• Jay Gohil
• Mili Trivedi

Most of mechanical systems exhibit nonlinear behavior and a great class of nonlinearities. In case of two degree of freedom system, normal mode vibrations are free vibrations that depend only on the mass and stiffness of the system and how they are distributed. In the present paper, mainly the nonlinearity is considered due to the non-symmetric arrangement of spring. Here, meaning of non- symmetric arrangement of the spring means, the stiffness of three/two springs are not equal. The general relations have been derived to eliminate the nonlinearity of the system due to difference in spring stiffness by varying the masses or initial displacement. It is observed that for mode 1 i.e. same displacement in same direction, the middle spring does not affect the frequencies of both the masses. The study has been done in four steps. First step is development of mathematical model by considering the nonlinearity, second is numerical solution of by matlab, third by experimental verification and finally by simulation in software. The mathematical model had been developed by Euler-Lagrangian method. The numerical technique Runge- Kutta-Fourth-Order method is used to solve the coupled nonlinear differential equations iteratively. Various techniques like Time-displacement response plot, Orbits plots, and Poincare map used to detect nonlinear behavior. The programmed code has been developed in the MATLAB software to solve the nonlinear equation of motion and to get the different plots.

Nonlinear, self excited, two degree of freedom

"NONLINEAR DYNAMIC ANALYSIS OF 2DOF SYSTEM FOR VIBRATION ABSORPTION AND ISOLATION IN FOUNDATION", International Journal of Emerging Technologies and Innovative Research (www.jetir.org), ISSN:2349-5162, Vol.6, Issue 4, page no.693-699, April-2019, Available :http://www.jetir.org/papers/JETIR1904G08.pdf

"NONLINEAR DYNAMIC ANALYSIS OF 2DOF SYSTEM FOR VIBRATION ABSORPTION AND ISOLATION IN FOUNDATION", International Journal of Emerging Technologies and Innovative Research (www.jetir.org | UGC and issn Approved), ISSN:2349-5162, Vol.6, Issue 4, page no. pp693-699, April-2019, Available at : http://www.jetir.org/papers/JETIR1904G08.pdf