates. Int J Solids Struct 36: 4629-4652.
[2] Wang Q, Quek ST, Sun CT, Liu X (2001) Analysis of piezoelectric coupled circular plate. Smart Mater Struct 10: 229-239.
[3] Liu X, Wang Q, Quek ST (2002) Analytical solution for free vibration of piezoelectric coupled moderately thick circular plates. Int J Solids Struct 39: 2129-215.
[4] Hosseini-Hashemi Sh, Es’haghi M, Rokni-Damavandi H, (2010) An exact analytical solution for freely vibrating piezoelectric coupled circular/anuular thick plates using Reddy plate theory. Compos Struct 92(6): 1333-1351.
[5] Hosseini-Hashemi Sh, Khorshidi K, Es’haghi M, Fadaee M, Karimi M (2012) On the effects of coupling between in-plane and out-of-plane vibrating modes of smart functionally graded circular/annular plates. Appl Math Model 36(3): 1132-1147.
[6] Khorshidi K, Rezaei E, Ghadimi AA, Pagoli M, (2015) Active vibration control of circular plates coupled with piezoelectric layers excited by plane sound wave. Appl Math Model 39(3): 1217-1228.
[7] Duan WH, Quek ST, Wang Q (2005) Free vibration analysis of piezoelectric coupled thin and thick annular plate. J Sound Vib 281: 119-139.
[8] Liu CF, Chen TJ, Chen YJ (2008) A modified axisymmetric finite element for the 3-D vibration analysis of piezoelectric laminated circular and annular plates. J Sound Vib 309: 794-804.
[9] Deresiewicz H, Mindlin RD (1955) Axially symetric flexural vibration of circular disk. J Appl Mech-T ASME 22: 86-88.
[10] Sony SR, Amba-Rao CL (1975) On radially symmetic vibration orthotropic non-uniform disc including shear deformation. J Sound Vib 42: 100-124.
[11] Cheung YK, Kwok WL (1975) Dynamic analysis of circular and sector thick layered plates. J Sound Vib 42: 147-158.
[12] Venkatesan R, Kunukkasseril VX (1978) Free vibration of layered circular plate. J Sound Vib 60: 511-534.
[13] Guruswamy P, Yung TY (1979) A sector element for dynamic analysis of thick plate. J Sound Vib 62: 505-516.
[14] Rao SS, Prasad AS (1975) vibration of annular plate including the effect of rotatory inertia Transverse shear deformation. J Sound Vib 42: 305-324.
[15] Irie T, Yamada G, Takagi T (1982) Natural frequencies of thick annular  plate. J Appl Mech-T ASME 49: 633-638.
[16] Huang CS, McGee OG, Leissa AW (1994) Exact analytical solutions for free vibrations of thick sectorial plates with simply supported radial edges. Solids Struct 31(11): 1609-1631.
[17] Liu FL, Liew KM (1999) Free vibration analysis of thin sector plates by the new version of differential quadrature method. Comput Meth Appl Mech Eng 177(1): 77-92.
[18] Qiang LY, Jian L (2007) Free vibration analysis of circular and annular sectorial thin plates using curve strip Fourier P-element. J Sound Vib 305(3): 457-466.
[19] Huang CS, Ho KH (2004) Ananalytical solution for vibrations of a polarly orthotropic Mindlin sectorial plate with simply supported radial edges. J Sound Vib 273(1): 277-294.
[20] McGee OG, Huang CS, Leisaa AW (1995) Comprehensivexact solutions for free vibrations of thick annular sectorial plates with simply supported radial edges. Mech Sci 37(5): 537-566.
[21] Nie GJ, Zhong Z (2008) Vibration analysis of functionally graded annular sectorial plates with simply supported radial edges. Compos Struct 84(2): 167-176.
[22] Aghdam MM, Mohammadi M, Erfanian V (2007) Bending analysis of thinannular sector plates using extended Kantorovich method. Thin-Walled Struct 45(12): 983-990.
[23] Reissner E (1985) Reflections on the theory of elastic plates. Appl Mech Rev 38: 1453-1464.
[24] Nosier A, Yavari A, Sarkani S (2001) A study of the edge-zone equation of Mindlin–Reissner plate theory in bending of laminated rectangular plates. Acta Mech 146: 227-238.
[25] Khorshidi K, Fallah A (2016) Buckling analysis of functionally graded rectangular nano-plate based on nonlocal exponential shear deformation theory. Int J Mech Sci 113: 94-104.
[26] Khorshidi K, Asgari T, Fallah A (2015) Free vibrations analysis of functionally graded rectangular nano-plates based on nonlocal exponential shear deformation theory. Mech Adv Compos Struct ‎2(2): 79-93.
[27] Khorshidi K, Khodadadi M (2016) Precision closed-form solution for out-of-plane vibration of rectangular plates via trigonometric shear deformation theory. Mech Adv Compos Struct 3(1): 31-43.
[28] Leissa AW, Qatu MS (2011) Vibrations of continuous systems. McGraw-Hill, New York.
[29] Jalili N (2009) Piezoelectric-based vibration control: From macro to micro/nano scale systems. Springer Science & Business Media.