Vibration Analysis of Beams with Arbitrary Elastic Boundary Conditions

2011 ◽  
Vol 66-68 ◽  
pp. 1325-1329
Author(s):  
Bing Lin Lv ◽  
Wan You Li ◽  
Jun Dai ◽  
Hai Jun Zhou ◽  
Fei Xiang Guo ◽  
...  
Keyword(s):  
Fourier Series ◽  
Vibration Analysis ◽  
Elastic Boundary ◽  
Stiffness Matrices ◽  
Fourier Series Method ◽  
Mass Matrices ◽  
Ritz Procedure ◽  
Elastically Supported ◽  
Elastic Boundary Conditions ◽  
Improved Fourier Series Method

In this paper, one newly developed method named the Improved Fourier Series method is applied to the vibration analysis of a beam elastically supported at the both end. The flexural displacement of the beam is supposed to be one set of Fourier Series coupled with four appended terms. Based on the Rayleigh-Ritz procedure and and the vibration characteristics of the beam are also acquired by solving these two matrices. In the end, the frequencies calculated are also compared with those from references and Results ar the Hamilton’s equation, the mass matrices and the stiffness matrices of the beam are obtained e all proved excellent.

scholarly journals Hypersonic Aeroelastic Response of Elastic Boundary Panel Based on a Modified Fourier Series Method

2019 ◽  
Vol 2019 ◽  
pp. 1-13 ◽  
Author(s):  
Xiyue Zhou ◽  
Lifeng Wang ◽  
Jingnong Jiang ◽  
Zhu Su
Keyword(s):  
Fourier Series ◽  
Time Domain ◽  
Series Method ◽  
Aeroelastic Response ◽  
Flutter Speed ◽  
Elastic Boundary ◽  
Fourier Series Method ◽  
Length Width ◽  
Time Domain Response ◽  
Elastic Boundary Conditions

In this paper, an analytical method is proposed to directly obtain the aeroelastic time domain response of the elastic boundary panel. Based on a modified Fourier series method (MFSM), the vibration analysis of elastic boundary panels is carried out, after the dynamics equation of the panel is obtained. Then, the vibrational functions are combined with the supersonic piston theory to establish the aeroelastic equation. The aeroelastic time domain response of the panel is obtained to analyze the flutter speed of the panel more intuitively. Finally, the flutter speeds of panels with different length-width ratios, thicknesses, and elastic boundary conditions are discussed in detail.

Free Vibration Analysis of Moderately Thick Coupled Plates with Elastic Boundary Conditions and Point Supports

2019 ◽  
Vol 19 (12) ◽  
pp. 1950150
Author(s):  
Qiuhong Li ◽  
Joey Sanchez ◽  
Haym Benaroya ◽  
Jiufa Wang ◽  
Kai Xue
Keyword(s):  
Finite Element ◽  
Fourier Series ◽  
Boundary Conditions ◽  
Series Method ◽  
Plate Model ◽  
Coupling Conditions ◽  
Elastic Boundary ◽  
Fourier Series Method ◽  
Coupled Plates ◽  
Elastic Boundary Conditions

Plates are applied to a wide array of structural applications of varying complexity. Each application requires rigorous analysis to determine the viability of the proposed model. One such application involves modeling a larger structure as a collection of smaller flat plates connected at the plate boundaries. Previous research into these types of structures has led to varying levels of accuracy. It has been dependent on the applications and assumptions involved. To improve the accuracy of these types of structures in a more general context, we propose expanding on current models of coupled plates by modeling the plates using Mindlin plate theory. We analyze the vibration of the improved model with general elastic boundary conditions, point supports and coupling conditions using the Fourier series method and finite element software. When the Fourier series method is applied directly, continuity issues arise at the plate coupling boundaries. To resolve these issues, the Fourier series solution of the vibration displacements is amended to include auxiliary functions. This improved coupled plate model is analyzed and numerically simulated for a variety of elastic boundary conditions and coupling conditions. The numerical results are produced using the Fourier series method and a finite element solution to demonstrate the validity of the improved coupled plate model.

Free vibration analysis of rectangular plates with arbitrary elastic boundary conditions

2021 ◽  
Vol 263 (5) ◽  
pp. 1891-1898
Author(s):  
Zhenshuai Wan
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Vibration Analysis ◽  
Free Vibration Analysis ◽  
Rectangular Plates ◽  
Different Boundary Conditions ◽  
Elastic Boundary ◽  
Fourier Series Method ◽  
The Matrix ◽  
Elastic Boundary Conditions

boundary conditions are In this paper, an improved Fourier series method is presented for the free vibration analysis of rectangular plates with arbitrary elastic conditions. The stiffness value of the restraining springs is determined as required to simulate the arbitrary elastic boundary conditions. The exact solution of plates with arbitrary elastic boundary conditions is solved by the introduced supplementary func-tions. The matrix eigenvalue equation of plates is derived by using boundary conditions and the governing equations. Compared with exist methods, the presented method can be easily applied to most of plate vibration problems with different boundary conditions. To validate the accuracy of the presented method, numerical simulations with different boundary conditions are presented.presented.

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