Prediction of natural frequency and buckling load variability due to uncertainty in material properties by convex modeling

1996 ◽  
pp. 139-154 ◽  
Author(s):  
Y Li ◽  
I Elishakoff ◽  
J Starnes ◽  
M Shinozuka
Keyword(s):  
Natural Frequency ◽  
Material Properties ◽  
Buckling Load

scholarly journals Effects of Elliptical Hole on the Correlation of Natural Frequency with Buckling Load of Basalt Laminates Composite Plates

2020 ◽  
Vol 27 (1) ◽  
pp. 216-225
Author(s):  
Buntheng Chhorn ◽  
WooYoung Jung
Keyword(s):  
Free Vibration ◽  
Natural Frequency ◽  
Natural Frequencies ◽  
Basalt Fiber ◽  
Orientation Angle ◽  
Elliptical Hole ◽  
Composite Plates ◽  
Buckling Load ◽  
Mode Shapes ◽  
Geometric Ratio

AbstractRecently, basalt fiber reinforced polymer (BFRP) is acknowledged as an outstanding material for the strengthening of existing concrete structure, especially it was being used in marine vehicles, aerospace, automotive and nuclear engineering. Most of the structures were subjected to severe dynamic loading during their service life that may induce vibration of the structures. However, free vibration studied on the basalt laminates composite plates with elliptical cut-out and correlation of natural frequency with buckling load has been very limited. Therefore, effects of the elliptical hole on the natural frequency of basalt/epoxy composite plates was performed in this study. Effects of stacking sequence (θ), elliptical hole inclination (ϕ), hole geometric ratio (a/b) and position of the elliptical hole were considered. The numerical modeling of free vibration analysis was based on the mechanical properties of BFRP obtained from the experiment. The natural frequencies as well as mode shapes of basalt laminates composite plates were numerically determined using the commercial program software (ABAQUS). Then, the determination of correlation of natural frequencies with buckling load was carried out. Results showed that elliptical hole inclination and fiber orientation angle induced the inverse proportion between natural frequency and buckling load.

Maximizing the Fundamental Natural Frequency of Triangular Composite Plates

1996 ◽  
Vol 118 (2) ◽  
pp. 141-146 ◽  
Author(s):  
S. Abrate
Keyword(s):  
Natural Frequency ◽  
Material Properties ◽  
Composite Structures ◽  
Natural Frequencies ◽  
Ritz Method ◽  
Laminated Composite ◽  
Composite Plates ◽  
Mode Shapes ◽  
Fundamental Natural Frequency ◽  
Wide Range

While many advances were made in the analysis of composite structures, it is generally recognized that the design of composite structures must be studied further in order to take full advantage of the mechanical properties of these materials. This study is concerned with maximizing the fundamental natural frequency of triangular, symmetrically laminated composite plates. The natural frequencies and mode shapes of composite plates of general triangular planform are determined using the Rayleigh-Ritz method. The plate constitutive equations are written in terms of stiffness invariants and nondimensional lamination parameters. Point supports are introduced in the formulation using the method of Lagrange multipliers. This formulation allows studying the free vibration of a wide range of triangular composite plates with any support condition along the edges and point supports. The boundary conditions are enforced at a number of points along the boundary. The effects of geometry, material properties and lamination on the natural frequencies of the plate are investigated. With this stiffness invariant formulation, the effects of lamination are described by a finite number of parameters regardless of the number of plies in the laminate. We then determine the lay-up that will maximize the fundamental natural frequency of the plate. It is shown that the optimum design is relatively insensitive to the material properties for the commonly used material systems. Results are presented for several cases.

Stochastic Extended Finite Element Implementation for Natural Frequency of Cracked Functionally Gradient and Bi-Material Structures

2020 ◽  
pp. 2150044
Author(s):  
Ahmed Raza ◽  
Himanshu Pathak ◽  
Mohammad Talha
Keyword(s):  
Finite Element ◽  
Natural Frequency ◽  
Material Properties ◽  
Perturbation Technique ◽  
Vibration Characteristics ◽  
Functionally Graded ◽  
Extended Finite Element ◽  
Material Interface ◽  
Level Set Function ◽  
Graded Material

In this work, stochastic perturbation-based vibration characteristics of cracked bi-material and functionally graded material (FGM) domain with uncertain material properties are investigated using the extended finite element method. The level set function is implemented to track the geometrical discontinuities. The partition of unity-based extrinsic enrichment technique is employed to model the crack and material interface. The exponential law is used to model the graded material properties of FGM. The First-order perturbation technique (FOPT) is implemented to predict the standard deviation of natural frequency for the given uncertainties in the material properties. The numerical results are presented to show the effect of geometrical discontinuities and material randomness on vibration characteristics.

