Analytical Solution for Rectangular Thick Laminated Plates Subjected to Arbitrary Boundary Conditions

In this study, an improved Fourier series method is presented for the vibration modeling and analysis of moderately thick laminated composite plates with arbitrary boundary conditions, in which the vibration displacements are sought as the linear combination of a double Fourier cosine series and auxiliary series functions. The vibration model was established using the Hamilton energy principle. To study the vibration characteristics of laminated composite plates more comprehensively, firstly, the accuracy of the current results were validated via comparison with previous results and finite element method data. A parametric study was conducted on the effects of several key parameters, such as the h/b ratio, orientation and number of layers. In this section, both solutions are applicable to various combinations of boundary constraints, including classical boundary conditions and elastic-supported boundary conditions. Secondly, in order to identify the action position of vibration and the transmission of vibration energy, the response analysis of laminated plates was studied, and the power flow field for laminated plates was analyzed. Finally, a modal test was introduced to further verify the accuracy of the method in this paper.

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Vibration Analysis of Fiber Reinforced Composite Laminated Plates with Arbitrary Boundary Conditions

Key Engineering Materials ◽

10.4028/www.scientific.net/kem.818.104 ◽

2019 ◽

Vol 818 ◽

pp. 104-112

Author(s):

Ze Chang Xue ◽

Qiu Hong Li ◽

Jiu Fa Wang ◽

Zhong Xin Lan

Keyword(s):

Boundary Conditions ◽

Structural Model ◽

Laminated Plates ◽

Variation Principle ◽

Energy Principle ◽

Arbitrary Boundary ◽

Fourier Cosine ◽

Cosine Series ◽

Arbitrary Boundary Conditions ◽

Composite Laminated Plates

A Fourier series method based on Mindlin theory and Hamilton variation principle has been proposed for the vibration modeling and analysis of composite laminated plates with arbitrary boundary conditions, in which the vibration displacements are sought as the linear combination of a double Fourier cosine series and auxiliary series functions. Three types of constrained springs are introduced to establish a general structural model of composite laminates, and the vibration model is established by combining the Hamilton energy principle. The accuracy, efciency and validity of the two solutions presented are demonstrated via comparison with published results. The influence of boundary conditions, laying angle and laying layer on vibration characteristics is analyzed. And it can be seen that the frequency of the structure increases with the increasing of the spring stiffness and the number of laying layers of the boundary of the laminated plate structure.

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Closed-form solutions for the coupled deflection of anisotropic Euler–Bernoulli composite beams with arbitrary boundary conditions

Thin-Walled Structures ◽

10.1016/j.tws.2021.107479 ◽

2021 ◽

Vol 161 ◽

pp. 107479 ◽

Cited By ~ 1

Author(s):

Pedram Khaneh Masjedi ◽

Olga Doeva ◽

Paul M. Weaver

Keyword(s):

Boundary Conditions ◽

Closed Form ◽

Composite Beams ◽

Arbitrary Boundary ◽

Closed Form Solutions ◽

Arbitrary Boundary Conditions

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A Unified Spectro-Geometric-Ritz Method for Vibration Analysis of Open and Closed Shells with Arbitrary Boundary Conditions

Shock and Vibration ◽

10.1155/2016/4097123 ◽

2016 ◽

Vol 2016 ◽

pp. 1-30 ◽

Cited By ~ 14

Author(s):

Dongyan Shi ◽

Yunke Zhao ◽

Qingshan Wang ◽

Xiaoyan Teng ◽

Fuzhen Pang

Keyword(s):

Boundary Conditions ◽

Vibration Analysis ◽

Ritz Method ◽

Free Vibration Analysis ◽

Analysis Model ◽

Arbitrary Boundary ◽

Fourier Cosine ◽

Auxiliary Functions ◽

Arbitrary Boundary Conditions ◽

Closed Shells

This paper presents free vibration analysis of open and closed shells with arbitrary boundary conditions using a spectro-geometric-Ritz method. In this method, regardless of the boundary conditions, each of the displacement components of open and closed shells is represented simultaneously as a standard Fourier cosine series and several auxiliary functions. The auxiliary functions are introduced to accelerate the convergence of the series expansion and eliminate all the relevant discontinuities with the displacement and its derivatives at the boundaries. The boundary conditions are modeled using the spring stiffness technique. All the expansion coefficients are treated equally and independently as the generalized coordinates and determined using Rayleigh-Ritz method. By using this method, a unified vibration analysis model for the open and closed shells with arbitrary boundary conditions can be established without the need of changing either the equations of motion or the expression of the displacement components. The reliability and accuracy of the proposed method are validated with the FEM results and those from the literature.

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