Abstract
The non-linear behaviour of a slender beam with an attached mass at an arbitrary position under vertical base excitation is investigated with combination parametric and internal resonances. The governing equation which retains the cubic non-linearities of geometric and inertial type is discretized by using Galerkin's method and the resulting second order temporal differential equation is then reduced by the method of multiple scales to a set of first order non-linear differential equations. Steady state response and its stability are obtained numerically from these reduced equations. Super- and sub-critical Hopf bifurcations in the trivial as well as non-trivial branches and the saddle-node or fold type bifurcations in the non-trivial branches of the response curves are found. The effect of damping, amplitude as well as frequency of base excitation, the mass ratio and the location of the concentrated mass on the non-linear response of the system having internal resonance of 3:1 is studied at length. Hysteresis, saturation and blue sky catastrophe phenomena with bistability interval in the response curves are observed for a wide range of bifurcating parameters.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
