Dynamic non-stationary mixed problem for cut circular hollow cone (Q2759494)

At spherical boundaries of isotropic hollow cone normal impulse pressure is prescribed, at the conical surfaces normal displacements and tangential stresses are zero. The problem of elastodynamics is solved using the Laplace transform with respect to time and a new finite integral transform in spherical coordinate \(\theta\) with the kernel containing the Legendre functions. In the result ordinary differential equations in radial coordinate are obtained. Asymptotic solution for small times is obtained by expanding solution in inverse powers of parameter of the Laplace transform and using the convolution theorem.