Mathematical Formulation for Bending Moment Wave in Non-Dispersive Finite Rod

(*) Corresponding author

Authors' affiliations

DOI's assignment:
the author of the article can submit here a request for assignment of a DOI number to this resource!
Cost of the service: euros 10,00 (for a DOI)


Natural rubber (NR) is an incompressible material and has potential to become vibration isolator for many engineering applications. In this study, mathematical formulation for bending moment wave is derived by using wave propagation method for non-dispersive finite rod. This finite rod is developed by NR material. Impedance matrix is developed in order to determine at which of four different locations the highest internal resonance wave occurred. Bending moment is used as an excitation force to create unstable energy for finite rod and to produce internal resonance wave. This wave is propagating from free boundary to fixed boundary and finally returns back to free boundary. This happens because of the nature of science where wave cannot pass the fixed boundary. The bending moment wave slowly changed to bending moment displacement at the free boundary. This phenomenon is recorded at plotted into frequency domain graph.
Copyright © 2014 Praise Worthy Prize - All rights reserved.


Bending Moment; Wave Propagation; Internal Resonance; Natural Rubber

Full Text:



James M. Kelly and Shakhzod M. Takhirov., Tension buckling in multilayer elastomeric isolation bearings, Journal of Mechanics of Materials and Structures, Vol. 2, No. 8, 2007, 1591-1605.

Chamindalal Sujeewa Lewangamage, Masato Abe, Yozo Fujino and Junji Yoshida, Design criteria for seismic isolation rubber bearings, 13th World Conference on Earthquake Engineering, 2004, paper no. 183.

Mineo Takayama and Keiko Morita, Maximum stress of interlayer steel plates in elastomeric isolator, Seismic, Shock and Vibration Isolation, Vol. 341, 1996.

M. Imbimbo and A. De Luca, F.E. stress analysis of rubber bearings under axial loads. Computers and Structures Vol. 68, 1998, 31-39.

Hsiang Chuan Tsai and Shaw Jiun Hsueh, Mechanical properties of isolation bearings identified by a viscoelastic model, International Journal of Solids and Structures, Vol. 38, 2001, 53-74.

Cheng Hsiung Chang, Modeling of laminated rubber bearings using an analytical stiffness matrix, International Journal of Solids and Structures, Vol. 39, 2002, 6055-6078.

A. Carrella, M.J. Brennan and T.P. Waters, Force transmissibility of a nonlinear vibration isolator with high-static-low-dynamic-stiffness. Sixth EUROMECH Nonlinear Dynamics Conference, 2008.

R. A. Ibrahim, Recent advances in nonlinear passive vibration isolators, Journal of Sound and Vibration, Vol. 314, 2008, 371-452.

J.R. Banerjee, Development of an exact dynamic stiffness matrix for free vibration analysis of a twisted Timoshenko beam, Journal of Sound and Vibration, Vol. 270, 2004, 379-401.

M.A. Salim, A. Putra and M.A. Abdullah, Analysis of axial vibration in the laminated rubber-metal spring, Advanced Materials Research, Vol. 845, 2014, 46-50.

M. A. Salim, A. Putra. D.J. Thompson, N. Ahmad and M. A. Abdullah, Transmissibility of a laminated rubber-metal spring: A preliminary study, Applied Mechanics and Materials, Vol. 393, 2013, 661-665.

The Malaysian Rubber Producers’ Research Association, Engineering design with natural rubber, NR Technical Bulletin, 1992, ISSN 0956-3856


  • There are currently no refbacks.

Please send any question about this web site to
Copyright © 2005-2024 Praise Worthy Prize