Abstract
In the present paper, the problem on normal low-velocity impact of a solid upon an isotropic spherical shell is studied without considering the changes in the geometrical dimensions of the contact domain. At the moment of impact, shock waves (surfaces of strong discontinuity) are generated in the target, which then propagate along the shell during the process of impact. Behind the wave fronts up to the boundary of the contact domain, the solution is constructed with the help of the theory of discontinuities and one-term ray expansions. The ray method is used outside the contact spot, but the Laplace transform method is applied within the contact region. It is assumed that the viscoelastic features of the shell are exhibited only in the contact domain, while the remaining part retains its elastic properties. In this case, the contact spot is assumed to be a plane disk with constant radius, and the viscoelastic features of the shell are described by the fractional derivative standard linear solid model. In the case under consideration, the governing differential equations are solved analytically by the Laplace transform technique. As a result, the exact solution of the contact force is determined as a function of time.
Published Version
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