Passive vibration shunt control using piezoelectric material (PZT) and an electrical network can remove considerable amount of vibration energy from flexible structures. In this paper, an analytical study of parallel passive resistor-inductor (R-L) piezoelectric vibration shunt control on a beam structure by using the Hamilton's principle, Galerkin's method is presented. However, the efficiency of such vibration control method relies on the optimization of vibration energy transfer between a structure and piezoelectric material. In this paper, the strain energy transfer within the composite material, which is made of two layers of different materials, is analyzed. It indicates that neutral axis of the composite material has some influence on the optimization of the strain energy transfer between the structure and PZT. The passive vibration shunt control is sensitive to frequency shift of structures. However, in reality, the natural frequencies of flexible structures often vary somewhat due to environment change, such as boundary conditions, temperature variation, etc. The effectiveness of the vibration shunt control will be significantly reduced when the frequency of the shunt circuit does not match the natural frequency of the structure. In this paper, a method of estimating the resonant frequencies of structures using adaptive IIR notch filter is presented. With online frequency detection, the inductor value is possible to be adjusted in real time by some kind of controllable capacitors and resistors to track the frequency change of structures.