Three-dimensional natural frequency analysis of anisotropic functionally graded annular sector plates resting on elastic foundations

2015 ◽  
Vol 22 (6) ◽  
Author(s):  
Kamran Asemi ◽  
Manouchehr Salehi ◽  
Mehdi Akhlaghi
Keyword(s):  
Natural Frequency ◽  
Frequency Analysis ◽  
Material Properties ◽  
Three Dimensional ◽  
Functionally Graded ◽  
Mode Shapes ◽  
Element Formulation ◽  
Elastic Foundations ◽  
Annular Sector ◽  
Natural Frequency Analysis

AbstractNatural frequency analysis of anisotropic functionally graded material (FGM) annular sector plates on Winkler elastic foundations based on three-dimensional theory of elasticity was investigated. The three-dimensional graded finite element formulation was derived based on the principle of minimum potential energy and the Rayleigh-Ritz method. For an orthotropic FGM, the material properties were assumed to have in-plane polar orthotropy and transverse heterogeneity according to an exponential law, whereas the mass density was assumed to be constant. For an isotropic FGM, material properties varied continuously through the thickness direction according to a power-law distribution, whereas Poisson’s ratio was set to be constant. The effects of material gradient exponents, different sector angles, different thickness ratio, Winkler parameter and two different boundary conditions on the natural frequencies and mode shapes of FGM annular sector plates have been investigated. Numerical solution was compared with the result of an FGM annular circular plate, which showed good agreement.

Effect of Distributed Attached Mass on the Vibration of Sandwich Panel Using Higher Order ESL Theory

2012 ◽  
Vol 488-489 ◽  
pp. 35-39 ◽  
Author(s):  
Shahab Tafazoli ◽  
S.M.R. Khalili
Keyword(s):  
Free Vibration ◽  
Natural Frequency ◽  
Material Properties ◽  
Sandwich Panel ◽  
Sandwich Panels ◽  
Single Layer ◽  
Higher Order ◽  
Design Parameters ◽  
Attached Mass ◽  
The Face

In this paper, effects of adding a distributed attached mass added to the face sheets of sandwich panels on free vibration of the system are investigated. Higher order equivalent single layer (ESL) theory is expanded and used. Mass Inertias of the distributed attached mass are taking into account. Various design parameters including geometrical and material properties, such as density, thickness of the attached mass and the panel are investigated to show the decreasing effect on the fundamental natural frequency of the system due to the adding of the distributed attached mass.

Free vibration and buckling of heavy column with regular polygon cross-section

2021 ◽  
pp. 095440622110293
Author(s):  
Joon Kyu Lee ◽  
Byoung Koo Lee
Keyword(s):  
Differential Equations ◽  
Free Vibration ◽  
Natural Frequency ◽  
Cross Section ◽  
Buckling Load ◽  
Mode Shapes ◽  
Equilibrium Equations ◽  
Direct Integration Method ◽  
Solution Methods ◽  
Buckling Length

This paper deals with the free vibration and buckling of heavy column, considering its own self-weight. The column has a regular polygonal cross-section with a constant area. The column is applied to an external axial load as well as the self-weight. The five end conditions of the column are considered. Based on equilibrium equations of the column element, differential equations governing the vibrational and buckled mode shapes of column are derived. In solution methods, differential equations are numerically integrated by the direct integration method and eigenvalues of the natural frequency, buckling load and self-weight buckling length are calculated by the determinant search method. The numerical results of this study were in good agreement with those of the reference. Parametric study of the end condition, side number and self-weight on the natural frequency and buckling load was carried out.

Optimal Design of Composite Laminate With Uncertainty in Loading and Material Properties Considered

2005 ◽  
Author(s):  
Tae-Uk Kim ◽  
In Hee Hwang ◽  
Hyo-Chol Sin
Keyword(s):  
Optimal Design ◽  
Material Properties ◽  
Composite Laminates ◽  
Buckling Load ◽  
Optimization Approach ◽  
Stacking Sequence ◽  
Simulation Techniques ◽  
Aspect Ratios ◽  
The One ◽  
Efficiency And Reliability

Optimal design of composite laminates with uncertain in-plane loadings and material properties is considered. The stacking sequence is designed to have maximum buckling load based on anti-optimization approach. To consider the above-mentioned uncertain properties, the convex modeling and Monte Carlo simulation techniques are used in calculating objective function. For the stacking sequence optimization, it is used the modified genetic algorithm which handles the discrete ply angles and the constraints easily. Numerical results are given for rectangular laminates of various aspect ratios. The optimal solutions from the deterministic and the stochastic cases are obtained and it is demonstrated the importance of considering uncertainty. The buckling load carried by a deterministic design is much less than the one carried by a design uncertainty considered when both are subjected to uncertain loads. Also, it is examined the effects of the method for considering uncertainty on the optimization process in the light of computational efficiency and reliability of solutions obtained.

Material Properties and Natural Frequency of Stator Core of Large Turbo-Generator

2011 ◽  
Vol 322 ◽  
pp. 81-84 ◽  
Author(s):  
Yi Xuan Wang ◽  
Ying Wang
Keyword(s):  
Natural Frequency ◽  
Material Properties ◽  
Six Sigma ◽  
Operating Temperature ◽  
Vibration Reduction ◽  
Silicon Steel ◽  
Core Material ◽  
Analysis Method ◽  
Stator Core ◽  
Turbo Generator

Techniques for vibration reduction and design of stator core require knowledge of its modal frequencies, which depend on the geometry shapes, dimensions and material properties. The material properties of stator core are mainly related to its laminated process and assembly as well as the operating temperature of turbo-generator. It is found that the generally accepted value of material properties is not valid for the stator core with laminated silicon steel slice and operating at about 110-120 Celsius. This paper simply summarizes the method of determining elastic properties of stator core material, considers these as uncertainty variables obeying Gaussain distribution and changing in the possible range, and then applies to Six Sigma Analysis method for the calculation of the modal frequencies of stator core.

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