Free vibration Study of simply supported cylindrical laminateds panels with piezoelectric layer
الموضوعات : فصلنامه شبیه سازی و تحلیل تکنولوژی های نوین در مهندسی مکانیک
مصطفی معطری
1
(کارشناس ارشد، دانشکده مهندسی مکانیک، دانشگاه آزاد اسلامی واحد همدان، همدان، ایران.)
فرزان براتی
2
(استادیار، دانشکده مهندسی مکانیک، دانشگاه آزاد اسلامی واحد همدان، همدان، ایران.)
الکلمات المفتاحية: Free vibration, Piezoelectric, Fourier series, Laminate, Plane strain,
ملخص المقالة :
In the present study, vibration of cylindrical laminates with different layers and angles were studied. In order to actuate and polarize in radial direction, a piezoelectric layer was located at outer surface of composite shell. Laminates were assumed long enough so that plane strain state analysis in 2D can be used properly. In order to satisfy the boundary conditions, variables in terms of Fourier series were obtained. The governing equations reduced to ordinary differential equations at thickness direction and by power series method, the exact solution equations were obtained, unknown coefficient were calculated with rapid convergence. By using the matrix transfer method, vibration response of composite shell were obtained. Finally, results for the first seven modes of natural frequency of multi layer cylindrical shell were obtained. In addition, for both state of one single piezoelectric layer and five layer shell at the end, variable response such as displacement, principal stress and strain were achieved.
[1] Qing-Hua, Q., Advanced Mechanics of Piezoelectricity, Springer Verlag, 2013, pp.1-4.
[2] Fernandes A., Pouget J., Two-dimensional modelling of laminated piezoelectric composites: analysis and numerical results, Journal of Thin Walled Structures, 39, 2000, pp.3-22.
[3] Chen W.Q., Lee K.Y., State-space approach for statics and dynamics of angle-ply laminated cylindrical panels in cylindrical bending, International Journal of Mechanical Sciences, 47, 2005, pp.374–387.
[4] Srinivas S., Rao A.K., Bending, vibration and buckling of simply supported thick orthotropic rectangular plates and laminates, International Journal of Solids Structures, 6, 1970, pp.1463–1481.
[5] Adelman N.T., Stavsky Y., Radial vibrations of axially polarized piezoelectric ceramic cylinders, Journal of Acoustical Society of America, 57, 1975, pp.356-360.
[6] Cho K.N., Bert C.W., Striz A.G., Free vibrations of laminated rectangular plates analyzed by high order individual-layer theory, Journal of Sounds & Vibration, 145(3), 1991, pp.429-442.
[7] Chen C.Q., Shen Y.P., Piezothermoelasticity analysis for circular cylindrical shell under the state of axisymmetric deformation, International Journal of Engineering Science, 34, 1996, pp.1585–1600.
[8] Chen C.Q., Shen Y.P., Three-dimensional analysis for free vibration of finite-length orthotropic piezoelectric circular cylindrical shells, Transactions of the ASME Journal of Vibration and Acoustics, 120, 1998, pp.194–198.
[9] Batra R.C., Aimmanee S., Missing frequencies in previous exact solutions of free vibrations of simply supported rectangular plates, Journal of Vibration Control, 265, 2003, pp.887-896.
[10] Aydogdu M., Timarchi T., Vibration analysis of cross-ply laminated square plates with general boundary conditions, Composite Science and Technology, 63 (7), 2003, pp.1061-1070.
[11] Liew K. M., Huang Y. Q., Reddy J. N., Vibration analysis of symmetrically laminated plates based on FSDT using the moving least squares differential quadrature method, Computer Methods in Applied Mechanics and Engineering, 192 (19), 2003, pp.2203-2222.
[12] Kang JH., and Shim HJ., Exact solutions for the free vibrations of rectangular plates having inplane moments acting on two opposite simply supported edges, Journal of Sounds & Vibration, 273, 2004, pp933–948.
[13] Chen W.Q, Lee K.Y., Static and dynamic behaviour of simply-supported cross-ply laminated piezoelectric cylindrical panels with imperfect bonding, Journal of Composite Structures, 74, 2006, pp.265–276.
[14] Chen W.Q, Lee K.Y., Benchmark solution of angle-ply piezoelectric-laminated cylindrical panels in cylindrical bending with weak interfaces, Archive of Applied Mechanics, 74, 2005, pp.466–476.
[15] Karami G., Malekzadeh P., Mohebpour S. R., DQM free vibration analysis of moderately thick symmetric laminated plates with elastically restrained edges, Journal of Composite Structures, 74 (1), 2006, pp.115-125.
[16] Shimpi R.P., Patel H.G., Free vibrations of plate using two variable refined plate theory, Journal of Sound & Vibration, 296, 2006, pp.979-999.
[17] Pandit M. K., Haldar S., Mukhopadhyay M., Free vibration analysis of laminated composite rectangular plate using finite element method, Journal of Reinforced Plastics and Composites, 26 (1), 2007, pp.69-80.
[18] Civalek O., Free vibration analysis of symmetrically laminated composite plates with first-order shear deformation theory (FSDT) by discrete singular convolution method, Journal of Finite Elements in Analysis and Design, 12-13, 2008, 44, pp.725-731.
[19] Brethee K. F., Free vibration analysis of a symmetric and anti-symmetric laminated composite plate with a cutout at the center, Al-Qadisiya Journal for Engineering Sciences, 42, 2009, 13, pp.43-56.
[20] Ngo-Cong D., Mai-Duy N., Karunasena W., Tran-Cong T., Free vibration analysis of laminated composite plates based on FSDT using one-dimensional IRBFN method, Journal of Computers and Structures, 89 (1-2),2011, pp.1-13.
[21] Messina A., Influence of the edge-boundary conditions on three-dimensional free vibrations of isotropic and cross-ply multilayered rectangular plates, Journal of Composite Structures, 93(8),2011, pp.2135–2151.
[22] Xiang S., Bi Z.Y., Jiang S.X., Jin Y.X., Yang M.S., Thin plate spline radial basis function for the free vibration analysis of laminated composite shells. Journal of Composite Structures, 93(2), 2011, pp.611-615.
[23] Boscolo M., Banerjee J.R., Layer-wise dynamic stiffness solution for free vibration analysis of laminated composite plates, Journal of Sound and Vibration, 333 (1), 2014, 200-227.
[24] Sadd Martin H., Elasticity: Theory, Applications and Numerics, Burlington, USA, Elsevier Inc., 2015, pp.61-63.
[25] Qing-Hua Q., Advanced Mechanics of Piezoelectricity, Springer-Verlag, 2013, pp.4-25.
[26] Kapuria S., Achary G.G.S., Exact 3D piezoelasticity solution of hybrid cross-ply plates with damping under harmonic electromechanical loads, Journal of Sound and Vibration, 282, 2005, pp.617–634.
[27] Kumari P., Nath J.K., Dumir P.C., Kapuria S., 2D exact solutions for flat hybrid piezoelectric and magnetoelastic angle-ply panels under harmonic load, Journal of Smart Materials and Structures, 16, 2007, pp.1651–1661.
