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1.
In machine dynamics impacts may occur by interaction of solid bodies. There is no doubt that the method of multibody systems is most efficient for the dynamical analysis of the overall motion. However, during impact energy is lost macromechanically measured by the coefficient of restitution. This coefficient has to be estimated from experiments and experience but cannot be computed within the multibody system approach. The impacts, on the other hand, are generating waves in the bodies which are propagating until they are vanishing due to material damping. These high frequency phenomena are analyzed using wave propagation, modal approach and finite elements. The results of the simulation on the fast time scale are used to compute the coefficient of restitution which is then fed back to the multibody system equations and the solution continues on the related slow time scale. The efficiency of the approach presented is shown for the impact of a steel sphere on four different shaped aluminum bodies of comparable mass. The simulation results are verified with experiments performed on different time scales, too. Using the impact of a double pendulum on a stop as example, the application of the multiscale approach to a multibody system is shown. 相似文献
2.
Nonholonomic constraint equations that are nonlinear in velocities are incorporated with Kane's dynamical equations by utilizing
the acceleration form of constraints, resulting in Kane's nonminimal equations of motion, i.e. the equations that involve
the full set of generalized accelerations. Together with the kinematical differential equations, these equations form a state-space
model that is full-order, separated in the derivatives of the states, and involves no Lagrange multipliers. The method is
illustrated by using it to obtain nonminimal equations of motion for the classical Appell–Hamel problem when the constraints
are modeled as nonlinear in the velocities. It is shown that this fictitious nonlinearity has a predominant effect on the
numerical stability of the dynamical equations, and hence it is possible to use it for improving the accuracy of simulations.
Another issue is the dynamics of constraint violations caused by integration errors due to enforcing a differentiated form
of the constraint equations. To solve this problem, the acceleration form of the constraint equations is augmented with constraint
stabilization terms before using it with the dynamical equations. The procedure is illustrated by stabilizing the constraint
equations for a holonomically constrained particle in the gravitational field. 相似文献