  In this work we study the dynamic behaviour of compound shells of revolution
partially filled with an ideal incompressible fluid based on boundary-value
problems. New analytical mathematical model with corresponding discrete scheme
for the elastic displacements and the dynamic liquid pressure is developed. The
discrete scheme is based on the method of discrete singularities. A code to
perform the numerical analysis is developed. Comprehensive benchmarking of the
obtained results against other methods is done and good agreement is observed.
The convergence of the proposed numerical method is demonstrated. One of the
advantages of this new model is that the initial 3D problem is analytically
reduced to a 1D integral equation. Moreover, it can handle the behaviour of the
pressure in the vicinity of the nodes explicitly and the computational
technique used has a quick convergence requiring a negligible amount of CPU
time.
