Dynamic behaviors of the 2-DOF axially telescopic mechanism for truss structure bridge inspection vehicle is investigated. The telescopic mechanism is a combination of one vertical beam that can move axially, one constant beam perpendicularly fixed at the end of the vertical beam and one telescopic beam that can move along the axial direction of the constant beam during work. The Euler-Bernoulli beam theory is utilized to simplify the beams. The Lagrangian description is adopted to account for the coordinate for the telescopic mechanism. The equations of motion are derived using the Hamilton’s principle and decomposed into a set of ordinary differential equations by employing the Galerkin’s method. The eigenfunctions are acquired based on the boundary conditions by adopting the dichotomy method. The solutions to the equations are acquired using the Newmark-β method. Experiments are carried out to prove the validity of the theoretical model. Numerical examples are simulated to explore whether the vertical beam and telescopic beam can extend or retract synchronously and obtain appropriate beam moving strategy. The results prove that synchronous motion of the vertical beam and telescopic beam will not always lead to pronounced stronger vibration than the separate ones. On the other hand, the beam moving strategies that the telescopic beam moving before the vertical beam when they all extend out or retract back and moving after the vertical beam when one extends out and the other retracts back will effectively reduce the vibration compared with otherwise.
Nonlinear dynamic analysis of an axially moving telescopic mechanism for truss structure bridge inspection vehicle under pedestrian excitation is carried out. A biomechanically inspired invertedpendulum model is utilized to simplify the pedestrian. The nonlinear equations of motion for the beam-pedestrian system are derived using the Hamilton's principle. The equations are transformed into two ordinary differential equations by applying the Galerkin's method at the first two orders. The solutions to the equations are acquired by using the Newmark-β method associated with the Newton-Raphson method. The time-dependent feature of the eigenfunctions for the two beams are taken into consideration in the solutions. Accordingly, the equations of motion for a simplified system, in which the pedestrian is regarded as moving cart, are given. In the numerical examples, dynamic responses of the telescopic mechanism in eight conditions of different beamtelescoping and pedestrian-moving directions are simulated. Comparisons between the vibrations of the beams under pedestrian excitation and corresponding moving cart are carried out to investigate the influence of the pedestrian excitation on the telescopic mechanism. The results show that the displacement of the telescopic mechanism under pedestrian excitation is smaller than that under moving cart especially when the pedestrian approaches the beams end. Additionally, compared with moving cart, the pedestrian excitation can effectively strengthen the vibration when the beam extension is small or when the pedestrian is close to the beams end.
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