scholarly journals Free Vibration of AFG Circular Arch with Symmetric and Anti-symmetric Boundary Conditions at Mid-Arc

Symmetry ◽  
2020 ◽  
Vol 12 (3) ◽  
pp. 417 ◽  
Author(s):  
Joon Kyu Lee ◽  
Byoung Koo Lee
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Cross Section ◽  
Solution Method ◽  
Regular Polygon ◽  
Axial Direction ◽  
Functionally Graded ◽  
Material Parameters ◽  
Finite Element Software ◽  
Uniform Cross Section

This paper studies the in-plane free vibration of axially functionally graded (AFG) circular arches with non-uniform cross-section. The geometric and material properties of circular arches with regular polygon cross-section vary symmetrically about the mid-arc along the axial direction in quadratic polynomial form. The governing differential equations of the motion are derived, and the symmetric and anti-symmetric boundary conditions of the arches are developed for applying initial and boundary value problems in the solution method. The computed results agree well with the results of the finite element software ADINA. The effects of geometrical and material parameters on the natural frequency and mode shape of AFG circular arches are investigated.

scholarly journals Free Vibration Analysis of Functionally Graded Spherical Torus Structure with Uniform Variable Thickness along Axial Direction

2019 ◽  
Vol 2019 ◽  
pp. 1-22
Author(s):  
Cong Gao ◽  
Xuhong Miao ◽  
Lin Lu ◽  
Ruidong Huo ◽  
Qiaolin Hu ◽  
...  
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Variable Thickness ◽  
Domain Decomposition Method ◽  
Ritz Method ◽  
Axial Direction ◽  
Functionally Graded ◽  
Spherical Torus ◽  
Different Boundary Conditions ◽  
Vibration Responses

Based on the Ritz method, this paper focused on the free vibration of functionally graded (FG) spherical torus with uniform variable thickness along axial direction under different boundary conditions. The first-order shear deformation theory (FSDT) is employed to formulate the analytical model. The method involves partitioning of the spherical torus structure into proper shell segments in order to satisfy the computing requirement of high-order vibration responses according to the domain decomposition method. The two adjacent segments are connected by using the penalty method, where penalty parameters are defined by the artificial springs; the continuity condition and different boundary conditions can be obtained by assigning the appropriate values of springs. The displacement functions’ components are double mixed series, in which Fourier series and unified Jacobi polynomials, respectively, represent displacement function along circumferential direction and axial direction. Then the Ritz method is used to obtain final solutions. The numerical results obtained by the proposed method show great agreement with previously published literatures and those from the finite element program ABAQUS. The effects of boundary conditions and geometric parameters on the vibration responses of the structure are also presented. The most novelty of this paper is to generalize the selection of admissible displacement functions by using Jacobi polynomial.

scholarly journals Free Vibration Analysis of Axially Functionally Graded (AFG) Cantilever Columns of a Regular Polygon Cross-Section with Constant Volume

Mathematics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 319
Author(s):  
Joon Kyu Lee ◽  
Byoung Koo Lee
Keyword(s):  
Free Vibration ◽  
Cross Section ◽  
Regular Polygon ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Constant Volume ◽  
Integral Approach ◽  
Element Analysis ◽  
Direct Integral ◽  
Material Inhomogeneity

This paper deals with the transverse free vibration of axially functionally graded (AFG) cantilever columns under the influence of axial compressive load. The columns possessing a regular polygon in their cross-section are tapered and their material properties vary along the axis of the column. An emphasis is placed on the columns with constant volume for admissible geometries and materials. The governing differential equation of the problem is derived and solved using the direct integral approach in conjunction with the determinant search technique. The obtained results are in good agreement with those in the available literature and computed by finite element analysis. Numerical examples for the natural frequency and mode shape of the columns are presented to investigate the effects of parameters related to geometrical nonuniformity and material inhomogeneity.

scholarly journals Free vibration analysis on axially graded beam resting on variable Pasternak foundation

2021 ◽  
Vol 1206 (1) ◽  
pp. 012016
Author(s):  
Saurabh Kumar
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Vibration Analysis ◽  
Ritz Method ◽  
Free Vibration Analysis ◽  
Axial Direction ◽  
Functionally Graded ◽  
Pasternak Foundation ◽  
Material Gradation ◽  
Euler Bernoulli Beam

