scholarly journals An efficient simple element for free vibration and buckling analysis of FG beam

2021 ◽  
Author(s):  
Majid Yaghoobi ◽  
◽  
Mohsen Sedaghatjo ◽  
Reyhaneh Alizadeh ◽  
Mohammad Karkon ◽  
...  
Keyword(s):  
Free Vibration ◽  
Convergence Rate ◽  
Beam Theory ◽  
High Accuracy ◽  
Model Material ◽  
Buckling Analysis ◽  
Rapid Convergence ◽  
Numerical Tests ◽  
Benchmark Tests ◽  
Fg Beam

In this paper, a simple and efficient element is proposed for the free vibration and buckling analysis of FGM beams. This element is formulating, based on Timoshenko beam theory. The assumption of constant shear strain in the element reduces the number of unknowns in addition to improving the efficiency of the new element. The performance of the new element is evaluated with the help of several benchmark tests. First, the accuracy and convergence rate of the proposed element response in the analysis of free vibration and buckling of the beam are investigated separately by exponential variations of the modulus of elasticity and density in each of the beams' thickness and length. Subsequently, the element's ability to model material variations in both longitudinal and thickness directions of the beam will be measured simultaneously. For comparison, the answers of good elements of other researchers are available in each of the numerical tests. These tests will prove the high accuracy and rapid convergence rate of the proposed element.

scholarly journals Solving biharmonic problems on irregular domains by stably evaluated Gaussian kernel

2020 ◽  
Vol 7 (1) ◽  
pp. 56-67
Author(s):  
Artur Krowiak
Keyword(s):  
Free Vibration ◽  
Shape Parameter ◽  
Cartesian Product ◽  
High Accuracy ◽  
Thin Plates ◽  
Gaussian Kernel ◽  
Irregular Domains ◽  
Numerical Tests ◽  
Interpolation Problems ◽  
Biharmonic Problems

AbstractThe paper extends recently developed idea of stable evaluation of the Gaussian kernel. Owing to this, the Gaussian radial basis function that is sensitive to the shape parameter can be stably evaluated and applied to interpolation problems as well as to solve differential equations, giving highly accurate results. But it can be done only with grids being the Cartesian product of sets of points, what limits the use of this idea to rectangular domains. In the present paper, by the association of an appropriate transformation with the mentioned method, the latter is applied to solve biharmonic problems on quadrilateral irregular domains. As an example, in the present work this approach is applied to solve bending as well as free vibration problem of thin plates. In the paper some strategies for the implementation of the boundary conditions are also presented and examined due to the accuracy. The numerical tests show high accuracy and usefulness of the method.

Free vibration analysis of composite foils with different ply angles based on beam theory

2021 ◽  
Vol 226 ◽  
pp. 108854
Author(s):  
Hanzhe Zhang ◽  
Qin Wu ◽  
Yunqing Liu ◽  
Biao Huang ◽  
Guoyu Wang
Keyword(s):  
Free Vibration ◽  
Vibration Analysis ◽  
Free Vibration Analysis ◽  
Beam Theory

A Method to Improve the Modal Convergence for Structures With External Forcing

1987 ◽  
Vol 54 (4) ◽  
pp. 904-909 ◽  
Author(s):  
Keqin Gu ◽  
Benson H. Tongue
Keyword(s):  
Spatial Distribution ◽  
Free Vibration ◽  
Convergence Rate ◽  
Traditional Approach ◽  
Vibration Modes ◽  
External Forcing ◽  
Slow Convergence ◽  
Assumed Mode Method ◽  
Mode Method ◽  
Assumed Mode

The traditional approach of using free vibration modes in the assumed mode method often leads to an extremely slow convergence rate, especially when discete interactive forces are involved. By introducing a number of forced modes, significant improvements can be achieved. These forced modes are intrinsic to the structure and the spatial distribution of forces. The motion of the structure can be described exactly by these forced modes and a few free vibration modes provided that certain conditions are satisfied. The forced modes can be viewed as an extension of static modes. The development of a forced mode formulation is outlined and a numerical example is presented.

scholarly journals A Refined Theory for Bending Vibratory Analysis of Thick Functionally Graded Beams

Mathematics ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 1422
Author(s):  
Youssef Boutahar ◽  
Nadhir Lebaal ◽  
David Bassir
Keyword(s):  
Beam Theory ◽  
Functionally Graded ◽  
Effective Characteristics ◽  
Hyperbolic Function ◽  
Transverse Displacement ◽  
Refined Theory ◽  
Distribution Law ◽  
Fg Beam ◽  
The Impact ◽  
Beam Theories

