Abstract
In the present work the dynamics of the system of a mass moving on the beam is investigated in detail numerically in the case of vibrations about a buckled state. The differential equation that describes the motion is strongly nonlinear. Simulations are based on the space-time finite element method. It enabled us easily determine the influence of the moving inertial particle. At the computational stage it becomes a real problem when the mass particle traverses joints of neighbouring elements. The results of representative and interesting computer simulations are enclosed.
Highlights
Structural elements that work in nonlinear range behave in a way far from the known for linear ranges
Well known jumps in trusses under nite displacements, natural frequencies varying under axial loads, buckling etc. are good examples
The distance between successive inertial loads was equal to the beam length
Summary
Structural elements that work in nonlinear range behave in a way far from the known for linear ranges. The motion of a point load travelling on a bending element is a typical problem in transportation Such systems were extensively investigated, mostly in a classical linear range. This makes the model, which is a coupled system of the Gao nonlinear beam equation and the motion of the mass, considerably more complex. The simple time integration method separated from the spatial discretization results in complexity in matrix formulation of a resulting systems of algebraic equations (see for example [13]) Both nonstationary discretization of the doman and nonstationary location of parameters describing moving inertia or granulated stiness can be applied with this approach relatively [14, 15]. The results of representative and interesting computer simulations are enclosed
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