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Two-dimensional analysis of simply supported piezoelectric beams with variable thickness. (English) Zbl 1225.74059
Summary: A two-dimensional analysis is presented for piezoelectric beam with variable thickness which is simply supported and grounded along its two ends. According to the governing equations of plane stress problems, the displacement solutions, which exactly satisfy the governing differential equations and the simply-supported boundary conditions at two ends of the beam, are derived. The unknown coefficients in the solution are then determined by using the Fourier sinusoidal series expansion to the boundary equations on the upper and lower surfaces of the beams. The present solutions show a good convergence and the numerical results are presented and compared with those available in the literature. The method could be applied to control engineering and other projects with highly accurate demand on stress and displacement analysis such as the design of micro-mechanical apparatuses.

MSC:
74M05 Control, switches and devices (“smart materials”) in solid mechanics
74F15 Electromagnetic effects in solid mechanics
35Q74 PDEs in connection with mechanics of deformable solids
74G10 Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of equilibrium problems in solid mechanics
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
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[1] Zhang, X.D.; Sun, C.T., Formulation of an adaptive sandwich beam, Smart. mater. struct., 5, 814-823, (1996)
[2] Bisegna, P.; Maceri, F., An exact three-dimensional solution for simply supported rectangular piezoelectric plates, ASME J. appl. mech., 63, 628-638, (1996) · Zbl 0886.73054
[3] Benjeddou, A.; Trindade, M.A.; Ohayon, R., A unified beam finite element model for extension and shear piezoelectric actuation mechanisms, J. intell. mater. syst. struct., 8, 1012-1025, (1997)
[4] Benjeddou, A.; Trindade, M.A.; Ohayon, R., New shear actuated smart structure beam finite element, Aiaa j., 37, 378-383, (1999)
[5] Ding, H.J.; Chen, W.Q.; Xu, R.Q., New state space formulations for transversely isotropic piezoelasticity with application, Mech. res. commun., 27, 319-326, (2000) · Zbl 0976.74017
[6] Lin, Q.R.; Liu, Z.X.; Jin, Z.L., A close-form solution to simply supported piezoelectric beams under uniform exterior pressure, Appl. math. mech., 21, 681-690, (2000) · Zbl 0995.74032
[7] Aldraihem, O.J.; Khdeir, A.A., Smart beams with extension and thickness-shear piezoelectric actuators, Smart. mater. struct., 9, 1-9, (2000)
[8] Aldraihem, O.J.; Khdeir, A.A., Exact deflection solutions of beams with shear piezoelectric actuators, Int. J. solids struct., 40, 1-12, (2003) · Zbl 1010.74559
[9] Zhong, Z.; Shang, E.T., Three-dimensional exact analysis of a simply supported functionally gradient piezoelectric plate, Int. J. solids struct., 40, 5335-5352, (2003) · Zbl 1060.74568
[10] Jiang, A.M.; Ding, H.J., Analytical solutions to magneto-electro-elastic beams, Struct. eng. mech., 18, 195-209, (2004)
[11] Shi, Z.F., Bending behavior of piezoelectric curved actuator, Smart. mater. struct., 14, 835-842, (2005)
[12] Shi, Z.F.; Xiang, H.J.; Spencer, B.F.J., Exact analysis of multi-layer piezoelectric/composite cantilevers, Smart. mater. struct., 15, 1447-1458, (2006)
[13] Huang, D.J.; Ding, H.J.; Chen, W.Q., Analytical solution for functionally graded magneto-electro-elastic plane beams, Int. J. eng. sci., 45, 467-485, (2007)
[14] Sheng, H.Y.; Wang, H.; Ye, J.Q., State space solution for thick laminated piezoelectric plates with clamped and electric open-circuited boundary conditions, Int. J. mech. sci., 49, 806-818, (2007)
[15] Leung, A.Y.T.; Zheng, J.J.; Lim, C.W.; Zhang, X.C.; Xu, X.S.; Gu, Q., A new symplectic approach for piezoelectric cantilever composite plates, Comput. struct., 86, 1865-1874, (2008)
[16] Li, Y.; Shi, Z.F., Free vibration of a functionally graded piezoelectric beam via state-space based differential quadrature, Compos. struct., 87, 257-264, (2009)
[17] Alibeigloo, A., Thermoelasticity analysis of functionally graded beam with integrated surface piezoelectric layers, Compos. struct., 92, 1535-1543, (2010)
[18] Liu, Q.T., Solution of static analysis of wedge-shaped beam by transmission matrix method, Mech. eng., 15, 64-66, (1993), (in Chinese)
[19] Zhou, D.; Cheung, Y.K., Eigenfrequencies of tapered beams with intermediate point supports, Int. J. space struct., 13, 87-95, (1998)
[20] Xu, Y.P.; Zhou, D.; Cheung, Y.K., Elasticity solution of clamped-simply supported beams with variable thickness, Appl. math. mech., 29, 279-290, (2008) · Zbl 1231.74035
[21] Xu, Y.P.; Zhou, D., Elasticity solution of simply-supported functionally graded beams with variable thickness, J. Nanjing univ. sci. tech., 33, 161-165, (2009), (in Chinese)
[22] Xu, Y.P.; Zhou, D., Elasticity solution of multi-span beams with variable thickness under static loads, Appl. math. model., 33, 2951-2966, (2009) · Zbl 1205.74100
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