Thermoelastic Vibration Analysis of Laminated Doubly Curved Shallow Panels Using Non-Linear FEM

Mahapatra, Trupti Ranjan; Panda, Sidhartha

doi:10.1080/01495739.2014.976125

Cited by 40 publications

(6 citation statements)

References 22 publications

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“…Some literature reviews on nonlinear vibrations of plates were given by Chia [2,3] and Mehar and Panda [4]. e nonlinear vibrations of laminated composite spherical shell panels were also entirely investigated by Mahapatra et al [5][6][7][8][9]. e vibration, bending, and buckling behaviors about the functionally graded sandwich structure have been investigated by Mehar et al [10][11][12][13] and Kar and Panda [14][15][16].…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Vibrations of Laminated Cross-Ply Composite Cantilever Plate in Subsonic Air Flow

Liu

Zhang

2020

Mathematical Problems in Engineering

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The nonlinear vibrations and responses of a laminated composite cantilever plate under the subsonic air flow are investigated in this paper. The subsonic air flow around the three-dimensional cantilever rectangle laminated composite plate is considered to be decreasing from the wing root to the wing tip. According to the ideal incompressible fluid flow condition and the Kutta–Joukowski lift theorem, the subsonic aerodynamic lift on the three-dimensional finite length flat wing is calculated by using the Vortex Lattice (VL) method. The finite length flat wing is modeled as a laminated composite cantilever plate based on Reddy’s third-order shear deformation plate theory and the von Karman geometry nonlinearity is introduced. The nonlinear partial differential governing equations of motion for the laminated composite cantilever plate subjected to the subsonic aerodynamic force are established via Hamilton’s principle. The Galerkin method is used to separate the partial differential equations into two nonlinear ordinary differential equations, and the four-dimensional nonlinear averaged equations are obtained by the multiple scale method. Through comparing the natural frequencies of the linear system with different material and geometric parameters, the relationship of 1 : 2 internal resonance is considered. Corresponding to several selected parameters, the frequency-response curves are obtained. The hardening-spring-type behaviors and jump phenomena are exhibited. The influence of the force excitation on the bifurcations and chaotic behaviors of the laminated composite cantilever plate is investigated numerically. It is found that the system is sensitive to the exciting force according to the complicate nonlinear behaviors exhibited in this paper.

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Section: Introductionmentioning

confidence: 99%

Nonlinear Vibrations of Laminated Cross-Ply Composite Cantilever Plate in Subsonic Air Flow

Liu

Zhang

2020

Mathematical Problems in Engineering

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“…These include the Ritz method [23,24,25,26,27], dynamic stiffness method [28], closed-form solution [29,30,31], boundary domain element method [32], Meshfree approach [33], Galerkin method [34,35], and finite element method [36,37,38].…”

Section: Introductionmentioning

confidence: 99%

Wave Based Method for Free Vibration Analysis of Cross-Ply Composite Laminated Shallow Shells with General Boundary Conditions

Shi

Wang

et al. 2019

Materials

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In this paper, a semi-analytical method is adopted to analyze the free vibration characteristics of composite laminated shallow shells under general boundary conditions. Combining two kinds of shell theory, that is, first-order shear deformation shell theory (FSDT) and classical shell theory (CST), to describe the dynamic relationship between the displacement resultants and force vectors, the theoretical formulations are established. According to the presented work, the displacement and transverse rotational variables are transformed into wave function forms to satisfy the theoretical formulation. Related to diverse boundary conditions, the total matrix of the composite shallow shell can be established. Searching the determinant of the total matrix using the dichotomy method, the natural frequency of composite laminated shallow shells is obtained. Through several classical numerical examples, it is proven that the results calculated by the presented method are more accurate and reliable. Furthermore, to discuss the effect of geometric parameters and material constants on the natural frequencies of composite laminated shallow shells, some numerical examples are calculated to analyze. Also, the influence of boundary elastic restrained stiffness is discussed.

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“…Based on Timoshenko beam theory (TBT) and Gurtin-Murdoch continuum elasticity, Ansari et al 7 presented the vibration and instability characteristics of fluid-conveying nanoscale pipes. Based on HSDT and non-linear finite element method (FEM), non-linear free vibration behavior of laminated composite shells were investigated under uniform thermal loading 8,9 and also considering hygrothermal environment. [10][11][12][13] Based on first-order shear deformation shell theory and Mindlin's strain gradient theory, Ansari et al 14 performed free vibration and stability analysis of FGM nanoshells with internal fluid flow in thermal environment.…”

Section: Introductionmentioning

confidence: 99%

Non-linear forced vibration analysis of higher-order shear-deformable functionally graded material beam in thermal environment subjected to harmonic excitation and resting on non-linear elastic foundation

Paul¹,

Das

2018

The Journal of Strain Analysis for Engineering Design

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Geometrically non-linear forced vibration analysis of higher-order shear-deformable functionally graded material beam under harmonic excitation and supported on three-parameter non-linear elastic foundation is presented. The beam is immovably clamped and is considered to be under static thermal loading due to uniform temperature rise. Reddy's third-order shear-deformable beam theory in conjunction with von Kármán geometric non-linearity is considered to derive the governing equations employing Hamilton's principle, and Ritz method is followed for approximating the displacement and rotation fields. A numerical algorithm based on iterative substitution method and Broyden's method is proposed to predict the stable regions of frequency-response behavior. The frequency-response curves are presented in normalized plane for variations of load-amplitude, elastic foundation parameters, temperature rise, gradation index and functionally graded material composition, and their effects are discussed in detail. It is found that the load-amplitude, elastic foundation parameters, thermal loading and some of the functionally graded material compositions significantly affect the frequency response; whereas, the effect of gradation index is found to be relatively small. A comparative frequency-response curve between Voigt model and Mori-Tanaka scheme of functionally graded material modeling is presented, and it shows negligible difference between these two models. The present problem under thermal environment is studied for the first time through this work, and the proposed model and the numerical algorithm provide a simplified approach to study the non-linear frequency-response behavior.

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Thermoelastic Vibration Analysis of Laminated Doubly Curved Shallow Panels Using Non-Linear FEM

Cited by 40 publications

References 22 publications

Nonlinear Vibrations of Laminated Cross-Ply Composite Cantilever Plate in Subsonic Air Flow

Nonlinear Vibrations of Laminated Cross-Ply Composite Cantilever Plate in Subsonic Air Flow

Wave Based Method for Free Vibration Analysis of Cross-Ply Composite Laminated Shallow Shells with General Boundary Conditions

Non-linear forced vibration analysis of higher-order shear-deformable functionally graded material beam in thermal environment subjected to harmonic excitation and resting on non-linear elastic foundation

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