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We analyze coupled flexural vibration of two elastically and electrically connected piezoelectric beams near resonance for converting mechanical vibration energy to electrical energy. Each beam is a so-called piezoelectric bimorph with two layers of piezoelectrics. The 1D equations for bending of piezoelectric beams are used for a theoretical analysis. An exact analytical solution to the beam equations is obtained. Numerical results based on the solution show that the two resonances of individual beams can be tuned as close as desired by design when they are connected to yield a wide-band electrical output. Therefore, the structure can be used as a wide-band piezoelectric power harvester.