In the recent work by the authors, high order spectral difference (SD) method has been formulated in a framework with dynamic deformable meshes, and been demonstrated to preserve the design accuracy of the underlying high order temporal and spatial discretization methods. In this study, the current SD method has been extended to solve fluid structure interaction problems on deforming meshes. The SD method with collocated solution and flux points is used as the spatial discretization method, while the explicit fourth order five-stage Runge-Kutta is used to advance the flow in time. The solid structure, which is the cylinder, is modelled as a spring-mass system. The movement of the solid cylinder is handled with a dynamic deforming mesh using an algebraic high order blending polynomial. The present work has focused on flow induced cylinder oscillation, bluff body wake and cylinder interaction, and control of flow induced oscillation through mechanism of counter-rotating cylinders. Numerical experiment for flow over counter-rotating cylinder pair shows that significant drag reduction and wake suppression can be obtained. Numerical calculation for a free-stream flow over a free-floating cylinder shows that the wake symmetry of a cylinder can not be maintained. The resultant wake instability propels the cylinder in the cross-flow direction, but the cylinder was found to eventually locked in a flow induced self-oscillation at an equilibrium position. Active control of the cylinder vibration through the mechanism of counter-rotation of solid bodies is finally investigated.