
References
Abarcar, R. B., and Cunniff, P. F., 1972, “The vibration of cantilever beams of fiber reinforced material,” Journal of Composite Materials, Vol. 6, pp. 504517. AlBedoor, B. O., and Khulief, Y. A., 1996, “Finite element dynamic modeling of a translating and rotating flexible link,” Computer Methods in Applied Mechanics and Engineering, Vol. 131, pp. 173189. Bellman, R., and Casti, J., 1971, “Differential quadrature and longterm integration,” Journal of Mathematical Analysis and Application, Vol. 34, pp. 235238. Bellman, R. E., Kashef, B. G., and Casti, J., 1972, “Differential quadrature : a technique for rapid solution of nonlinear partial differential equations,” Journal Computational Physics, Vol. 10, pp. 4052. Bert, C. W., Jang, S. K., and Striz, A. G., 1988, “Two new approximate methods foranalyzing free vibration of structural components,” AIAA Journal, Vol. 26, No. 5, pp. 612618. Bert, C. W., and Malik, M., 1996a, “Free vibration analysis of tapered rectangular plates by differential quadrature method: a semianalytical approach,” Journal of Sound and Vibration, Vol. 190, No. 1, pp. 4163. Bert, C. W., and Mailk, M., 1996b, “Differential quadrature method in computational mechanics: A review,” Applied Mechanics Review, Vol. 49, No. 1, pp. 128. Bert, C. W., and Malik, M., 1996c, “On the relative effects of transverse shear deformation and rotary inertia on the free vibration of symmetric crossply laminated plates,” Journal of Sound and Vibration, Vol. 193, No. 4, pp. 927933. Bert, C. W., Wang, X., and Striz, A. G., 1993, “Differential quadrature for static and free vibration analysis of anisotropic plates,” International Journal of Solids and Structures, Vol. 30, pp. 17371744. Bert, C. W., Wang, X., and Striz, A. G., 1994, “Convergence of the DQ method in the analysis of anisotropic plates,” Journal of Sound and Vibration, Vol. 170, pp. 140144. Burnett, D. S., Finite Element Analysis, AddisonWesley Publishing Company, 1987. Chen, C. K., and Ho, S. H., 1999, “Transverse vibration of a rotating twisted Timoshenko beams under axial loading using differential transform,” International Journal of Mechanical Sciences, Vol. 41, pp. 13391356. Chen, C. L., and Chen, L. W., 2001a, “Random vibration and reliability of a damped thick rotating blade of generally orthotropy material,” Composite Structures, Vol. 53, pp. 365377. Chen, C. L., and Chen, L. W., 2001b, “Random response of a rotating composite blade with flexuretorsion coupling effect by the finite element method,” Composite Structures, Vol. 54, pp. 407415. Chen, C. N., 1998, “The warping torsion bar model of the differential quadrature element method,” Computers & Structures, Vol. 66, No. 23, pp. 249257. Chen, L. W., and Shen, G. S., 1997, “Dynamic stability of cracked rotating beams of general orthotropy,” Composite Structures, Vol. 37, pp. 165172. Chen, W. L., Striz, A. G., and Bert, C. W., 2000, “Highaccuracy plane stress and plate elements in the quadrature element method,” International Journal of Solid and Structures, Vol. 37, pp. 627647. Chen, W. R., and Keer, L. M., 1993, “Transverse vibrations of a rotating twisted Timshenko beam under axial loading,” ASME Journal of Vibration and Acoustics, Vol. 115, pp. 285294. Choi, S. T., Wu, J. D., and Chou, J. D., 2000, “Dynamic analysis of a spinning Timoshenko beam by the differential quadrature method,” AIAA Journal, Vol. 38, No. 5, pp.851856. Civan, F., 1994, “Solving multivariable mathematical models by the quadrature and cubature methods,” Numerical Methods for Partial Differential Equations, Vol. 10, pp. 545567. Clough, R. W., and Penzien, J., Dynamics of Structures, McGrawHill, 1975. Dawson, B., 1968, “Couple bendingbending vibrations of pretwisted cantilever blading treated by RayleighRitz energy method,” Journal of Mechanical Engineering Science, Vol. 10, pp. 381388. Dawson, B., and Carneige, W., 1969, “Model curves of pretwisted beams of rectangular crosssection,” Journal of Mechanical Engineering Science, Vol. 11, pp. 113. De