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In this article the vibration analysis of a viscoelastic cantilever beam with piezoelectric layers under aeroelastic force and base excitation is investigated. The beam viscoelastic material is assumed to obey the Kelvin-Voight model. Also the piezoelectric layers are located at the top and bottom beam surfaces with series connections. The aeroelastic force based on piston theory is considered to act as an external force on the beam and also the base excitation is assumed to be random. In this research the cantilever beam with two piezoelectric layers are considered as a mechanism to harvest the bending vibration energy. First, the Galerkin method is used to convert the governing partial differential equation into a set of ordinary differential equations. Then the resulted nonlinear ordinary differential equation coupled with electrical circuit equation of piezoelectric layer are solved numerically by Rung-Kutta method. Finally, by analyzing the response of the governing equations, the influence of the system parameters on the vibration behavior of beam and output voltage are discussed. Results show that the increase of fluid velocity increases vibrational energy system which leads to increase of both vibration amplitude and output voltage. In addition, it was shown that structural damping has a significant impact on the output voltage.

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The aim of the proposed study is to investigate the size dependent behavior of the micro-bridge gyroscopes under the combined effects of instantaneous DC voltage and harmonic base excitation. To do so, modified couple stress theory is utilized to model the size-dependent behavior of the micro-gyroscope. To avoid resonance, viscous damping is used. Hamilton’s principle is then employed to derive the governing equations of motion. Afterwards, to convert the partial differential equations of motion to ordinary differential equations of motion, a Galerkin based single mode approximation is made. Then fourth-order Range-Kutta method is used to solve the governing equations of motion. To check the accuracy of the present model, the results are then validated through comparison with the available results in the literature and the comparison shows good agreements. In addition to the previous comparison, the present results are the validated through comparison with the results of COMSOL simulation. Furthermore, the effects of different parameters on the dynamic pull-in instability and amplitude of the vibrations are investigated. The observation shows that for the case of the harmonic base excitation, the system will be excited on two frequencies.

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The theory of mechanical-vibration energy harvesting from the environment has been studied by researchers in the recent decade. In the present research, the vibration of the viscoelastic cantilever beam was analyzed with two piezoelectric layers including series and parallel connections. The beam was exposed under moving and rotating base excitation and aero-elastic force. The beam viscoelastic material was described using the generalized Kelvin-Voigt mechanical model. The aero-elastic force based on piston theory is considered while the base excitation is selected harmonic and randomly. The stress field coupling among the beam and piezoelectric as well as Gauss equation were utilized to extract the vibration and electrical equations respectively. The vibratory equation was converted into a set of ordinary differential equations using the Galerkin approach. The obtained equations with electrical equation were solved by the Runge-Kutta method numerically. Then, by studying the response of the governing equations, the effect of system parameters on the vibrational behavior of the beam and the output voltage was investigated. The results showed that the system and response frequencies are not affected via circuit connection types (series or parallel). The natural vibratory frequency is increased with enhancing the beam stiffness. The structural damping has a significant effect on the output voltage value. Also, the output voltage is increased by enhancing the environmental pressure.