A simple first-order shear deformation shell theory for vibration analysis of composite laminated open cylindrical shells with general boundary conditions

Wang, Qingshan; Shao, Dong; Qin, Bin

doi:10.1016/j.compstruct.2017.09.070

Cited by 122 publications

(27 citation statements)

References 93 publications

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“…Each column of the eigenvector matrix is the set of coefficients for the corresponding modes. By substituting the solution from (23) into (18), the corresponding mode shapes can be retrieved accordingly.…”

Section: Admissible Displacement Functions and Deriving Solutionsmentioning

confidence: 99%

“…As one important alternative, the managerial theory-based FSDT were developed, which abandons the hypothesis in CSDT that the transverse normal is still perpendicular to the mid-surface after structural deformation, thus overcoming the defect that the neglect of transverse shear deformation in CSDT [17]. In light of the increasing options of admissible displacement function, the FSDT have been widely used in modeling and analysis of medium thick plates, laminated plates, and moderately thick shells [18][19][20]. Moreover, to further enhance the analysis precision, HSDT were developed, in which the transverse normal is no longer perpendicular to the middle after deformation [21,22].…”

Section: Introductionmentioning

confidence: 99%

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A Unified Approach of Free Vibration Analysis for Stiffened Cylindrical Shell with General Boundary Conditions

Zhang

Yang

Song

2019

Mathematical Problems in Engineering

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A unified approach of free vibration analysis for stiffened cylindrical shell with general boundary conditions is presented in this paper. The vibration of stiffened cylindrical shell is modeled mathematically involving the first-order shear deformation shell theory. The improved Fourier series is selected as the admissible displacement function while the arbitrary boundary conditions are simulated by adjusting the equivalent spring stiffness. The natural frequencies and modal shapes of the stiffened shell are obtained by solving the dynamic model with the Rayleigh-Ritz procedure. Various numerical results of free vibration analysis for stiffened cylindrical shell are obtained, including natural frequencies and modes under simply supported, free, and clamped boundary conditions. Moreover, the effects of stiffener on natural frequencies are discussed. Compared with several state-of-the-art methods, the feasibility and validity of the proposed method are verified.

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Section: Admissible Displacement Functions and Deriving Solutionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A Unified Approach of Free Vibration Analysis for Stiffened Cylindrical Shell with General Boundary Conditions

Zhang

Yang

Song

2019

Mathematical Problems in Engineering

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“…and ρ(z) is the mass density, and the mass moments of inertia I i (i = 0, 1, 2) are defined as [30,33]:…”

Section: Governing Equationsmentioning

confidence: 99%

Free Vibration Analysis of Laminated Functionally Graded Carbon Nanotube-Reinforced Composite Doubly Curved Shallow Shell Panels Using a New Four-Variable Refined Theory

2019

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In this paper, a new four-variable refined shell theory is developed for free vibration analysis of multi-layered functionally graded carbon nanotube-reinforced composite (FG-CNTRC) doubly curved shallow shell panels. The theory has only four unknowns and satisfies zero stress conditions at the free surfaces without correction factor. Five different types of carbon nanotube (CNTs) distribution through the thickness of each FG-CNT layer are considered. Governing equations of simply supported doubly curved FG-CNTRC panels are derived from Hamilton's principle. The resultant eigenvalue system is solved to obtain the frequencies and mode shapes of the anti-symmetric cross-ply laminated panels by using the Navier solution. The numerical results in the comparison examples have proved the accuracy and efficiency of the developed model. Detailed parametric studies have been carried out to reveal the influences of CNTs volume fraction, CNTs distribution, CNTs orientation, dimension ratios and curvature on the free vibration responses of the doubly curved laminated FG-CNTRC panels.

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“…Mindlin plate with arbitrary elastic point edge supports is shown in Figure 1. The boundary conditions are presented by three kinds of restraining springs [29][30][31][32][33][34], namely, translational, rotational, and torsional springs. Springs are evenly arranged on each edge of Mindlin plate.…”

Section: Point-supported Edge Conditions the Rectangularmentioning

confidence: 99%

A Series Solution for the Vibration of Mindlin Rectangular Plates with Elastic Point Supports around the Edges

Pang

et al. 2018

Shock and Vibration

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A series solution for the transverse vibration of Mindlin rectangular plates with elastic point supports around the edges is studied. The series solution for the problem is obtained using improved Fourier series method, in which the vibration displacements and the cross-sectional rotations of the midplane are represented by a double Fourier cosine series and four supplementary functions. The supplementary functions are expressed as the combination of trigonometric functions and a single cosine series expansion and are introduced to remove the potential discontinuities associated with the original admissible functions along the edges when they are viewed as periodic functions defined over the entire x-y plane. This series solution is approximately accurate in the sense that it explicitly satisfies, to any specified accuracy, both the governing equations and the boundary conditions. The convergence, accuracy, stability, and efficiency of the proposed method have been examined through a series of numerical examples. Some numerical examples about the nondimensional frequency and mode shapes of Mindlin rectangular plates with different point-supported edge conditions are given.

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A simple first-order shear deformation shell theory for vibration analysis of composite laminated open cylindrical shells with general boundary conditions

Cited by 122 publications

References 93 publications

A Unified Approach of Free Vibration Analysis for Stiffened Cylindrical Shell with General Boundary Conditions

A Unified Approach of Free Vibration Analysis for Stiffened Cylindrical Shell with General Boundary Conditions

Free Vibration Analysis of Laminated Functionally Graded Carbon Nanotube-Reinforced Composite Doubly Curved Shallow Shell Panels Using a New Four-Variable Refined Theory

A Series Solution for the Vibration of Mindlin Rectangular Plates with Elastic Point Supports around the Edges

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