In this paper, with the utilization of a transport theorem and three-dimensional version of Leibniz’s rule, the procedure for deriving the time rate of change of an energy functional for axially moving continua is investigated. In the control engineering, the correct solution of the time derivation of an energy functional is essential for designing an effective controller, especially, in the Ly...

We present a stability result for a class of non-trivial self-similarly vanishing solutions to a 3D Hele-Shaw moving boundary problem with surface tension and single-point suction. These solutions are domains that bifurcate from the trivial spherical solution. The moving domains have a geometric centre located at the suction point and they are axially symmetric. We show stability with respect t...

In this paper, the postbuckling problem and free linear nonlinear vibration surrounding configuration are accurately analyzed. The placement of translating beams that undergo significant overall buckling deformations in high-speed region, leading to strongly vibration, is studied. Using Galerkin method, we found partial differential equation reduced an ordinary with cubic quadratic terms, which...