Manipulators are widely used in all areas of science and technology. Effective trajectory tracking and quick deflection suppression are the two main aspect of research for a flexible manipulator. The paper reports aperiodic signal like trajectory tracking control for a planar assumed modes modelled two-link flexible manipulator (TLFM). The aperiodic chaotic signal is used as a desired trajectory for the TLFM. Thus, designing of a robust controller for the aperiodic signal tracking control is a challenging task. A backstepping based adaptive SMC technique is designed for the considered problem. In adaptive SMC, the gain of the switching control law is estimated online. The effectiveness of the considered controller is compared to an available backstepping controller. It is found that the designed backstepping based adaptive SMC perform better in terms of smaller tracking time, quick tip deflection suppression and lesser, smoother control efforts. Proposed trajectory strategy is validated on a two-link flexible manipulator in MATLAB simulation environment.