###### Abstract
It is important to emphasize that in our previous works on energy harvesting models (see [PERSON] [1; 2; 3], [PERSON] and [PERSON] [4]), we considered the Euler-Bernoulli beam model as a vibrating structure. In the present work, we deal with the Timoshenko beam model, which makes mathematical treatment much more challenging. Before we turn to the mathematical statements and results, we would like to mention several research directions closely related to the topic of the present paper. The development of micro and nano technologies, smart sensors, and health monitoring devices created the need of independent energy sources for small devices and self-powered sensors. [PERSON] et al. [5] studied the electro-mechanical system of vibrational energy harvester, where the beam is excited by external and kinematic periodic forces and damped by an electrical resistor through the coupled piezoelectric transducer. Nonlinearities are introduced by stoppers limiting the transverse displacement of the beam, and the action of the stoppers is modeled as Winkler elastic foundation. To study the composite beam, the authors used the geometrical nonlinear version of _Timoshenko beam theory_[5]. Using their models, the authors can capture discontinuities of structural parameters such as thickness discontinuities or impact of stoppers, which is important in engineering practice. [PERSON] and [PERSON] [6] discussed the way by which self-sustained oscillations resulting from air-solid instabilities, such as _flutter of a flexible flag in an axial_ air flow, can be used for energy harvesting. Piezoelectric patches attached to the surface of the flag transform the solid deformation into an electric current powering purely resistive output circuits. A flexible plate becomes unstable due to flutter above the critical flow velocity which depends on the plate's properties (e.g., density and rigidity) and can be chosen to be lower than the typical flow velocity, which leads to self-sustained large-amplitude flapping of the plate. The study is focused on numerical analysis of the nonlinear dynamics of the system and on determination of its harvesting efficiency and robustness of the process. In the review paper, [PERSON] [7] discussed different issues on the energy harvesting from _aeroelastic vibrations_. These harvesters can be placed in such areas as high wind spaces, ventilation outlets, ducts of buildings, lifting surfaces of aircraft structures, and biomedical implants. Qualitative and quantitative characteristics of various types of flow-induced vibrations energy harvesters are presented in the paper. Limitations and recommendations on mechanical and aerodynamic modeling, power conditioning circuits optimization, and prototypes fabrications are discussed in detail. [PERSON] and [PERSON] [8] performed a concept study on piezoelectric energy harvesting in unmanned air vehicle (UAV) applications through flight testing of a remote controlled aircraft. It is stated that the choice of their particular plane is of primary importance because of its long wingspan and flexible foam wings, which provide a good environment for piezoelectric vibration harvesting using wing deflections. It is reported that a small battery can be fully charged when increasing the volume of piezoelectric material. [PERSON] and [PERSON] [9] are among the first researchers who analyzed theoretically and experimentally a two-degree-of-freedom typical section model as a power harvesting device driven by aeroelastic vibrations. In [9], a time-domain switching energy extracting scheme is considered in order to increase the level of the harvested power. A wind tunnel testing demonstrates that the wing section geometry does not affect the linear flutter speed and its frequency. The authors show that the optimal wing profile depends on the operating range of wind speeds and on the required level of harvested power.