## 1 Introduction  
Vibration energy harvesting is considered as a promising alternative approach to power wireless sensors nets and ultra low power microelectronics devices [1; 2]. Piezoelectric and electromagnetic energy harvesting are the most reported transduction mechanisms. Traditional linear vibration energy harvester (VEH) has been usually considered as single degree-of-freedom (1 DOF) model [3], which has a narrow operating frequency bandwidth. Once the excitation frequency shifts away from the resonant frequency, the performance of the VEH drops dramatically. In practice, the vibration source is random and time-varying. Some vibration sources especially exhibit multiple discrete frequency peaks in a large frequency range. For example, HVAC vents have three vibration frequencies of 21.8, 29 and 127.3 Hz [4]. Laptops exhibit two vibration frequencies of 43.2 and 90.2 Hz [5]. To effectively scavenge energy from vibration sources with multiple discrete frequencies is the first concerned research question. As we know, the resonant frequency of the piezoelectric energy harvester (PEH) increases sharply when the device size reduces to micro level. To date, most of the micro-scale PEHs operate at frequencies of more than 100 Hz [6; 7], even at the level of 1 kHz [8]. This limits their applications to harvest some ambient vibration energy, which occurs in the frequency range below 30 Hz, such as those caused by wind or human motions. The micro electromagnetic energy harvester (EMEH) [9] exhibits lower power density due to the decreased flux density and smaller velocity of the magnet. Therefore, another concerning question is how to improve the performance of VEHs in the low frequency range. To improve the performances of VEHs, a number of solutions have been proposed by researchers. These solutions include generator array [10; 11; 12], mechanical impact [13; 14], nonlinear spring stiffness [15; 16], magnetic coupling [17; 18; 19; 20], hybrid conversion mechanism [21; 22] and active/passive tuning techniques [23; 24; 25]. However, these generators are only effective in a continuous frequency range or at a single dominant resonant frequency. To harvest energy from vibration sources with discrete frequency peaks over a wide range, [PERSON] and [PERSON] [26] reported a PEH composed by a series of piezoelectric beams, which are connected end-to-end. The resonant frequencies vary from 100 to 1000 Hz with different numbers of beams. [PERSON] _et al._[27] presented an array-type PEH made of three piezoelectric bimorphs. The respective three fundamental resonant frequencies are about 113, 183 and 281 Hz. [PERSON] _et al._[28] designed a multi-frequency EMEH with three resonant modes of 369, 938 and 1184 Hz. [PERSON] _et al._[29] added a nonlinear spring oscillator to a PEH to scavenge the multi-frequency vibration energy. [PERSON] _et al._[30] developed a multi-mode EMEH for three-dimensional (3D) excitation at different frequencies. [PERSON] _et al._[31] reported a hybrid energy harvester (HEH) using piezoelectric and electromagnetic mechanisms. It consisted of a piezoelectric cantilever beam and a permanent magnet attached at the tip, which oscillated within a stationary coil. The first and the second resonances of such device were 20 Hz and 300 Hz. [PERSON] _et al._[32] and [PERSON] _et al._[33] analyzed the characteristics of the two degree-of-freedom (2 DOF) HEH. Among these works, the resonant frequencies of VEHs are fixed when the prototypes are assembled. It is not convenient to tune the resonances according to the change of excitation frequency. In this paper, we report a novel tunable multi-frequency HEH, using piezoelectric and electromagnetic conversion mechanisms. The design procedure is explained by considering two generating elements coupled with magnetic interaction. An electromechanical coupling model of the HEH is established. The energy harvesting characteristics are numerically simulated and verified by experiments.