Free and forced vibration analysis of functionally graded piezoelectric energy harvesters using weak form quadrature element method

Date

2023-8-23

Author

Yıldız, Ragıp Sarper

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The weak form quadrature element method is used in this study to examine the free and forced vibration behavior of functionally graded piezoelectric energy harvester Timoshenko beams. Six piezoelectric energy harvester structures with and without tip mass are formulated, including unimorph and series- or parallel-connected bimorph types. Piezoelectric constitutive equations that couple mechanical strain with electrical displacement are derived to specify piezoelectric materials’ electrical and mechanical characteristics. The Timoshenko Beam Theory is used to determine the displacement fields. The beam’s total kinetic, strain, and internal electrical energies and the non-conservative mechanical and electrical forces are computed to obtain the equation of motion by applying the extended Hamilton’s principle. The quadrature beam element is constructed after a detailed description of the weak-form quadrature element method principles. The displacement functions are altered in accordance with the numerical technique. The free and forced vibration governing formulations are defined separately. Harmonic base displacement is applied to the equation of motion for a steady-state response. In contrast, the work equivalent method is implemented to incorporate externally applied forces into the numerical computation for forced vibration. The used external load types are uniformly distributed step, concentrated step, concentrated harmonic, and concentrated impulsive loads. Dynamic outcomes are achieved by applying the Houbolt and Newmark methods. The steady-state behavior of the piezoelectric energy harvester under base excitation is formulated to validate the methodology by comparing the voltage output frequency response function and natural frequency values in open- and short-circuit states with experimental findings in the literature. Moreover, an analytical solution constructed for the beam displacement response under the four types of external loads is used to validate the numerical method’s efficiency for forced vibration. In parametric analysis, while the Mori-Tanaka micromechanical model is used to demonstrate the influence of substructure material inhomogeneity, Voigt’s rule serves for the piezoelectric characteristics. Frequency response curves and dynamic analysis results are analyzed for six piezoelectric energy harvester configurations regarding load resistance, power-law exponent, tip mass addition, boundary condition, and material structure changes. The weak form quadrature element method is an alternative numerical analysis approach that gives accurate and precise free and forced vibration results that can be easily applied in the design and analysis studies of non-homogeneous functionally graded materials.

Subject Keywords

Functionally graded piezoelectric material, WQEM, Timoshenko beam theory, Frequency response function, Dynamic analysis

URI

https://hdl.handle.net/11511/105269

Collections

Graduate School of Natural and Applied Sciences, Thesis