Transverse Impact of a Solid against Orthotropic Plate with Consideration for Propagation of Elastics Waves

Authors: Loktev А.А. Published: 05.09.2013
Published in issue: #2(41)/2011  

Category: Mechanics  
Keywords: impact interaction, Ufland-Mindlin plate, cylindrical anisotropy, contact force

The problem of transverse impact of a solid against an orthotropic plate with cylindrical anisotropy is solved. Dynamical behavior of the plate is described by non-classical equations of Ufland-Mindlin type, where five displacements of points of the target are included. The wave equations allow one to suppose that longitudinal and transverse waves, arising after the contact between the striker and the plate, propagate at a finite speed and influence the plate deformation outside the contact zone. For determination of the displacements and the contact force in the zone of interaction, the Laplace transform and the asymptotic method of unknown quantities' expansions in power series in terms of small parameter are used. A relation between the local crushing and a force at the zone of contact is expressed using the Hertz model for a solid with spherical striker. The results of solving the problem are presented as analytical expressions and graphical dependences. The influence of anisotropic properties of the plate material on the dynamic deflection and contact force is investigated in the zone of interaction.