A refined beam theory that takes the thickness-stretching into account is presented in this study for the bending vibratory behavior analysis of thick functionally graded (FG) beams. In this theory, the number of unknowns is reduced to four instead of five in the other approaches. Transverse displacement is expressed through a hyperbolic function and subdivided into bending, shear, and thickness-stretching components. The number of unknowns is reduced, which involves a decrease in the number of the governing equation. The boundary conditions at the top and bottom FG beam faces are satisfied without any shear correction factor. According to a distribution law, effective characteristics of FG beam material change continuously in the thickness direction depending on the constituent’s volume proportion. Equations of motion are obtained from Hamilton’s principle and are solved by assuming the Navier’s solution type, for the case of a supported FG beam that is transversely loaded. The numerical results obtained are exposed and analyzed in detail to verify the validity of the current theory and prove the influence of the material composition, geometry, and shear deformation on the vibratory responses of FG beams, showing the impact of normal deformation on these responses which is neglected in most of the beam theories. The obtained results are compared with those predicted by other beam theories. It can be concluded that the present theory is not only accurate but also simple in predicting the bending and free vibration responses of FG beams.

scholarly journals Free Vibration Analysis of Single Walled Carbon Nanotube with Exponentially Varying Stiffness

2018 ◽  
Vol 5 (1) ◽  
pp. 201-212 ◽  
Author(s):  
Subrat Kumar Jena ◽  
S. Chakraverty
Keyword(s):  
Free Vibration ◽  
Differential Quadrature Method ◽  
Free Vibration Analysis ◽  
Beam Theory ◽  
Single Walled Carbon Nanotube ◽  
Single Walled Carbon ◽  
Scaling Parameters ◽  
Governing Differential Equation ◽  
Theory Application ◽  
Walled Carbon Nanotubes

Abstract In this paper, Differential Quadrature Method (DQM) is applied to investigate free vibration of Single Walled Carbon Nanotubes (SWCNTs) with exponentially varying stiffness based on non-local Euler-Bernoulli beam theory. Application of DQ method in the governing differential equation converts the problem to a generalized eigenvalue problem and its solution gives frequency parameters. Convergence of the results show that DQM solutions converge fast. In this article, a detailed investigation has been reported and MATLAB code has been developed to analyze the numerical results for different scaling parameters as well as for four types of boundary conditions. Present results are compared with other available results and are found to be in good agreement.

scholarly journals Instability Analysis of a Woven Fibre Composite Plate

2019 ◽  
Vol 8 (4) ◽  
pp. 2449-2454
Keyword(s):  
Mechanical Properties ◽  
Finite Element ◽  
Free Vibration ◽  
Epoxy Matrix ◽  
Composite Plate ◽  
Fibre Composite ◽  
Buckling Analysis ◽  
Instability Analysis ◽  
Critical Buckling Load ◽  
Modal Response

The instability behaviour of a woven fibre composite plate in respect of its free vibration and buckling analysis has been presented in this paper. The woven fibre composite plate has been prepared by hand layup with bidirectional woven glass fibres in epoxy matrix. The mechanical properties of the woven fibre composite plate have been characterised experimentally and a finite element investigation has been done for the instability analysis. Modal response of the plate and the critical buckling load leading to instability of the plate to varying parameters are studied and numerical results have been presented.

FREE VIBRATION OF PLATES BY THE HIGH ACCURACY QUADRATURE ELEMENT METHOD

1997 ◽  
Vol 202 (5) ◽  
pp. 689-702 ◽  
Author(s):  
A.G. Striz ◽  
W.L. Chen ◽  
C.W. Bert
Keyword(s):  
Free Vibration ◽  
High Accuracy ◽  
Quadrature Element Method ◽  
Element Method

Free Vibration of Curvilinearly Stiffened Shallow Shells

2013 ◽  
Author(s):  
Peng Shi ◽  
Rakesh K. Kapania
Keyword(s):  
Free Vibration ◽  
Ritz Method ◽  
Beam Theory ◽  
Fe Method ◽  
Shallow Shells ◽  
First Order ◽  
Stiffened Shells ◽  
Method Base ◽  
Doubly Curved ◽  
Good Agreement

The free vibration of curvilinearly stiffened doubly curved shallow shells is investigated by the Ritz method. Base on the first order shear deformation shell theory and Timoshenko’s 3-D curved beam theory, the strain and kinetic energies of the stiffened shells are introduced. Numerical results with different geometrical shells and boundary conditions, and different stiffener locations and curvatures are analyzed to verify the feasibility of the presented Ritz method for solving the problems. The results show good agreement with those using the FE method.

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