关键词: Timoshenko beam, finite-deflection, shock wave, chaos motion, Jacobi elliptic function expansion, Melnikov function

Abstract: In this paper, V. V. Golubef method is first extended to the diffuse laminar flow between two parallel spherical surfaces. With the boundary layer motion equation in spherical coordinates, we derive the momentum integral equation together with the energy integral equation for the laminar boundary layer of the entrance region between two parallel spherical surfaces. And then by applying Picards gradually approaching method for the momentum integral equation, we get the approximate expression which the entrance region length varies with the thickness of boundary layer. In the end every coefficient of entrace region effect is analyzed and calculated.

Key words: Timoshenko beam, finite-deflection, shock wave, chaos motion, Jacobi elliptic function expansion, Melnikov function