This paper presents experimental and theoretical studies on segregation of granular media subjected to external vertical sinusoidal vibration, vibration energy absorption properties of granular materials, dynamic behaviors of sandpile formation, and the stop-and-go motion in vertical pipe flow. Results of our studies not only extend the knowledge of non-linear properties of granular media under some dynamical conditions, such as vibrating, shearing, and flowing etc, but also is a theoretical instruction in the processing, storing and transporting of granular media in applied engineering. In the experiments with vertical sinusoidal vibration of granular material in containers with bottleneck(s), new segregation patterns and convection properties were found: (1)Under the condition of two-dimensional containers with one bottleneck, with the variation of the width of bottleneck, big and small particles show