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

Wang, Qingshan; Shi, Dongyan; Pang, Fuzhen; Liang, Qian

doi:10.1515/cls-2016-0010

Cited by 26 publications

(10 citation statements)

References 55 publications

(69 reference statements)

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“…For the arbitrary elastic-supported case, the potential energy with the five kinds of restrained springs [68][69][70][71][72][73][74], which is the simulation of boundary conditions, should be written as…”

Section: Energy Expressionsmentioning

confidence: 99%

Free Vibration Analysis of the Unified Functionally Graded Shallow Shell with General Boundary Conditions

Shi

Zha

Zhang

et al. 2017

Shock and Vibration

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The free vibration analysis of the functionally graded (FG) double curved shallow shell structures with general boundary conditions is investigated by an improved Fourier series method (IFSM). The material properties of FG structures are assumed to vary continuously in the thickness direction, according to the four graded parameters of the volume distribution function. Under the current framework, the displacement and rotation functions are set to a spectral form, including a double Fourier cosine series and two supplementary functions. These supplements can effectively eliminate the discontinuity and jumping phenomena of the displacement function along the edges. The formulation is based on the first-order shear deformation theory (FSDT) and RayleighRitz technique. This method can be universally applied to the free vibration analysis of the shallow shell, because it only needs to change the relevant parameters instead of modifying the basic functions or adapting solution procedures. The proposed method shows excellent convergence and accuracy, which has been compared with the results of the existing literatures. Numerous new results for free vibration analysis of FG shallow shells with various boundary conditions, geometric parameter, material parameters, gradient parameters, and volume distribution functions are investigated, which may serve as the benchmark solution for future researches.

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Section: Energy Expressionsmentioning

confidence: 99%

Free Vibration Analysis of the Unified Functionally Graded Shallow Shell with General Boundary Conditions

Shi

Zha

Zhang

et al. 2017

Shock and Vibration

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“…The first two laminated shells are taken from the work by Wang et al [13] and they are employed to compare the results given by the current approach with the ones obtained by using the Fourier-Ritz Method. The reference surface of the toro-circular panel at issue (Figure 4a,b) can be described by the following position vector r(ϕ, ϑ)…”

Section: Free Vibrations Of Laminated Composite Shellsmentioning

confidence: 99%

“…Their interest in this subject is mainly due to the fact that the use of advanced materials has shown inadequacy of the classical or first-order theories to capture the effective mechanical behavior of this class of materials, such as laminated composites or functionally graded materials [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. In these particular circumstances, the fundamental hypotheses of a lower-order model could lead to inaccurate results since some effects are neglected or not even considered.…”

Section: Introductionmentioning

confidence: 99%

An Equivalent Layer-Wise Approach for the Free Vibration Analysis of Thick and Thin Laminated and Sandwich Shells

et al. 2016

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Abstract:The main purpose of the paper is to present an innovative higher-order structural theory to accurately evaluate the natural frequencies of laminated composite shells. A new kinematic model is developed starting from the theoretical framework given by a unified formulation. The kinematic expansion is taken as a free parameter, and the three-dimensional displacement field is described by using alternatively the Legendre or Lagrange polynomials, following the key points of the most typical Layer-wise (LW) approaches. The structure is considered as a unique body and all the geometric and mechanical properties are evaluated on the shell middle surface, following the idea of the well-known Equivalent Single Layer (ESL) models. For this purpose, the name Equivalent Layer-Wise (ELW) is introduced to define the present approach. The governing equations are solved numerically by means of the Generalized Differential Quadrature (GDQ) method and the solutions are compared with the results available in the literature or obtained through a commercial finite element program. Due to the generality of the current method, several boundary conditions and various mechanical and geometric configurations are considered. Finally, it should be underlined that different doubly-curved surfaces may be considered following the mathematical framework given by the differential geometry.

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“…The improved Fourier series was proposed in 2000 by Li [47][48][49] to solve the free vibrations of beams with general boundary conditions. Later, the method has been fast extended by Du [50][51][52][53], Jin [54][55][56][57][58], Wang [59][60][61][62][63][64][65][66][67][68][69][70][71][72][73][74][75][76][77]et al in the last ten years. Thus, as a powerful method, the reasonable and superiority has been widely validated by comparing with other methods.…”

Section: Introductionmentioning

confidence: 99%

Free vibration of functionally graded parabolic and circular panels with general boundary conditions

Zhang

Shi

Wang

et al. 2017

Curved and Layered Structures

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Abstract:The purpose of this content is to investigate the free vibration of functionally graded parabolic and circular panels with general boundary conditions by using the Fourier-Ritz method. The first-order shear deformation theory is adopted to consider the effects of the transverse shear and rotary inertia of the panel structures. The functionally graded panel structures consist of ceramic and metal which are assumed to vary continuously through the thickness according to the power-law distribution, and two types of power-law distributions are considered for the ceramic volume fraction. The improved Fourier series method is applied to construct the new admissible function of the panels to surmount the weakness of the relevant discontinuities with the original displacement and its derivatives at the boundaries while using the traditional Fourier series method. The boundary spring technique is adopted to simulate the general boundary condition. The unknown coefficients appearing in the admissible function are determined by using the Ritz procedure based on the energy functional of the panels. The numerical results show the present method has good convergence, reliability and accuracy. Some new results for functionally graded parabolic and circular panels with different material distributions and boundary conditions are provided, which may serve as benchmark solutions.

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

Cited by 26 publications

References 55 publications

Free Vibration Analysis of the Unified Functionally Graded Shallow Shell with General Boundary Conditions

Free Vibration Analysis of the Unified Functionally Graded Shallow Shell with General Boundary Conditions

An Equivalent Layer-Wise Approach for the Free Vibration Analysis of Thick and Thin Laminated and Sandwich Shells

Free vibration of functionally graded parabolic and circular panels with general boundary conditions

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