What is needed to convert these vibrations into electrical energy is the piezo vibration sensor. An example of a piezo electric sensor is like this:
This typical sensor can produce low alternating current but large voltage ranging from 1v up to 90v. The electrical energy produced by the sensor goes out of the 2 leads. There is an integrated circuit designed specifically to regulate the output of the sensor, I am referring to LTC3588. This system on chip electronic component requires minimal external component and the typical circuit provided by the manufacturer is in the following circuit diagram:
This is basically a piezoelectric energy harvester with 9V battery as back up power. There are also other implementations like Sparkfun's LTC3588 breakout board uses solar energy as power source instead of the piezo vibration sensor. This works like you have to set a certain output voltage, the role of the solar panel is to charge the super capacitors connected in series, if the voltage across the input of the breakout board reaches the preselected voltage output, the LTC3588 circuit will be awaken and start to power a device connected to its output, if the supercaps were fully discharge or their output voltage is less than the preselected output voltage, then the circuit will enter the sleep mode.