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A New Numerical Modeling of an Axially Functionally Graded Piezoelectric Beam

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Abstract

Purpose

In this work, a new numerical modeling is proposed to demonstrate vibration behavior of an axially functionally graded piezoelectric material (AFGPM) beam. The effective material constants are supposed to have an axial variation in accordance with power law and exponential law distributions. The beam is actuated using the piezoelectric shear effect.

Methods

The Hamilton principle is employed to derive the equations of motion and boundary conditions. The generalized differential quadrature technique is used to convert available partial differential equations into linear algebraic form. The MATLAB code is developed to solve the linear algebraic equations. The natural frequencies are compared with the natural frequencies obtained in previous published work for reduce case.

Results

The effects of slenderness ratios, volume fraction indices, boundary conditions and exponent parameters on the natural frequencies of the AFGPM beam are reported.

Conclusions

It can be observed that the natural frequency decreases with increase in volume fraction index under both clamped-clamped (C-C) and clamped-free (C-F) boundary conditions. With the increase of length of the beam, the natural frequency decreases under both clamped-clamped (C-C) and clamped-free (C-F) boundary conditions. The clamped-clamped AFGPM beam has large frequency as compared to the natural frequency of clamped-free AFGPM beam. The above observations are made for the AFGPM beam where the material properties are varied along the axial direction according to the power law. Next, the observations are made for the AFGPM beam where the material properties are varied in the axial direction according to an exponential law. It can be seen that the natural frequency decreases with an increase in the exponent parameter from -1 to 0 for all slenderness ratios. When the exponent parameter is further increases from 0 to 1, the natural frequency increases under clamped-clamped boundary condition. While, the natural frequency decreases continuously with the increase of the exponent parameters under clamped-free boundary condition.

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The authors received no financial support for the research, authorship, and/or publication of this article.

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  1. Department of Mechanical Engineering, Rajasthan Technical University Kota, Kota, India

    B. Gupta, P. Sharma & S. K. Rathore

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  1. B. Gupta
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Correspondence to B. Gupta.

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Gupta, B., Sharma, P. & Rathore, S.K. A New Numerical Modeling of an Axially Functionally Graded Piezoelectric Beam. J. Vib. Eng. Technol. 10, 3191–3206 (2022). https://doi.org/10.1007/s42417-022-00550-8

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  • DOI: https://doi.org/10.1007/s42417-022-00550-8

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