###### Abstract
A linear coupled lumped-parameter model is presented including both the piezoelectric and electromagnetic couplings. Theoretical results show that the linear flutter speed decreases for large values of the eccentricity and plunge-to-pitch frequency ratio. [PERSON] et al. [19] proposed various mathematical models for beam energy harvesters: lumped-parameter and distributed-parameter models. They designed and studied a unimorph cantilever beam-based harvester that undergoes _bending-torsion vibrations_ by creating an offset between its center of gravity and the shear center, thereby leading to a coupling between the bending and torsion vibrations. The offset is created by placing two masses asymmetrically at the tip of the beam. The beam-mass system is modeled using the Euler-Bernoulli beam theory and Hamilton's principle to derive the coupled governing equations of motion and associated boundary conditions for a base excitation. The exact mode shapes and natural frequencies of the harvester are calculated and used as basis functions in [PERSON]'s scheme to derive a reduced-order model. Closed-form expressions are obtained for all needed outputs. It is demonstrated that, when the lowest global frequencies are close to each other, an interesting broadband frequency harvester appears. It is also shown that, when the asymmetry between the two masses increases, the electrical harvested power as well as the produced voltage increases. [PERSON] and [PERSON] [20] investigated the harvester which consists of a _rigid airfoil_ supported by nonlinear flexural and torsional springs which is placed in an incompressible air flow and subjected to a harmonic base excitation in the plunge direction. The flow field sets the elastic structure into limit-cycle oscillations that induce an alternating strain, and, hence, a charge in the piezoelectric laminates. The paper investigates the transduction of _piezoeleclastic_ energy harvesters under the combination of vibratory base excitations and aerodynamic loadings. An approximate analytical solution describing the harvester response is obtained using the center manifold reduction and the method of normal forms. The analytical solution is used in conjunction with numerical simulations to investigate the harvester's performance below and above the flutter speed. [PERSON] and [PERSON] [21] presented a comprehensive review on the history and current state-of-the art piezoelectric energy harvesting. A brief theory section presents the basic principles of piezoelectric energy conversion and introduces the most commonly used mechanical architectures. The theory section is followed by a literature survey on piezoelectric energy harvesters, which are classified into three groups depending on the size of the devise. The size of a harvester affects parameters such as its weight, fabrication method, achievable power output level, and potential application. Having in mind potential applications of piezoelectric energy harvesters, it is important to extend the thin-beam models to reasonably thick-beam configurations as well as to varying geometries of the harvesters. The dynamics of a beam-like flexible structure strongly depends on its aspect ratio and the operating frequency range. The Euler-Bernoulli model is the classical model for slender beam configurations with sufficiently high length-to-thickness aspect ratio so that the shear distortion and rotary inertia effects can be neglected. The Rayleigh model introduces the effect of rotary inertia to the Euler-Bernoulli model but it neglects the effect of transverse shear distortion. The Timoshenko beam model accounts for both the shear distortion and rotary inertia effects and is widely used for modeling the dynamics of moderate length-to-thickness ratio beams. [PERSON] [22] presents approximate analytical distributed-parameter electromechanical modeling of cantilevered piezoelectric energy harvesters based on the Euler-Bernoulli, Rayleigh, and Timoshenko beam theories. The technique of [22] is an electromechanical version of the assumed-modes method.