Abstract Free vibration analysis is conducted on axially functionally graded Euler-Bernoulli beam resting on variable Pasternak foundation. The material properties of the beam and the stiffness of the foundation are considered to be varying linearly along the axial direction. Two types of boundary conditions namely; clamped and simply supported are used in the analysis. The problem is formulated using Rayleigh-Ritz method and governing equations are derived with the help of Hamilton’s principle. The numerical results are generated for different material gradation parameter, foundation parameter and boundary conditions and the effect of these parameters on the free vibration behaviour of the beam is discussed.

Analysis of vibration in rotating pretwisted functionally graded graphene platelets reinforced nanocomposite laminated blades with an attached point mass

2021 ◽  
pp. 095440622110084
Author(s):  
Amin Ghorbani Shenas ◽  
Parviz Malekzadeh ◽  
Sima Ziaee
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Polymer Matrix ◽  
Natural Frequencies ◽  
Weight Fraction ◽  
Functionally Graded ◽  
Point Mass ◽  
Attached Mass ◽  
Graphene Platelets ◽  
Twisted Beam

This work presents an investigation on the free vibration behavior of rotating pre-twisted functionally graded graphene platelets reinforced composite (FG-GPLRC) laminated blades/beams with an attached point mass. The considered beams are constituted of [Formula: see text] layers which are bonded perfectly and made of a mixture of isotropic polymer matrix and graphene platelets (GPLs). The weight fraction of GPLs changes in a layer-wise manner. The effective material properties of FG-GPLRC layers are computed by using the modified Halpin-Tsai model together with rule of mixture. The free vibration eigenvalue equations are developed based on the Reddy’s third-order shear deformation theory (TSDT) using the Chebyshev–Ritz method under different boundary conditions. After validating the approach, the influences of the GPLs distribution pattern, GPLs weight fraction, angular velocity, the variation of the angle of twist along the beam axis, the ratio of attached mass to the beam mass, boundary conditions, position of attached mass, and geometry on the vibration behavior are investigated. The findings demonstrate that the natural frequencies of the rotating pre-twisted FG-GPLRC laminated beams significantly increases by adding a very small amount of GPLs into polymer matrix. It is shown that placing more GPLs near the top and bottom surfaces of the pre-twisted beam is an effective way to strengthen the pre-twisted beam stiffness and increase the natural frequencies.

scholarly journals Free Vibration Analysis of a Graphene-Reinforced Porous Composite Plate with Different Boundary Conditions

Materials ◽  
2021 ◽  
Vol 14 (14) ◽  
pp. 3879
Author(s):  
Hong-Gang Pan ◽  
Yun-Shi Wu ◽  
Jian-Nan Zhou ◽  
Yan-Ming Fu ◽  
Xin Liang ◽  
...  
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Composite Plate ◽  
Porous Plate ◽  
Micromechanical Model ◽  
Value Added ◽  
Porous Composite ◽  
Finite Element Software ◽  
Free Vibration Frequency ◽  
Graphene Platelets

Plates are commonly used in many engineering disciplines, including aerospace. With the continuous improvement in the capacity of high value-added airplanes, large transport aircrafts, and fighter planes that have high strength, high toughness, and corrosion resistance have gradually become the development direction of airplane plate structure production and research. The strength and stability of metal plate structures can be improved by adding reinforced materials. This paper studies graphene platelets (GPLs) reinforced with a free vibration porous composite plate. The porous plate is constructed with a multi-layer model in a metal matrix containing uniform or non-uniformly distributed open-cell internal pores. Considering the random and directional arrangement of graphene platelets in the matrix, the elastic modulus of graphene composites was estimated using the Halpin–Tsai micromechanical model, and the vibration frequencies of graphene composite were calculated using the differential quadrature method. The effects of the total number of layers, GPL distribution pattern, porosity coefficient, GPL weight fraction, and boundary conditions on the free vibration frequency of GPLs reinforced porous composite plates are studied, and the accuracy of the conclusions are verified by the finite element software.

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