A modified Fourier series solution for vibration analysis of truncated conical shells with general boundary conditions

Jin, Guoyong; Ma, Xianglong; Shi, Shuangxia; Ye, Tiangui; Liu, Zhigang

doi:10.1016/j.apacoust.2014.04.007

Cited by 83 publications

(23 citation statements)

References 21 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The static and dynamic characteristics of this shell-type of structures have been of great interest to many researchers [1][2][3][4][5][6][7][8][9][10][11][12][13]. Irie et al [1,2] analyzed free vibration characteristics of conical shells with constant and variable thickness using the transfer matrix method.…”

Section: Introductionmentioning

confidence: 99%

“…Lam and Hua [10] also presented the influence of orthotropic material on frequencies characteristics of thin truncated circular symmetrical cross-ply laminated conical shells using the GDQ method. Omer [11], Liew et al [12], Jin et al [13] performed free vibration analysis of conical shells using discrete singular convolution (DSC) method, the element-free kp-Ritz method and the modified Fourier series solution, respectively. The literature clearly shows that there is few investigation on vibration of conical shells with variable thickness.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Free vibration analysis of truncated circular conical shells with variable thickness using the Haar wavelet method

Dai¹,

Cao²,

Chen³

2016

J. vibroeng.

View full text Add to dashboard Cite

Abstract. This paper investigates the free vibration characteristics of truncated conical shells with variable thickness using the Haar wavelet method. Based on the Love first-approximation theory, the governing partial differential equations are formulated, which are transformed into ordinary differential equations using the separation of variables. The Haar wavelet discretization method is introduced to predict the dynamic characteristics of truncated circular conical shells with linearly and parabolically varying thickness. The present analysis is validated by comparing the numerical results with those available in the literature and very good agreement is achieved. The effects of geometrical parameters and boundary conditions on the vibration characteristics of conical shells with variable thickness are presented. The advantages of this method consist in its simplicity, fast convergence and high precision.

show abstract

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Free vibration analysis of truncated circular conical shells with variable thickness using the Haar wavelet method

Dai¹,

Cao²,

Chen³

2016

J. vibroeng.

View full text Add to dashboard Cite

show abstract

“…In order to verify the results, the reduced case of constant thickness is compared with the value of fundamental frequency λ obtained by Daneshjou Table 2. 16,[31][32][33] In this study, the frequency parameter λ for antisymmetric angle-ply of conical shells is investigated using two different material properties, i.e., Graphite Epoxy (AS4/3501-6) (AGE) and Kevler-49 Epoxy (KGE). Two and four layers of materials are considered to analyse the problem where the materials are arranged in the form of KGE-KGE and AGE-KGE-KGE-AGE respectively.…”

Section: Resultsmentioning

confidence: 99%

“…15 A modified Fourier series was used by Jin et al to analyse the vibration of truncated conical shells with general boundary conditions and the effect of elastic restraint parameters, semi-vertex angle and the ratio of length to radius. 16 Malekzadech and Daraie presented a study on the dynamic behaviour of functionally graded (FG) truncated conical shells subjected to asymmetric internal ring-shaped moving loads. 17 He used FEM alongside Newmark's time integration scheme to discretize the equations of motion in the spatial and temporal domain, respectively to solve the problem.…”

Section: Introductionmentioning

confidence: 99%

Free Vibration of Angle-ply Laminated Conical Shell Frusta with Linear and Exponential Thickness Variations

Viswanathan¹,

Hafizah²,

Aziz³

2018

IJAV

View full text Add to dashboard Cite

Free vibration of laminated conical shell frusta of variable thickness is studied using spline approximation. This problem includes first order shear deformation and considers shells as antisymmetric angle-ply orientation. The governing differential equations of the shells are resolved in terms of displacement functions and rotational functions. These functions are approximated using splines and the method of collocation is adopted for simultaneous algebraic equations. These equations become generalized eigenvalue problems and are solved numerically to avail eigenfrequencies and the corresponding eigenvectors. The variation of frequencies is analysed with respect to the cone angle, aspect ratio, material properties, number of layers, and thickness variation.

show abstract

“…Later, the method fast extended to cope with other structures (i.e. beams, plates, shells and coupled structures) by the Du [27][28][29][30], Jin [31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46], Wang et al [47][48][49][50][51][52] in the last ten years due to the superiority compared with other methods. The detailed theoretical analyses and mathematical principle can been seen in Refs [24][25][26].…”

Section: Introductionmentioning

confidence: 99%

Vibrations of Composite Laminated Circular Panels and Shells of Revolution with General Elastic Boundary Conditions via Fourier-Ritz Method

Wang

Shi

Pang

et al. 2016

Curved and Layered Structures

View full text Add to dashboard Cite

A Fourier-Ritz method for predicting the free vibration of composite laminated circular panels and shells of revolution subjected to various combinations of classical and non-classical boundary conditions is presented in this paper. A modified Fourier series approach in conjunction with a Ritz technique is employed to derive the formulation based on the first-order shear deformation theory. The general boundary condition can be achieved by the boundary spring technique in which three types of liner and two types of rotation springs along the edges of the composite laminated circular panels and shells of revolution are set to imitate the boundary force. Besides, the complete shells of revolution can be achieved by using the coupling spring technique to imitate the kinematic compatibility and physical compatibility conditions of composite laminated circular panels at the common meridian with θ = 0 and 2π. The comparisons established in a sufficiently conclusive manner show that the present formulation is capable of yielding highly accurate solutions with little computational effort. The influence of boundary and coupling restraint parameters, circumference angles, stiffness ratios, numbers of layer and fiber orientations on the vibration behavior of the composite laminated circular panels and shells of revolution are also discussed.

show abstract

A modified Fourier series solution for vibration analysis of truncated conical shells with general boundary conditions

Cited by 83 publications

References 21 publications

Free vibration analysis of truncated circular conical shells with variable thickness using the Haar wavelet method

Free vibration analysis of truncated circular conical shells with variable thickness using the Haar wavelet method

Free Vibration of Angle-ply Laminated Conical Shell Frusta with Linear and Exponential Thickness Variations

Vibrations of Composite Laminated Circular Panels and Shells of Revolution with General Elastic Boundary Conditions via Fourier-Ritz Method

Contact Info

Product

Resources

About