Affiliations: Department of Theoretical Mechanics, Voronezh State
University of Architecture and Civil Engineering, ul. Svobodu 45-53, Voronezh
394018, Russia. | Dedicated to the 75th Birthday of our teacher Professor Duis D.
Ivlev
Abstract: The problem on low-velocity impact of an elastic body upon a
pre-stressed circular orthotropic plate possessing cylindrical anisotropy is
considered. The dynamic behavior of the plate is described by equations taking
the rotary inertia and transverse shear deformations into account. Longitudinal
compressing forces are uniformly distributed along the plate's median plane.
Contact interaction is modeled by a linear spring, and a force arising in it is
the linear approximation of Herts'z contact force. During the shock interaction
of the impactor with the plate, the waves which are the surfaces of strong
discontinuity are generated in the plate and begin to propagate. Behind the
fronts of these waves, the solution is constructed in terms of ray series,
which coefficients are the different order discontinuities in partial
time-derivatives of the desired functions, and a variable is the time elapsed
after the wave arrival at the plate's point under consideration. The ray series
coefficients are determined from recurrent equations within accuracy of
arbitrary constants, which are then determined from the conditions of dynamic
contact interaction of the impactor with the target. The found arbitrary
constants allow one to construct the solution both within and out of the
contact region. The analysis of the solution obtained enables one to find out
the new effect and to make the inference that under a certain critical
magnitude of the compression force the orthotropic plate goes over into the
critical state, what is characterized by 'locking' the shear wave within the
contact region, resulting in plate damage within this zone as soon as the
compression force exceeds its critical value.
