Mechanical behavior and free vibration analysis of FG doubly curved shells on elastic foundation via a new modified displacements field model of 2D and quasi-3D HSDTs

Rachid, Abderrahman; Ouinas, Djamel; Lousdad, Abdelkader; Zaoui, Fatima Zohra; Achour, Belkacem; Gasmi, Hatem; Butt, Tayyab Ashfaq; Tounsi, Abdelouahed

doi:10.1016/j.tws.2021.108783

Cited by 58 publications

(5 citation statements)

References 54 publications

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“…Li et al [23] investigated the effect of the power law index of the material, pore volume fraction, and temperature variation on the free vibration, steady state, and transient response of functionally graded porous-stepped cylindrical shells based on higher-order shear deformation theory (HSDT). Rachid et al [24] studied the effect of geometric parameters, volume fraction, and base stiffness on the free vibration of functionally graded double-curved shells concerning bending and free vibration. Qin et al [25] studied the effect of the boundary conditions, elastic foundation, and pore coefficient on the vibration characteristics of functionally graded porous graphene platelet reinforced composite (FGP-GPLRC) based on the third-order shear deformation theory (TSDT) cylindrical shells.…”

Section: Of 24mentioning

confidence: 99%

Free Vibration Characteristics Analysis of Metal-Rubber Cylindrical Shells Based on Viscoelastic Theory

Deng

et al. 2023

Applied Sciences

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The cylindrical shell made of metal rubber has a strong ability to reduce and absorb vibration, which widens its application in the industrial field. Therefore, it is of great significance to study the vibration characteristics of metal-rubber cylindrical shells (MRCSs). However, there is relatively little research on this aspect. Based on this, the dynamic properties of MRCS are investigated in this paper based on viscoelastic theory, the Rayleigh–Ritz method, and the Gram–Schmidt orthogonal polynomials. The correctness of the proposed model was verified by comparison with the literature and experimental verification. The results show that the preloading state and boundary conditions have significant effects on the natural frequency and modal loss factor of MRCS. The effect of the Pasternak elastic foundation on the natural frequency and modal loss factor of MRCS varies with the change of the axial half wave number m. The effect of the Pasternak elastic foundation on higher-order vibrations is similar to that of the artificial spring technique.

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Section: Of 24mentioning

confidence: 99%

Free Vibration Characteristics Analysis of Metal-Rubber Cylindrical Shells Based on Viscoelastic Theory

Deng

et al. 2023

Applied Sciences

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“…The Navier's procedure [18,57], based on double Fourier series, is employed herein to define the closed-form solution of the partial differential equations (Equation ( 18)) for which the displacement variables satisfying the boundary conditions can be given as…”

Section: Closed-form Solutions For Simply Supported Fg Platesmentioning

confidence: 99%

Mathematical Approach for Mechanical Behaviour Analysis of FGM Plates on Elastic Foundation

et al. 2022

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This paper presents the flexural analysis of functionally graded plates resting on elastic foundations using new two-dimensional (2D) and quasi-three-dimensional (quasi-3D) higher order shear deformation theories. The main interesting feature of this theory is that it proposes a new displacement field with undetermined integral variables which involves only five unknown functions, unlike other shear and normal deformation theories, hence making it easier to use. A parabolic transverse shear deformation shape function satisfying the zero shear stress conditions on the plate outer surfaces is considered. The elastic foundation follows the Pasternak mathematical model. The material properties change continuously across the thickness of the FG plate using different distributions: power law, exponential, and Mori–Tanaka models. The governing equations of FG plates subjected to sinusoidal and uniformly distributed loads are established through the principle of virtual works and then solved via Navier’s procedure. In this work, a detailed discussion on the influence of material composition, geometric parameters, stretching effect, and foundation parameters on the deflection, axial displacements, and stresses is given, and the obtained results are compared with those published in previous works to demonstrate the accuracy and the simplicity of the present formulations. The different obtained results were found to be in good agreement with the available solutions of other higher-order theories. The proposed model is able to represent the cross section warping in the deformed shape and to demonstrate the validity and efficiency of the approach, the findings reported herein prove that this theory is capable of predicting displacements and stresses more accurately than other theories, as its results are closer when compared to numerical methods reported in other literatures.

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“…Huang et al [22] studied the nonlinear dynamic performance of functionally graded material plates using an improved perturbation technique. Rachid et al [23] and Vu et al [24] used different quasi-3D theories to analyze the static response of the plate. Kumar et al [25] investigated the vibration performance of stepped FGM plates using the dynamic stiffness method.…”

Section: Introductionmentioning

confidence: 99%

Bending Analysis of Stepped Rectangular Plates Resting on an Elastic Half-Space Foundation

Zhang

2023

Buildings

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In this paper, the bending behavior of rectangular plates with stepped thickness resting on an elastic half-space foundation is investigated through an analytic method. Combined with the bending theory of the rectangular thin and moderately thick plate, the stepped rectangular plate is divided into upper and lower plates, and the Fourier series is used to obtain the analytical solution of the deflection of the plate and the interaction force between the plate and foundation. The influence of the elastic modulus of the plate, plate theory, and the dimension of the plate on the deflection of the stepped rectangular plate is also discussed. The results show that the analytical solution is basically the same as the existing research results, and it is also verified by the analysis results of the models established by ABAQUS software. The deflection at the center of the stepped rectangular plate increases with the increase of the elastic modulus of the upper plate and the decrease of the side length of the upper plate, while the plate theory has little effect on the deflection of the plate. This method not only overcomes some of the disadvantages of numerical methods but also eliminates the assumptions of the Winkler foundation model and the two-parameter foundation model, thus obtaining a more reasonable and accurate bending performance of the stepped rectangular plate resting on the elastic half-space foundation.

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Mechanical behavior and free vibration analysis of FG doubly curved shells on elastic foundation via a new modified displacements field model of 2D and quasi-3D HSDTs

Cited by 58 publications

References 54 publications

Free Vibration Characteristics Analysis of Metal-Rubber Cylindrical Shells Based on Viscoelastic Theory

Free Vibration Characteristics Analysis of Metal-Rubber Cylindrical Shells Based on Viscoelastic Theory

Mathematical Approach for Mechanical Behaviour Analysis of FGM Plates on Elastic Foundation

Bending Analysis of Stepped Rectangular Plates Resting on an Elastic Half-Space Foundation

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