Free vibration analysis of porous plates with porosity distributions in the thickness and in-plane directions using isogeometric approach

Xue, Yaqiang; Jin, Guoyong; Ma, Xianglong; Chen, Hailong; Ye, Tiangui; Chen, Mingfei; Zhang, Yantao

doi:10.1016/j.ijmecsci.2019.01.004

Cited by 119 publications

(16 citation statements)

References 65 publications

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“…e artificial spring boundary technique and the method of reverberation ray matrix are used together to derive the reverberation ray matrix approach in this section and then to conduct the analysis of in-plane vibration for orthotropic rectangular plates with general boundary conditions [28][29][30][31][32][33].…”

Section: Accurate Solutions For Free In-plane Vibration Of Rectangulamentioning

confidence: 99%

Free In-Plane Vibrations of Orthotropic Rectangular Plates by Using an Accurate Solution

Cao¹,

Zhong

Shao

et al. 2019

Mathematical Problems in Engineering

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Many numerical methods have been developed for in-plane vibration of orthotropic rectangular plates with various boundary conditions; however, the exact results for such structures with elastic boundary conditions are very scarce. Therefore, the object of this paper is to present an accurate solution for free in-plane vibration of orthotropic rectangular plates with various boundary conditions by the method of reverberation ray matrix (MRRM) and improved golden section search (IGSS) algorithm. The boundary condition studied in this paper is defined as that a set of opposite edges is with one kind of simply supported boundary conditions, while the other set is with any kind of classical and general elastic boundary conditions or their combination. Its accuracy, reliability, and efficiency are verified by some numerical examples where the results are compared with other exact solutions in the published literature and the FEA results based on the ABAQUS software. Finally, some new accurate results for free in-plane vibration of orthotropic rectangular plates with elastic boundary conditions are examined and further can be treated as the reference data for other approximate methods or accurate solutions.

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Section: Accurate Solutions For Free In-plane Vibration Of Rectangulamentioning

confidence: 99%

Free In-Plane Vibrations of Orthotropic Rectangular Plates by Using an Accurate Solution

Cao¹,

Zhong

Shao

et al. 2019

Mathematical Problems in Engineering

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“…In this approach, non-uniform rational B-splines (NURBS) functions are used to exactly model the geometry by a coarse discretization mesh (Cottrell et al, 2009). For recent important work on the IGA, one can refer to Lieu et al (2018), Lee et al (2017), Chen et al (2018), Chen et al (2019), Jin et al (2019), and Xue et al (2019).…”

Section: Introductionmentioning

confidence: 99%

Applying isogeometric approach for free vibration, mechanical, and thermal buckling analyses of functionally graded variable-thickness blades

Ansari

Setoodeh

2020

Journal of Vibration and Control

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This article presents free vibration and buckling analyses of functionally graded blades with variable thickness subjected to mechanical and thermal loading using isogeometric analysis as a powerful numerical method. The proposed method is based on deployment of Hamilton’s principle to the two-dimensional kinematics of blades. The governing equations are derived in the context of a modified form of higher order shear deformation plate theory that merely needs C0-continuity (C0-higher order shear deformation plate theory). Without the necessity of defining a shear correction factor, the theory can accurately predict the solution for different thickness-to-length ratios. The numerical predictions for the buckling loads and natural frequencies are successfully compared with the available solutions in the published articles and in the lack of relevant results, finite element analysis using ANSYS is used for verification of the model. The effects of variable thickness and aspect ratio on the natural frequencies and mode shapes known as the frequencies loci veering phenomena are assessed for the first time, which is an important design factor for the blades. The proposed method uses non-uniform rational B-spline element, which is able to approximate linear and nonlinear thickness distribution and the couple modes with an excellent numerical consistency. The influences of aspect ratio, thickness variation, taper ratio, volume fraction exponent, and boundary conditions on the free vibration and buckling of variable-thickness functionally graded blades are also examined.

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“…In their works, they assumed the geometrical nonlinearity based on von Karman's nonlinear theory and used Galerkin's method to solve the equations of motion. Based on FSDT, Xue et al [43] analyzed the free vibration behavior of porous square, circular, and rectangular plates with central hole using isogeometric approach. They considered different types of porosity distribution along the thickness and in-plane directions of the plate.…”

Section: Introductionmentioning

confidence: 99%

Electromechanical Vibration Characteristics of Porous Bimorph and Unimorph Doubly Curved Panels

2020

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The aim of this study is developing an analytical solution for the free vibration of piezoelectric bimorph and unimorph doubly curved panels with a porous substrate. The panel is assumed to be relatively thick, and the effects of its shear deformation are taken into account. Nonlinear models are considered to describe the variation of mechanical properties and of the electric potential within porous host and piezoelectric layers, respectively. Furthermore, short and open circuit electrical conditions are studied to predict the frequency response for sensing and actuation applications. Employing the first-order shear deformation theory (FSDT), in conjunction with the Hamilton’s variational principle and Maxwell’s equation allows deriving six highly coupled partial differential equations to describe the system dynamics under electromechanical coupling. After analytically solving those equations for simply supported panels, the system frequency response is investigated, for various values of design parameters such as porosity, electrical boundary conditions, and geometry. Moreover, some types of smart panels, including bimorphs and unimorphs layouts, are analyzed. The analysis confirms that the above-mentioned parameters play major roles in the natural frequency response of this system and must be carefully considered in the mechatronic design of this smart structure, although they allow to tailor the system behaviour to the selected application.

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Free vibration analysis of porous plates with porosity distributions in the thickness and in-plane directions using isogeometric approach

Cited by 119 publications

References 65 publications

Free In-Plane Vibrations of Orthotropic Rectangular Plates by Using an Accurate Solution

Free In-Plane Vibrations of Orthotropic Rectangular Plates by Using an Accurate Solution

Applying isogeometric approach for free vibration, mechanical, and thermal buckling analyses of functionally graded variable-thickness blades

Electromechanical Vibration Characteristics of Porous Bimorph and Unimorph Doubly Curved Panels

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