Nonlinear Impact Responses for a Damped Frame Supported by Nonlinear Springs with Hysteresis Using Fast FEA
This paper deals with nonlinear vibration analysis
using finite element method for frame structures consisting of elastic
and viscoelastic damping layers supported by multiple nonlinear
concentrated springs with hysteresis damping. The frame is supported
by four nonlinear concentrated springs near the four corners. The
restoring forces of the springs have cubic non-linearity and linear
component of the nonlinear springs has complex quantity to represent
linear hysteresis damping. The damping layer of the frame structures
has complex modulus of elasticity. Further, the discretized equations in
physical coordinate are transformed into the nonlinear ordinary
coupled differential equations using normal coordinate corresponding
to linear natural modes. Comparing shares of strain energy of the
elastic frame, the damping layer and the springs, we evaluate the
influences of the damping couplings on the linear and nonlinear impact
responses. We also investigate influences of damping changed by
stiffness of the elastic frame on the nonlinear coupling in the damped
impact responses.
[1] E. Pesheck, N. Boivin, C. Pierre and S. W. Shaw, “Non-linear modal
analysis of structural systems using multi-mode invariant manifolds”,
Nonlinear Dynamics, Vol.25, pp.183-205, 2001.
[2] T. Yamaguchi, Y. Fujii, K. Nagai and S. Maruyama, “FEM for vibrated
structures with non-linear concentrated spring having hysteresis”,
Mechanical Systems and Signal Processing, Vol.20, pp.1905-1922, 2006.
[3] C. D. Johnson and D. A. Kienholz, “Finite element prediction of damping
structures with constrained viscoelastic layers”, AIAA Journal,
Vol.20,No.9, pp.1284-1290,1982.
[4] B. A. Ma and J. F. He, “A finite element analysis of viscoelastically
damped sandwich plates”, Journal of Sound and VibrationVol.152,No.1,
pp.107-123.
[5] O. C. Zienkiewicz and Y. K. Cheung,The finite element method in
structural and continuum mechanics, MacGraw-Hill, 1967.
[6] T. Yamaguchiand K. Nagai, “Chaotic vibration of a cylindrical shell-panel
with an in-plane elastic support at boundary”, Nonlinear Dynamics,
Vol.13, pp.259-277, 1997.
[7] T. Yamaguchi, Y. Kurosawa and H. Enomoto, “Damped vibration analysis
using finite element method with approximated modal damping for
automotive double walls with a porous material”, Journal of Sound and
Vibration, Vol.325, pp.436-450, 2009.
[8] H. Oberst, Akustische Beihefte, Vol.4, pp.181-194,1952.
[1] E. Pesheck, N. Boivin, C. Pierre and S. W. Shaw, “Non-linear modal
analysis of structural systems using multi-mode invariant manifolds”,
Nonlinear Dynamics, Vol.25, pp.183-205, 2001.
[2] T. Yamaguchi, Y. Fujii, K. Nagai and S. Maruyama, “FEM for vibrated
structures with non-linear concentrated spring having hysteresis”,
Mechanical Systems and Signal Processing, Vol.20, pp.1905-1922, 2006.
[3] C. D. Johnson and D. A. Kienholz, “Finite element prediction of damping
structures with constrained viscoelastic layers”, AIAA Journal,
Vol.20,No.9, pp.1284-1290,1982.
[4] B. A. Ma and J. F. He, “A finite element analysis of viscoelastically
damped sandwich plates”, Journal of Sound and VibrationVol.152,No.1,
pp.107-123.
[5] O. C. Zienkiewicz and Y. K. Cheung,The finite element method in
structural and continuum mechanics, MacGraw-Hill, 1967.
[6] T. Yamaguchiand K. Nagai, “Chaotic vibration of a cylindrical shell-panel
with an in-plane elastic support at boundary”, Nonlinear Dynamics,
Vol.13, pp.259-277, 1997.
[7] T. Yamaguchi, Y. Kurosawa and H. Enomoto, “Damped vibration analysis
using finite element method with approximated modal damping for
automotive double walls with a porous material”, Journal of Sound and
Vibration, Vol.325, pp.436-450, 2009.
[8] H. Oberst, Akustische Beihefte, Vol.4, pp.181-194,1952.
@article{"International Journal of Mechanical, Industrial and Aerospace Sciences:70753", author = "T. Yamaguchi and M. Watanabe and M. Sasajima and C. Yuan and S. Maruyama and T. B. Ibrahim and H. Tomita", title = "Nonlinear Impact Responses for a Damped Frame Supported by Nonlinear Springs with Hysteresis Using Fast FEA", abstract = "This paper deals with nonlinear vibration analysis
using finite element method for frame structures consisting of elastic
and viscoelastic damping layers supported by multiple nonlinear
concentrated springs with hysteresis damping. The frame is supported
by four nonlinear concentrated springs near the four corners. The
restoring forces of the springs have cubic non-linearity and linear
component of the nonlinear springs has complex quantity to represent
linear hysteresis damping. The damping layer of the frame structures
has complex modulus of elasticity. Further, the discretized equations in
physical coordinate are transformed into the nonlinear ordinary
coupled differential equations using normal coordinate corresponding
to linear natural modes. Comparing shares of strain energy of the
elastic frame, the damping layer and the springs, we evaluate the
influences of the damping couplings on the linear and nonlinear impact
responses. We also investigate influences of damping changed by
stiffness of the elastic frame on the nonlinear coupling in the damped
impact responses.", keywords = "Dynamic response, Nonlinear impact response, Finite
Element analysis, Numerical analysis.", volume = "8", number = "10", pages = "1808-8", }