A unified analysis for the transient response of composite laminated curved beam with arbitrary lamination schemes and general boundary restraints

Shao, Dong; Hu, Shenghai; Wang, Qingshan; Pang, Fuzhen

doi:10.1016/j.compstruct.2016.07.070

Cited by 58 publications

(12 citation statements)

References 55 publications

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“…Five types of spring are used to describe the boundary conditions of laminated foundation plate, which are linear springs ( , V , and ) and rotational springs ( , ), respectively. The arbitrary boundary conditions can be realized by setting the stiffness values of the five different springs [46][47][48][49][50]. For instance, the free boundary condition can be easily gained when the spring stiffness values on the four edges are zero.…”

Section: Establishment Of the Modelmentioning

confidence: 99%

Free and Forced Vibration of the Moderately Thick Laminated Composite Rectangular Plate on Various Elastic Winkler and Pasternak Foundations

Shi

Zhang

Wang

et al. 2017

Shock and Vibration

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An improved Fourier series method (IFSM) is applied to study the free and forced vibration characteristics of the moderately thick laminated composite rectangular plates on the elastic Winkler or Pasternak foundations which have elastic uniform supports and multipoints supports. The formulation is based on the first-order shear deformation theory (FSDT) and combined with artificial virtual spring technology and the plate-foundation interaction by establishing the two-parameter foundation model. Under the framework of this paper, the displacement and rotation functions are expressed as a double Fourier cosine series and two supplementary functions which have no relations to boundary conditions. The Rayleigh-Ritz technique is applied to solve all the series expansion coefficients. The accuracy of the results obtained by the present method is validated by being compared with the results of literatures and Finite Element Method (FEM). In this paper, some results are obtained by analyzing the varying parameters, such as different boundary conditions, the number of layers and points, the spring stiffness parameters, and foundation parameters, which can provide a benchmark for the future research.

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Section: Establishment Of the Modelmentioning

confidence: 99%

Free and Forced Vibration of the Moderately Thick Laminated Composite Rectangular Plate on Various Elastic Winkler and Pasternak Foundations

Shi

Zhang

Wang

et al. 2017

Shock and Vibration

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“…In the practical application, the Pasternak model (also referred to as the two-parameter model) [24][25][26] is widely used to describe the mechanical behavior of the foundation, in which the wellknown Winkler model [27] is a special case. In addition, the boundary condition may not always be classical case in reality, and a variety of possible boundary conditions including classical boundary conditions, elastic boundary restraints, and the combinations of two or more conditions may be encountered [6][7][8][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47]. Based on the open published paper, we can know that merely Zhou et al [48,49] extended the Chebyshev-Ritz method to study the free vibration characteristics of rectangular thick plates and thick circular plates resting on elastic foundations, respectively.…”

Section: Introductionmentioning

confidence: 99%

Three-Dimensional Vibration Analysis of Rectangular Thick Plates on Pasternak Foundation with Arbitrary Boundary Conditions

Liu

Jing

et al. 2017

Shock and Vibration

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This paper presents the first known vibration characteristic of rectangular thick plates on Pasternak foundation with arbitrary boundary conditions on the basis of the three-dimensional elasticity theory. The arbitrary boundary conditions are obtained by laying out three types of linear springs on all edges. The modified Fourier series are chosen as the basis functions of the admissible function of the thick plates to eliminate all the relevant discontinuities of the displacements and their derivatives at the edges. The exact solution is obtained based on the Rayleigh-Ritz procedure by the energy functions of the thick plate. The excellent accuracy and reliability of current solutions are demonstrated by numerical examples and comparisons with the results available in the literature. In addition, the influence of the foundation coefficients as well as the boundary restraint parameters is also analyzed, which can serve as the benchmark data for the future research technique.

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“…The method has been subsequently exploited to determine the vibration behaviors of structures [33][34][35][36][37][38][39][40][41][42][43][44][45][46][47][48]. Recently, a new method of Fourier-Ritz approach was proposed by Jin et al [49], based on the improved Fourier series method to analyze the free vibration of laminated functionally graded shallow shells with general boundary conditions.…”

Section: Introductionmentioning

confidence: 99%

The Modified Fourier-Ritz Approach for the Free Vibration of Functionally Graded Cylindrical, Conical, Spherical Panels and Shells of Revolution with General Boundary Condition

Pang

et al. 2017

Mathematical Problems in Engineering

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The aim of this paper is to extend the modified Fourier-Ritz approach to evaluate the free vibration of four-parameter functionally graded moderately thick cylindrical, conical, spherical panels and shells of revolution with general boundary conditions. The first-order shear deformation theory is employed to formulate the theoretical model. In the modified Fourier-Ritz approach, the admissible functions of the structure elements are expanded into the improved Fourier series which consist of two-dimensional (2D) Fourier cosine series and auxiliary functions to eliminate all the relevant discontinuities of the displacements and their derivatives at the edges regardless of boundary conditions and then solve the natural frequencies by means of the Ritz method. As one merit of this paper, the functionally graded cylindrical, conical, spherical shells are, respectively, regarded as a special functionally graded cylindrical, conical, spherical panels, and the coupling spring technology is introduced to ensure the kinematic and physical compatibility at the common meridian. The excellent accuracy and reliability of the unified computational model are compared with the results found in the literatures.

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A unified analysis for the transient response of composite laminated curved beam with arbitrary lamination schemes and general boundary restraints

Cited by 58 publications

References 55 publications

Free and Forced Vibration of the Moderately Thick Laminated Composite Rectangular Plate on Various Elastic Winkler and Pasternak Foundations

Free and Forced Vibration of the Moderately Thick Laminated Composite Rectangular Plate on Various Elastic Winkler and Pasternak Foundations

Three-Dimensional Vibration Analysis of Rectangular Thick Plates on Pasternak Foundation with Arbitrary Boundary Conditions

The Modified Fourier-Ritz Approach for the Free Vibration of Functionally Graded Cylindrical, Conical, Spherical Panels and Shells of Revolution with General Boundary Condition

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