Numerical modeling of the dynamic behavior of spatial elements of machine-building constructions

For the dynamic analysis of spatial elements of machine-building constructions, new approaches are needed which will take into account such peculiarities of their behavior as the high angular speed of rotation and the significant initial stress caused by temperature gradients, centrifugal loads and element interfacing. The linearized equations of motion have been derived by applying the variational principle. The developed equations describe the influence of the pre-stress state on the dynamic characteristics of elastic systems. The use of three-dimensional relationships essentially improves the accuracy of the results obtained by the theory of plates. Besides, the proposed approach allows us to determine vibration eigenmodes corresponding to the disk motion in the in-plane direction. Numerical results demonstrate that the pre-stress state has a strong effect on the natural vibration frequencies of the system. For real angular speed of rotation, the centrifugal effects lead to an increase (by a factor of 1.5-2) in natural vibration frequencies compared to the steady-state frequency. More complex effects are observed when taking into account the non-uniform temperature field, though its effect on eigenfrequencies is of less significance.