A substructure synthesis method is proposed for modeling the dynamic behavior of viscoelastic- elastic multibody system. The governing differential equations of motion are derived based on the Lagrange equations. Viscoelastic damping is incorporated into multibody systems to evaluate its effect on structural response. The viscoelastic damping proposed is based on layers of viscoelastic polymer directly attached to the systems. With the use of substructure synthesis method, the number of elastic coordinates needed in the approximate procedure is reduced. Numerical examples are presented to demonstrate the capabilities and efficiency of the proposed method. A comparison of the dynamic response has been presented for a two-link system with and without viscoelastic damping.
Bagley, R.L. and Torvik, P.J., 1983, "Fractional calculus—A different approach to the analysis of viscoclastically damped structures," AIAA Journal21, 741-748.
2.
Baker, E.M. and Shabana, A.A., 1987, "Timoshenko beams and flexible multibodies system dynamics ," Journal of Sound and Vibration116, 89-107.
3.
Belivean, J.G. and Soucy, Y., 1985, "Damping synthesis using complex substructure modes and a Hermitian system representation," AIAA Journal23, 1952-1956.
4.
Christensen, R.M., 1971, Theory of Viscoelasticity: An Introduction, Academic Press, New York.
5.
Craig, R.R., Jr. and Chung, Y.T., 1982, "Generalized substructure Coupling procedure for damped systems," AIAA Journal20, 442-444.
6.
Craig, R.R., Jr. and Ni, Z.H., 1989, "Component mode synthesis for model order reduction of nonclassically damped systems," Journal of Guidance, Control and Dynamics12, 577-584.
7.
DiTarato, R.A., 1965, "Theory of vibrator bending for elastic viscoelastic largered finite length Beams," ASME Journal of Applied Mechanics32, 881-886.
8.
Gau, W.H. and Shabana, A.A., 1990, "Effects of shear deformation and rotary inertia on the nonlinear dynamics of rotating curved beams," ASME Journal of Vibration and Acoustics112, 183-193.
9.
Gladwell, G.M.L., 1964, "Branch mode analysis of vibrating systems," Journal of Sound and Vibration1, 41-59. Hurty, W.C., 1960, "Vibration of structural systems by component mode synthesis," ASCE Journal of the Engineering Mechanics Division86, 51-69.
10.
Hurty, W.C., 1965, "Dynamics analysis of structural systems using component modes," AIAA Journal3, 678-685.
11.
Johnson, C.D. and Kienholz, D.A., 1982, "Finite element prediction of damping in structures with constrained viscoelastic layers," AIAA Journal20, 1284-1290.
12.
Knauss, W.G. and Emri, I.J., 1981, "Non-linear viscoelasticity based on free volume consideration ," Computers & Structures13, 123-128.
13.
Kuomura, K., 1987, "Component mode synthesis for damping structures ," AIAA Journal25, 740-745.
14.
Lu, Y.P., Douglas, B.E., and Thomas, E.V., 1973, "Mechanical impedance of damped three-layer sandwich rings ," AIAA Journal11, 300-304.
15.
Rao, D.K., 1978, "Frequency and loss factors of sandwich beam under various boundary conditions," Journal of Mechanical Engineering Science20, 271-282.
16.
Reddy, J.N., 1997, Mechanics of Laminated Composite Plates: Theory and Analysis , CRC Press, Boca Raton, FL. in Numerical Methods in Engineering, Vol. 3, pp. 495-510.
17.
Reddy, J.N., Wang, C.M., and Lam, K.Y., 1997, "Unified finite elements based on the classical and shear deformation theories of beams and axisymmetric circular plates," Communications in Numerical Methods in Engineering, 13, 495-510.
18.
Segalman, D.J., 1987, "Calculation of damping matrices for linearly viscoelastic structures," ASME Journal of Applied Mechanics54, 585-588.
19.
Shabana, A.A., 1985, "Viscoelastic analysis of multi-body system using the finite element method," Journal of Sound and Vibration100, 271-284.
20.
Singh, M.P. and Suarez, L.E., 1988, "A method for dynamic coupling with nonclassical damping effects," Journal of Sound and Vibration120, 539-555.
21.
Thompson, B.S. and Sung, C.K., 1984, "A variational formulation for the dynamic viscoelastic finite element analysis of robotics manipulators constructed from composite materials," Journal of Mechanisms, Transmissions, and Automation in Design106, 183-190.
22.
Thompson, B.S., Zuccaro, R.G., and Gandhi, M.V., 1983a, "An experimental and analytical study of a four bar mechanism with links fabricated from a fiber-reinforced composite material ," Mechanism and Machine Theory18, 165-171.
23.
Thompson, B.S., Zuccaro, R.G., and Gandhi, M.V., 1983b, "An experimental and analytical study of the dynamic response of a linkage fabricated from a unidirectional fiber-reinforced composite laminate," ASME Journal of Mechanisms, Transmissions, and Automation in Design105, 528-536.
24.
Tzou, H.S. and Gadre, M., 1988, "Finite element modeling of nonlinear active and passive dampers applied to vibration controls," Computers & Structures28, 453-460.
25.
Tzou, H.S. and Schiff, A.J., 1987, "Development and evaluation of a pseudo-force approximation applied to nonlinear dynamic contact and viscoelastic damping," Computers & Structures26, 481-493.
26.
Tzou, H.S. and Wan, G.C., 1990, "Distributed structural dynamic control of flexible manipulators-I. Structural dynamic and distributed viscoelastic actuator," Computers & Structures36, 669-677.
