Free vibration of a conical shell with variable thickness

An analytical method is presented for the free vibration of a fluid loaded (submerged) ring-stiffened conical shell with variable thickness in the low frequency range. Based on the Flügge theory and equivalent method of ring-stiffeners, the governing equations of vibration of a ring-stiffened conical shell are developed in the form of a coupled set of the first order differential equations. Fluid loading is taken into account by dividing the shell into narrow strips which are considered to be locally cylindrical. Analytical solutions are presented by using the transfer matrix method, which is suitable for structures broken into a sequence of subsystems that interact only with adjacent subsystems. By comparing the results from the present method and the finite element model, good agreement are obtained. The effects of the spacing of the stiffeners, the shell thickness, the shell thickness ratio, the ring's height, and the boundary conditions on the natural frequencies of the fluid loaded ring-stiffened conical shell with variable thickness are discussed.

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Free vibration analysis of laminated composite conical, cylindrical shell and annular plate with variable thickness and general boundary conditions

10.21203/rs.3.rs-1096118/v1 ◽

2021 ◽

Author(s):

Kwang Hun Kim ◽

Songhun Kwak ◽

Kwangil An ◽

Kyongjin Pang ◽

Pyol Kim

Keyword(s):

Cylindrical Shell ◽

Free Vibration ◽

Boundary Conditions ◽

Variable Thickness ◽

Conical Shell ◽

Annular Plate ◽

Laminated Composite ◽

Haar Wavelet ◽

Algebraic Equations ◽

Arbitrary Boundary

Abstract This paper presents a unified solution method to investigate the free vibration behaviors of laminated composite conical shell, cylindrical shell and annular plate with variable thickness and arbitrary boundary conditions using the Haar wavelet discretization method (HWDM). Theoretical formulation is established based on the first order shear deformation theory(FSDT) and displacement components are extended Haar wavelet series in the axis direction and trigonometric series in the circumferential direction. The constants generating by the integrating process are disposed by boundary conditions, and thus the equations of motion of total system including the boundary condition are transformed into an algebraic equations. Then natural frequencies of the laminated composite structures are directly obtained by solving these algebraic equations. Stability and accuracy of the present method are verified through convergence and validation studies. Effects of some material properties and geometric parameters on the free vibration of laminated composite shells are discussed and some related mode shapes are given. Some new results for laminated composite conical shell, cylindrical shell and annular plate with variable thickness and arbitrary boundary conditions are presented, which may serve as benchmark solutions.

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Free vibration of symmetric angle-ply layered conical shell frusta of variable thickness under shear deformation theory

STRUCTURAL ENGINEERING AND MECHANICS ◽

10.12989/sem.2013.45.2.259 ◽

2013 ◽

Vol 45 (2) ◽

pp. 259-275 ◽

Cited By ~ 7

Author(s):

K.K. Viswanathan ◽

Saira Javed ◽

Zainal Abdul Aziz

Keyword(s):

Free Vibration ◽

Shear Deformation ◽

Variable Thickness ◽

Conical Shell ◽

Deformation Theory ◽

Shear Deformation Theory

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Exact solution for free vibration analysis of linearly varying thickness FGM plate using Galerkin-Vlasov’s method

Proceedings of the Institution of Mechanical Engineers Part L Journal of Materials Design and Applications ◽

10.1177/1464420720980491 ◽

2020 ◽

pp. 146442072098049

Author(s):

V Kumar ◽

SJ Singh ◽

VH Saran ◽

SP Harsha

Keyword(s):

Free Vibration ◽

Variable Thickness ◽

Vibration Analysis ◽

Shear Deformation Theory ◽

Free Vibration Analysis ◽

Functionally Graded ◽

Constant Thickness ◽

Engineering Structures ◽

Property Variation ◽

Varying Thickness

The present paper investigates the free vibration analysis for functionally graded material plates of linearly varying thickness. A non-polynomial higher order shear deformation theory is used, which is based on inverse hyperbolic shape function for the tapered FGM plate. Three different types of material gradation laws, specifically: a power (P-FGM), exponential (E-FGM), and sigmoid law (S-FGM) are used to calculate the property variation in the thickness direction of FGM plate. The variational principle has been applied to derive the governing differential equation for the plates. Non-dimensional frequencies have been evaluated by considering the semi-analytical approach viz. Galerkin-Vlasov’s method. The accuracy of the preceding formulation has been validated through numerical examples consisting of constant thickness and tapered (variable thickness) plates. The findings obtained by this method are found to be in close agreement with the published results. Parametric studies are then explored for different geometric parameters like taper ratio and boundary conditions. It is deduced that the frequency parameter is maximum for S-FGM tapered plate as compared to E- and P-FGM tapered plate. Consequently, it is concluded that the S-FGM tapered plate is suitable for those engineering structures that are subjected to huge excitations to avoid resonance conditions. In addition, it is found that the taper ratio is significantly affected by the type of constraints on the edges of the tapered FGM plate. Some novel results for FGM plate with variable thickness are also computed that can be used as benchmark results for future reference.

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