To optimize cantilevered piezoelectric vibration energy harvesters according to the characters of the environmental vibration and the electrical loads, a differential equation of motion and the boundary conditions for a cantilevered piezoelectric vibration energy harvester were established in consideration of the position difference between the center of proof mass and the free end of cantilever. A uniform coupled circuit equation applicable to the harvesters with one piezoelectric layer, two series connected piezoelectric layers and two parallel connected piezoelectric layers was developed by introducing several constants,and the expressions of the natural frequencies and corresponding mode shapes were obtained.Furthermore, the closed-form expressions of the output voltages were derived for harmonic base accelerometer excitations and arbitrary base accelerometer excitations. Experimental results indicate that the relative errors of the natural frequency expression and the output voltage expression are smaller than 10% and 20% respectively for three harvester prototypes,which shows that the model satisfies the requirements of optimizing harvesters.