Rosa, M. A., and Franciosi, C., 2000, “Exact and approximate dynamic analysis of circular arches using DQM,” International Journal of Solids and Structures, Vol. 37, pp. 11031117. Dimarogonas, A. D., and Haddad, S., Vibration for Engineers, A Prentice Hall, 1992. Du, H., Lim, M. K., and Lin, R. M., 1994, “Application of generalized differential quadrature method to structural problems,” International Journal for Numerical Methods in Engineering, Vol. 37, pp. 18811896. Du, H., Liew, K. M., and Lim, M. K., 1996, “Generalized differential quadrature method for buckling analysis,” Journal of Engineering Mechanics, Vol. 122, No. 2, pp. 95100. Elwenspoek, M., Weustink, M., and Legtenberg, R., 1995, “Static and dynamic properties of active joints,” The 8th International Conference on SolidState Sensors and Actuators, pp. 412415. Feng, Y., and Bert, C. W., 1992, “Application of the quadrature method to flexural vibration analysis of a geometrically nonlinear beam,” Nonlinear Dynamics, Vol. 3, pp. 1318. Gilbert, J.R., Legtenberg, R., and Senturia, S. D., 1995, “3D coupled electromechanics for MEMS: application of CoSolveEM,” Proceedings of 1995 IEEE Conference on Micro Electro Mechanical System, pp. 122127. Griffin, J. H., 1980, “Friction damping of resonant stresses in gas turbine engine airfoils,” ASME Journal of Engineering for Power, Vol. 102, pp. 329333. Griffin, J. H., and Sinha, A., 1985, “The interaction between mistuning and friction in the forced response of bladed disk assemblies,” ASME Journal of Engineering for Gas Turbines and Power, Vol. 107, pp. 107205. Gu, H. Z., and Wang, X. W., 1997, “On the free vibration analysis of circular plates with stepped thickness over a concentric region by the differential quadrature element method,” Journal of Sound and Vibration, Vol. 202, No. 3, pp. 452459. Gupa, R. S., and Rao, S. S., 1978, “Finite element eigenvalue analysis of tapered and twisted Timoshenko beams,” Journal of Sound and Vibration, Vol. 56, No. 2, pp. 187200. Han, J. B., and Liew, K. M., 1999, “Axisymmetric free vibration of thick annular plates,” International Journal of Mechanical Science, Vol. 41, pp. 10891109. Hirai, Y., Marushima, Y., Nishikawa, K., and Tanaka, Y., 2002, “Young’s modulus evaluation of Si thin film fabricated by compatiable process with Si MEMS’s,” International Conference on Microprocesses and Nanotechnology, pp. 8283. Hirai, Y., Marushima, Y., and Soda, S., 2000, “Electrostatic actuator with novel shaped cantilever,” Proceedings of 2000 Internal Symposium on Micromechatronics and Human Science, pp.223227. Hirai, Y., Shindo, M., and Tanaka, Y., 1998, “Study of large bending and low voltage drive electrostatic actuator with novel shaped cantilever and electrode,” Proceedings of 1998 Internal Symposium on Micromechatronics and Human Science, pp.161164. Huang, B. W., and Kuang, J. H., 2001, “Mode localization in a rotating mistuned turbo disk with Coriolis effect,” International Journal of Mechanical Sciences, Vol. 43, pp. 16431660. Huebner, K. H., and Thrnton, E. A., The Finite Element Method for Engineers, John Wiley & Sons, 1982. Jang, S. K., Bert, C. W., and Striz, A. G., 1989, “Application of differential quadrature to static analysis of structural components,” International Journal for Numerical Methods in Engineering, Vol. 28, pp. 561577. Kang, K., Bert, C. W., and Striz, A. G., 1996, “Static analysis of a curved shaft subjected to end torques,” International Journal of Solids and Structures, Vol. 33, No. 11, pp. 15871596. Kenneth, H. H., and Earl, A. T., The Finite Element Method for Engineers, A WileyInterscience publication, 1982. Kuang, J. H., and Huang, B. W., 1999a, “Mode localization of a cracked blade disk,” ASME Journal of Engineering for Gas Turbines and Power, Vol. 121, pp. 335341. Kuang, J. H., and Huang, B. W., 1999b, “The effect of blade crack on mode localization in rotating bladed disks,” Journal of Sound and Vibration, Vol. 227, No. 1, pp. 85103. Legtenberg, R., Berenschot, E., Elwenspoek, M., and