A Simple-FSDT-Based Isogeometric Method for Piezoelectric Functionally Graded Plates

Liu, Tao; Li, Chaodong; Wang, Chao; Lai, Joel Weijia; Cheong, Kang Hao

doi:10.3390/math8122177

Cited by 15 publications

(5 citation statements)

References 46 publications

(55 reference statements)

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“…In the literature various numerical methods were combined for predicting the behaviors of FGM plates. A broad review of them is presented (e.g., in Refs [17,18]). The authors of Refs [17,18] proposed novel numerical methods for the analysis of FGM and piezoelectric FGM structure (square plates, skew plates, and toruses).…”

Section: Methods Of the Solutionmentioning

confidence: 99%

Triangular Functionally Graded Porous Moderately Thick Plates—Deformations and Free Vibrations

Muc

2021

J. Compos. Sci.

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Since the finite element analysis of deformations for plates made of functionally graded materials cannot be carried out with the use of commercial FE packages, aconsistent method of analytical analysis is proposed in the paper. The method of the analysis is based on the application of the weighted residuals and the Bubnov–Galerkin method. The 2D formulation of moderately thick plates is adopted herein for classical and transverse shear deformation plate models (first and third order). Plate deformations subjected to uniform normalpressure and free vibrations are considered. The validity of the analytical model was verified by the comparison of results with FE analysis for isotropic plates. Two correction multipliers were proposed in order to take into account the unsymmetric composition of functionally graded porous plate walls.

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Section: Methods Of the Solutionmentioning

confidence: 99%

Triangular Functionally Graded Porous Moderately Thick Plates—Deformations and Free Vibrations

Muc

2021

J. Compos. Sci.

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“…By converging unmanned aerial vehicles, the expected handiwork creates new fields of inquiry [42]. A Simple-FSDT-based iso-geometric approach with the mathematical expression for piezoelectric functionally graded plates has been studied on vibration analysis [43]. Such studies have been found to shape the control of the antenna reflector to the desired shape-a closed-loop iteration based on the influence coefficient matrix and FE model [44].…”

Section: Vibration Controlmentioning

confidence: 99%

A Review of Piezoelectric Material-Based Structural Control and Health Monitoring Techniques for Engineering Structures: Challenges and Opportunities

Aabid

Parveez

Raheman³

et al. 2021

Actuators

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With the breadth of applications and analysis performed over the last few decades, it would not be an exaggeration to call piezoelectric materials “the top of the crop” of smart materials. Piezoelectric materials have emerged as the most researched materials for practical applications among the numerous smart materials. They owe it to a few main reasons, including low cost, high bandwidth of service, availability in a variety of formats, and ease of handling and execution. Several authors have used piezoelectric materials as sensors and actuators to effectively control structural vibrations, noise, and active control, as well as for structural health monitoring, over the last three decades. These studies cover a wide range of engineering disciplines, from vast space systems to aerospace, automotive, civil, and biomedical engineering. Therefore, in this review, a study has been reported on piezoelectric materials and their advantages in engineering fields with fundamental modeling and applications. Next, the new approaches and hypotheses suggested by different scholars are also explored for control/repair methods and the structural health monitoring of engineering structures. Lastly, the challenges and opportunities has been discussed based on the exhaustive literature studies for future work. As a result, this review can serve as a guideline for the researchers who want to use piezoelectric materials for engineering structures.

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“…Using the simple FSDT (which involves four displacement functions) to model the mechanical displacement of a sandwich plate, in addition to assuming a linearly varying electric potential along the thickness and neglecting the electric field in in-plane directions, Liu et al [38] adopted an isogeometric analysis method to analyze the free vibration, static bending, and dynamic vibration control of sandwich rectangular plates. Rouzegar and Abad [39] proposed a Navy-type solution for a sandwich rectangular plate by using the refined four-variable plate theory to model mechanical displacement and assuming a quadratic electric potential distribution along the thickness direction.…”

Section: Introductionmentioning

confidence: 99%

Levy-type analytical series solution for the three-dimensional free vibrations of functionally graded material rectangular plates with piezoelectric layers

Huang,

Chen,

2023

Smart Mater. Struct.

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Analytical solutions founded on three-dimensional theories play a crucial role in evaluating the credibility and precision of different plate theories and numerical methodologies. While Levy-type analytical solutions are widely recognized, they have been primarily confined to purely elastic plates. This study introduces a Levy-type analytical series solution for three-dimensional vibrations in a sandwich rectangular plate featuring a functionally graded material (FGM) core, along with piezoelectric material (PM) layers on the top and bottom surfaces. The behaviors of the FGM and PM layers were described using three-dimensional elasticity and piezoelasticity theories, respectively. In this study, the displacement functions and electric potential of each layer were expanded by Fourier series and polynomial auxiliary functions. An analytical series solution was then established by satisfying the governing equations of each layer, the mechanical and electric boundary conditions on the six faces of the plate, and the continuity conditions on the interfaces between the PM and FGM layers. To validate the proposed solutions, in-depth convergence studies were conducted for the vibration frequencies of the first six modes of sandwich square plates with various boundary conditions on the other pair of side faces. The well-converged results were then compared with published data based on various plate theories to verify the accuracy of these published data. Finally, accurate nondimensional frequencies were tabulated for the first six modes of sandwich rectangular plates with various aspect ratios, thickness-to-width ratios, PM-to-FGM layer thickness ratios, power law indices for the FGM layer, and six combinations of boundary conditions. These new numerical results when piezoelectric coupling is considered should be very useful to future analytical and numerical studies.

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A Simple-FSDT-Based Isogeometric Method for Piezoelectric Functionally Graded Plates

Cited by 15 publications

References 46 publications

Triangular Functionally Graded Porous Moderately Thick Plates—Deformations and Free Vibrations

Triangular Functionally Graded Porous Moderately Thick Plates—Deformations and Free Vibrations

A Review of Piezoelectric Material-Based Structural Control and Health Monitoring Techniques for Engineering Structures: Challenges and Opportunities

Levy-type analytical series solution for the three-dimensional free vibrations of functionally graded material rectangular plates with piezoelectric layers

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