scholarly journals Free Vibration Analysis of Laminated Composite Double-Plate Structure System with Elastic Constraints Based on Improved Fourier Series Method

2021 ◽  
Vol 2021 ◽  
pp. 1-25
Author(s):  
Ying Zhang ◽  
Dongyan Shi ◽  
Dongze He ◽  
Dong Shao
Keyword(s):  
Fourier Series ◽  
Free Vibration ◽  
Boundary Conditions ◽  
Laminated Composite ◽  
Mode Shapes ◽  
Series Method ◽  
Plate Structure ◽  
Fourier Series Method ◽  
Linear Algebraic Equations ◽  
Improved Fourier Series Method

An analytical model of laminated composite double-plate system (LCDPS) is established, which efficiently analyzes the common 3D plate structure in engineering applications. The proposed model combines the first-order shear deformation theory (FSDT) and the classical delamination theory, and then the LCDPS’s vibration characteristics are investigated. In the process of analysis, the improved Fourier series method (IFSM) is used to describe the displacement admissible function of the LCDPS, which can remove the potential discontinuities at the boundaries. Five sets of artificial springs are introduced to simulate the elastic boundary constraints, and the restraints of the Winkler elastic layer can be adjustable. The improved Fourier series is substituted into the governing equations and boundary conditions; then, applying the Rayleigh–Ritz method, we take all the series expansion coefficients as the generalized coordinates. After that, a set of standard linear algebraic equations was obtained. On this basis, the natural frequency and mode shapes of the LCDPS can be obtained by solving the standard eigenvalue problem. By the discussion of numerical examples and the comparison with those of the reports in the literature, the convergence and the reliability of the present approach are validated. Finally, the parametric investigations of the free vibration with complex boundary conditions are carried out, including the influence of boundary conditions, lamination scheme, plate geometric parameters, and elastic coefficient between two plates.

scholarly journals Vibration Characteristics Analysis of Cylindrical Shell-Plate Coupled Structure Using an Improved Fourier Series Method

2018 ◽  
Vol 2018 ◽  
pp. 1-19 ◽  
Author(s):  
Yipeng Cao ◽  
Runze Zhang ◽  
Wenping Zhang ◽  
Jinzhao Wang
Keyword(s):  
Cylindrical Shell ◽  
Fourier Series ◽  
Boundary Conditions ◽  
Accurate Solution ◽  
Vibration Characteristics ◽  
Series Method ◽  
Mechanical Coupling ◽  
Fourier Series Method ◽  
Characteristics Analysis ◽  
Improved Fourier Series Method

A simple yet accurate solution procedure based on the improved Fourier series method (IFSM) is applied to the vibration characteristics analysis of a cylindrical shell-circular plate (S-P) coupled structure subjected to various boundary conditions. By applying four types of coupling springs with arbitrary stiffness at the junction of the coupled structure, the mechanical coupling effects are completely considered. Each of the plate and shell displacement functions is expressed as the superposition of a two-dimensional Fourier series and several supplementary functions. The unknown series-expansion coefficients are treated as the generalized coordinates and determined using the familiar Rayleigh-Ritz procedure. Using the IFSM, a unified solution for the S-P coupled structure with symmetrical and asymmetrical boundary conditions can be derived directly without the need to change either the equations of motion or the expressions of the displacements. This solution can be verified by comparing the current results with those calculated by the finite-element method (FEM). The effects of several significant factors, including the restraint stiffness, the coupling stiffness, and the situation of coupling, are presented. The forced vibration behaviors of the S-P coupled structure are also illustrated.

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

2017 ◽  
Vol 4 (1) ◽  
pp. 52-84 ◽  
Author(s):  
Hong Zhang ◽  
Dongyan Shi ◽  
Qingshan Wang ◽  
Bin Qin
Keyword(s):  
Fourier Series ◽  
Free Vibration ◽  
Boundary Conditions ◽  
Power Law ◽  
Admissible Function ◽  
Functionally Graded ◽  
General Boundary ◽  
General Boundary Conditions ◽  
Series Method ◽  
Fourier Series Method

AbstractThe 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.

A new Fourier series method and displacement function for in-plane vibration and power flow characteristics analysis of isotropic rectangular plates

2019 ◽  
Vol 50 (6) ◽  
pp. 176-194
Author(s):  
Kavikant Mahapatra ◽  
SK Panigrahi
Keyword(s):  
Fourier Series ◽  
Boundary Conditions ◽  
Power Flow ◽  
Flow Characteristics ◽  
Displacement Function ◽  
Rectangular Plates ◽  
Series Method ◽  
Plane Vibration ◽  
Fourier Series Method ◽  
Beam Displacement

The generation of in-plane vibration in plates is an important issue and frequently occurs due to the presence of excitations in the ship’s hull due to turbulent fluid flows, turbulent airflow excitation on aerospace structures, gear system subjected to axial excitation, assemblies housing piezoelectric crystals and sandwiched plates, and so on. The present analysis aims to establish a universal and numerically efficient method for determination of in-plane vibration characteristics of isotropic rectangular plates both for conventional and general boundary conditions. The new in-plane Fourier series and displacement function of the plate have been developed using beam displacement functions in x and y directions, respectively, under in-plane condition. A modified Fourier series assumption for the in-plane beam displacement has been utilised and further developed as plate displacement function. The computational efficiency of the present method is compared in terms of convergence of natural frequency parameter, speed of execution and manual convenience to reduce human errors with the frequently used Fourier series method by various researchers. Rayleigh–Ritz procedure has been applied to determine the in-plane natural frequencies. The mode shapes for few conventional and generally varying boundary conditions have been presented and analysed. The dynamic response has been obtained and analysed in terms of the in-plane mobility and power flow characteristics of the plate under varying boundary conditions. The validity of results obtained by the current method has shown excellent accuracy and faster convergence with the existing results. The present results can provide a benchmark to analyse the dynamic in-plane response of plate systems being used for built-up structures in real engineering applications.

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