Fluitman, J., 1995, “Electrostatic curved electrode actuators,” Proceedings of 1995 IEEE Conference on Micro Electro Mechanical Systems, pp. 3742. Legtenberg, R., Gilbert, Senturia, J. S. D., and Elwenspoek, M., 1997, “Electrostatic curved electrode actuators,” Journal of Microelectromechanical Systems, Vol. 6, No. 3, pp. 257265. Lekhnitskii, S. G., Theory of Elasticity of an Anisotropic Body, HoldenDay, San Francisco, 1963. Li, G., and Aluru, N. R., 2002, “A lagrangian approach for electrostatic analysis of deformable conductors,” Journal of Microelectromechanical Systems, Vol. 11, No. 3, pp. 245254. Liao, C. L., and Huang, B. W., 1995, “Parametric resonance of a spinning pretwisted beam with timedependent spinning rate,” Journal of Sound and Vibration, Vol. 180, No. 1, pp. 4765. Liew, K. M., Han, J. B., and Xiao, Z. M., 1996, “Differential quadrature method for thick symmetric crossply laminates with firstorder shear flexibility,” International Journal of Solids and Structures, Vol. 33, No. 18, pp. 26472658. Liew, K. M., Han, J. B., Xiao, Z. M., and Du, H., 1996, “Differential quadrature method for mindlin plates on winkler foundations,” International Journal of Mechanical Sciences, Vol. 38, No. 4, pp. 405421. Lin, C. Y., and Chen, L.W., 2002, “Dynamic stability of rotating composite beams with a viscoelastic core,” Composite Structures, Vol. 58, pp. 185194. Lin, S. M., Wang, W. R., and Lee, S. Y., 2001, “The dynamic analysis of nonuniformly pretwisted Timoshenko beams with elastic boundary conditions,” International Journal of Mechanical Sciences, Vol. 43, pp. 23852406. Malik, M., and Bert, C. W., 1996, “Implementing multiple boundary conditions in the DQ solution of higherorder PDE’s application to free vibration of plates,” International Journal for Numerical Methods in Engineering, Vol. 39, pp. 12371258. Malik, M., and Bert, C. W., 1998, “Threedimensional elasticity solutions for free vibrations of rectangular plates by the differential quadrature method,” International Journal of Solids and Structures, Vol. 35, No. 34, pp. 299318. Mirfakhraei, P., and Redekop, D., 1998, “Buckling of circular cylindrical shells by the differential quadrature method,” International Journal of Pressure and Piping, Vol. 75, pp. 347353. Moradi, S., and Taheri, F., 1999, “Delamination buckling analysis of general laminated composite beams by differential quadrature method,” Composite: Part B, Vol. 30, pp. 503511. Osterberg, P., Yie, H., Cai, X., White, J., and Senturia, S., 1994, “Selfconistent simulation and modeling of electrostatically deformed diaphragms,” Proceedings of 1994 IEEE Conference on Micro Electro Mechanical Systems, pp. 2832. Petersen, K. E., 1978, “Dynamic micromechanics on silicon: techniques and devices,” IEEE Transactions on Electron Devices, Vol. ED25, pp. 12411250. Quan, J. R., and Chang, C. T., 1989a, “New insights in solving distributed system equations by the quadrature methodI. analysis,” Computers in Chemical Engineering, Vol. 13, pp.779788. Quan, J. R., and Chang, C. T., 1989b, “New insights in solving distributed system equations by the quadrature methodII. numerical experiments,” Computers in Chemical Engineering, Vol. 13, pp. 10171024. Rand, O., and Barkai, S. M., 1997, “A refined nonlinear analysis of pretwisted composite blades,” Composite Structures, Vol. 39, No. 12, pp. 3954. Rao, J. S., 1972, “Flexural vibration of pretwisted tapered cantilever blades,” ASME Journal of Engineering for Industry, Vol. 94, No. 1, pp. 343346. Rao, J. S., 1977, “Vibration of rotating, pretwisted and tapered blades,” Mechanism and Machine Theory, Vol. 12, pp. 331337. Rao, S. S., Mechanical Vibrations, AddisonWesley, 1990. Schultz, A. B., and Tsai, S. W., 1968, “Dynamic moduli and damping ratios in fiberreinforced composites,” Journal of Composite Materials, Vol. 2, No. 3, pp. 368379. Sherbourne, A. N., and Pandey, M. D., 1991, “Differential quadrature method in the buckling analysis of beams and composite plates,” Computers and Structures, Vol. 40, pp. 