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

Shi, Dongyan; Zhang, Hong; Wang, Qingshan; Zha, Shuai

doi:10.1155/2017/7820130

Cited by 18 publications

(8 citation statements)

References 66 publications

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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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“…Meanwhile, the HPM also suffers the setback of finding the embedded parameter and initial approximation of the governing equation that satisfies the given conditions. Nonetheless, several researches on a free vibration of circular plates using different methods have been presented in the literature [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25]. Moreover, the reliability and flexibility of the Galerkin method of weighted residual [26] have made it more effective than any other semi-numerical method.…”

Section: Introductionmentioning

confidence: 99%

Investigation of the Dynamic Behaviour of Non-Uniform Thickness Circular Plates Resting on Winkler and Pasternak Foundations

2020

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The study of the dynamic behaviour of non-uniform thickness circular plate resting on elastic foundations is very imperative in designing structural systems. This present research investigates the free vibration analysis of varying density and non-uniform thickness isotropic circular plates resting on Winkler and Pasternak foundations. The governing differential equation is analysed using the Galerkin method of weighted residuals. Linear and nonlinear case is considered, the surface radial and circumferential stresses are also determined. Thereafter, the accuracy and consistency of the analytical solutions obtained are ascertained by comparing the existing results available in pieces of literature and confirmed to be in a good harmony. Also, it is observed that very accurate results can be obtained with few computations. Issues relating to the singularity of circular plate governing equations are handled with ease. The analytical solutions obtained are used to determine the influence of elastic foundations, homogeneity and thickness variation on the dynamic behaviour of the circular plate, the effect of vibration on a free surface of the foundation as well as the influence of radial and circumferential stress on mode shapes of the circular plate considered. From the results, it is observed that a maximum of 8.1% percentage difference is obtained with the solutions obtained from other analytical methods. Furthermore, increasing the elastic foundation parameter increases the natural frequency. Extrema modal displacement occurs due to radial and circumferential stress. Natural frequency increases as the thickness of the circular plate increases, Conversely, a decrease in natural frequency is observed as the density varies. It is envisioned that; the present study will contribute to the existing knowledge of the classical theory of vibration.

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“…In an attempt to fill this gap, the current work presents the dynamic analysis of the rectangular beam-reinforced plate with general boundary restraints, including classical and the elastic restraints as well as elastic coupling of beams and plate. IFSM is extended to construct displacement field of the beam-stiffened plate, which has proven to be a very effective method from existing research [10,[36][37][38].…”

Section: Introductionmentioning

confidence: 99%

Dynamic Analysis of Rectangular Plate Stiffened by Any Number of Beams with Different Lengths and Orientations

Cao¹,

Zhong

Shao

et al. 2019

Shock and Vibration

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The present work is concerned with dynamic characteristics of beam-stiffened rectangular plate by an improved Fourier series method (IFSM), including mobility characteristics, structural intensity, and transient response. The artificial coupling spring technology is introduced to establish the clamped or elastic connections at the interface between the plate and beams. According to IFSM, the displacement field of the plate and the stiffening beams are expressed as a combination of the Fourier cosine series and its auxiliary functions. Then, the Rayleigh–Ritz method is applied to solve the unknown Fourier coefficients, which determines the dynamic characteristics of the coupled structure. The Newmark method is adopted to obtain the transient response of the coupled structure, where the Rayleigh damping is taken into consideration. The rapid convergence of the current method is shown, and good agreement between the predicted results and FEM results is also revealed. On this basis, the effects of the factors related to the stiffening beam (including the length, orientations, and arrangement spacing of beams) and elastic parameters, as well as damping coefficients on the dynamic characteristics of the stiffened plate are investigated.

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

Cited by 18 publications

References 66 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

Investigation of the Dynamic Behaviour of Non-Uniform Thickness Circular Plates Resting on Winkler and Pasternak Foundations

Dynamic Analysis of Rectangular Plate Stiffened by Any Number of Beams with Different Lengths and Orientations

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