In many technical applications spring-like flexible elements or real springs connected in series are used. The operation range of these components determines whether the system behaviour has a linear or nonlinear characteristic. A mechanical system is said to be linear or nonlinear according to the type of differential equations of motion. The linearity or nonlinearity of a conservative system is determined essentially by the algebraic relationship between restoring forces and displacement/deflections. During the past two decades, a large number of studies have shown that bifurcation phenomena are observed in many physical systems that possess non-linearity. A mechanical system with single degree of freedom including both linear and nonlinear springs in series is named mass grounded system. This system can be set parallel to linear or nonlinear dampers. Applications of this system are suspensions and vibration isolators. In the first part of the thesis, nonlinear vibrations of three grounded mass systems that are described below are investigated: 1) First system includes linear and nonlinear springs in series and the whole spring system is connected to a lumped mass. 2) Second system is the same as the first system but a linear damper in parallel is also added to the system. 3) Third system is the same as the second system but a nonlinear damper in parallel is added to the system. By using a perturbation method such as Multiple Time Scale (MTS) or Averaging, free and forced vibrations of these systems are analyzed. For free vibrations, the analytical results are compared with the numerical integration results. Also, forced vibrations of the systems, including primary and secondary resonances are studied and the effects of different parameters on the frequency-responses are investigated. In the second part of the thesis, the possibility of bifurcation in these systems is investigated by changing different control parameters. Bifurcation diagrams, phase-plane diagrams, Poincare maps and time responses are employed to distinguish periodic, quasi-periodic and chaotic responses. Keywords : Grounded Mass. Perturbation Analysis. Multiple Time Scale. Averaging. Primary and Secondary Resonances. Bifurcation.