903913. Shiau, T. N., Yu, Y. D., and Kuo, C. P., 1996, “Vibration and optimum design of rotating laminated blades,” Composites, Vol. 27B, pp. 395405. Shu, C., 1996, “A efficient approach for free vibration analysis of conical shells,” International Journal of Mechanical Sciences, Vol. 38, No. 89, pp. 935949. Shu, C., and Du, H., 1997, “Free vibration analysis of laminated composite cylindrical shells by DQM,” Composites Part B, Vol. 28B, pp. 267274. Shu, C., and Richards, B. E., 1992, “Application of generalized differential quadrature to solve twodimensional incompressible NaviorStokes equations,” International Journal of Numerical Methods in Fluids, Vol. 15, pp. 791798. Shu, C., and Wang, C. M., 1999, “Treatment of mixed and nonuniform boundary conditions in GDQ vibration analysis of rectangular plates,” Engineering Structures, Vol. 21, pp. 125134. Storiti, D., and Aboelnaga, Y., 1987, “Bending vibrations of a class of rotating beams with hypergeometric solutions,” Journal of Applied Mechanics, Vol. 54, pp. 311314. Striz, A. G., Chen, W., and Bert, C. W., 1994, “Static analysis of structures by the quadrature element method (QEM),” International Journal of Solids and Structures, Vol. 31, pp. 28072818. Sun, J., and Zhu, Z., 2000, “Upwind local differential quadrature method for solving incompressible viscous flow,” Computer Methods in Applied Mechanics and Engineering, Vol. 188, pp. 495504. Surace, G., Anghel, V., and Mares, C., 1997, “Coupled bendingbendingtorsion vibration analysis of rotating pretwisted blades: an integral formulation and numerical examples,” Journal of Sound and Vibration, Vol. 206, No. 4, pp. 473486. Swaminathan, M., and Rao, J. S., 1977, “Vibrations of rotating, pretwisted and tapered blades,” Mechanism and Machine Theory, Vol. 12, pp. 331337. Tanaka, M., and Chen, W., 2001, “Dual reciprocity BEM applied to transient elastodynamic problems with differential quadrature method in time,” Computer Methods in Applied Mechanics and Engineering, Vo. 190, pp. 23312347. Teh, K. K., and Huang, C. C., 1980, “The effects of fibre orientation on free vibrations of composite beams,” Journal of Sound and Vibration, Vol. 69, No. 2, pp. 327337. Thomas, C. R., 1975, “Mass optimization of nonconservative cantilever beams with internal and external damping,” Journal of Sound and Vibration, Vol. 43, No. 3, pp. 483498. Tomasiello, S., 1998, “Differential quadrature method: application to initialboundaryvalue problems,” Journal of Sound and Vibration, Vol. 218, No. 4, pp. 573585. Wagner, J. T., 1967, “Coupling of turbomachine blade vibrations through the rotor,” ASME Journal of Engineering for Power, Vol. 89, pp.502512. Wagner, L. F., and Griffin, J. H., 1996a, “Forced harmonic response of grouped blade systems: part I—discrete theory,” ASME Journal of Engineering for Gas Turbines and Power, Vol. 118, pp. 130136. Wagner, L. F., and Griffin, J. H., 1996b, “Forced harmonic response of grouped blade systems: part II—application,” ASME Journal of Engineering for Gas Turbines and Power, Vol. 118, pp. 137145. Wang, P. K. C., 1998, “Feedback control of vibrations in a micromachined cantilever beam with electrostatic actuators,” Journal of Sound and Vibration, Vol. 213, No. 3, pp. 537550. Wang, X., and Bert, C. W., 1993, “A new approach in applying differential quadrature to static and free vibrational analyses of beams and plates,” Journal of Sound and Vibration, Vol. 162, No. 3, pp. 566572 Wang, X., and Gu, H., 1997, “Static analysis of frame structures by the differential quadrature element method,” International Journal for Numerical Methods in Engineering, Vol. 40, pp. 759772. Wang, X., Yang, J., and Xiao, J., 1995, “On free vibration analysis of circular annular plates with nonuniform thickness by the differential quadrature method,” Journal of Sound and Vibration, Vol. 184, No. 3 pp. 547551
Young, T. H., 1991, “Dynamic response of a pretwisted tapered beam with nonconstant rotating speed,” Journal of Sound and Vibration, Vol. 150, No. 3, pp. 435446.
