Vibration of Beams with a Single Delamination under Axial Loading

2011 ◽  
Vol 675-677 ◽  
pp. 477-480
Author(s):  
Dong Wei Shu
Keyword(s):  
Free Vibration ◽  
Natural Frequency ◽  
Analytical Solutions ◽  
Axial Load ◽  
Natural Frequencies ◽  
Axial Loading ◽  
Composite Beams ◽  
Mode Shapes ◽  
Equilibrium Conditions ◽  
Monotonic Relation

In this work analytical solutions are developed to study the free vibration of composite beams under axial loading. The beam with a single delamination is modeled as four interconnected Euler-Bernoulli beams using the delamination as their boundary. The continuity and the equilibrium conditions are satisfied between the adjoining beams. The studies show that the sizes and the locations of the delaminations significantly influence the natural frequencies and mode shapes of the beam. A monotonic relation between the natural frequency and the axial load is predicted.

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.

Postbuckling and Free Vibrations of Composite Beams

2007 ◽  
Author(s):  
Samir A. Emam ◽  
Ali H. Nayfeh
Keyword(s):  
Natural Frequency ◽  
Axial Load ◽  
Closed Form Solution ◽  
Composite Beams ◽  
Free Vibrations ◽  
Form Solution ◽  
Mode Shapes ◽  
Axial Stiffness ◽  
Fundamental Natural Frequency ◽  
Transverse Vibrations

An exact solution for the postbuckling configurations of composite beams is presented. The equations governing the axial and transverse vibrations of a composite laminated beam accounting for the midplane stretching are presented. The inplane inertia and damping are neglected, and hence the two equations are reduced to a single equation governing the transverse vibrations. This equation is a nonlinear fourth-order partial-integral differential equation. We find that the governing equation for the postbuckling of a symmetric or antisymmetric composite beam has the same form as that of a metallic beam. A closed-form solution for the postbuckling configurations due to a given axial load beyond the critical buckling load is obtained. We followed Nayfeh, Anderson, and Kreider and exactly solved the linear vibration problem around the first buckled configuration to obtain the fundamental natural frequencies and their corresponding mode shapes using different fiber orientations. Characteristic curves showing variations of the maximum static deflection and the fundamental natural frequency of postbuckling vibrations with the applied axial load for a variety of fiber orientations are presented. We find out that the line-up orientation of the laminate strongly affects the static buckled configuration and the fundamental natural frequency. The ratio of the axial stiffness to the bending stiffness is a crucial parameter in the analysis. This parameter can be used to help design and optimize the composite beams behavior in the postbuckling domain.

scholarly journals Theoretical Analysis on the Nonlinear Free Vibration of a Tri-Cross String

2017 ◽  
Vol 2017 ◽  
pp. 1-17
Author(s):  
Bo Pan ◽  
Jingda Tang ◽  
Ryuichi Tarumi ◽  
Fulin Shang ◽  
Yanbo Wang ◽  
...  
Keyword(s):  
Constitutive Equation ◽  
Theoretical Analysis ◽  
Free Vibration ◽  
Natural Frequency ◽  
Analytical Solutions ◽  
Vibration Amplitude ◽  
Natural Frequencies ◽  
Geometrical Nonlinearity ◽  
Governing Equations ◽  
Nonlinear Free Vibration

Here we present a theoretical analysis on the nonlinear free vibration of a tri-cross string system, which is an element of space net-antennas. We derived the governing equations from Hamilton’s principle and obtained a linearized solution by the standard perturbation method. The semi-analytical solutions of the governing equations have not been provided referring to the solution of plate vibrating problem. This analysis revealed that natural frequencies of the tri-cross string depend on the vibration amplitude due to the geometrical nonlinearity in the constitutive equation. The geometric parameters, such as the diameters and the lengths of the constituent strings, also affect the frequency through the nonlinearity of the tri-cross string. The nonlinear natural frequency shows coupled characteristic; that is, the natural frequency of the tri-cross string varies with that of the constituent strings, but the contribution of each constituent string to the natural frequency is in different proportions.

scholarly journals The Effect of Axial Force on the Free Vibration of an Euler-Bernoulli Beam Carrying a Number of Various Concentrated Elements

2013 ◽  
Vol 20 (3) ◽  
pp. 357-367 ◽  
Author(s):  
Gürkan Şcedilakar
Keyword(s):  
Free Vibration ◽  
Vibration Analysis ◽  
Axial Load ◽  
Natural Frequencies ◽  
Free Vibration Analysis ◽  
Mode Shapes ◽  
The Finite Element Method ◽  
Bernoulli Beam ◽  
Euler Beam ◽  
Euler Bernoulli Beam

In this study, free vibration analysis of beams carrying a number of various concentrated elements including point masses, rotary inertias, linear springs, rotational springs and spring-mass systems subjected to the axial load was performed. All analyses were performed using an Euler beam assumption and the Finite Element Method. The beam used in the analyses is accepted as pinned-pinned. The axial load applied to the beam from the free ends is either compressive or tensile. The effects of parameters such as the number of spring-mass systems on the beam, their locations and the axial load on the natural frequencies were investigated. The mode shapes of beams under axial load were also obtained.

Effect of crack on free vibration of a pre-stressed curved plate

2021 ◽  
pp. 095440622199486
Author(s):  
Can Gonenli ◽  
Hasan Ozturk ◽  
Oguzhan Das
Keyword(s):  
Finite Element ◽  
Free Vibration ◽  
Natural Frequency ◽  
Present Model ◽  
Mode Shapes ◽  
Load Parameter ◽  
Flexible Plate ◽  
Cantilever Plate ◽  
Finite Element Software ◽  
Aspect Ratios

In this study, the effect of crack on free vibration of a large deflected cantilever plate, which forms the case of a pre-stressed curved plate, is investigated. A distributed load is applied at the free edge of a thin cantilever plate. Then, the loading edge of the deflected plate is fixed to obtain a pre-stressed curved plate. The large deflection equation provides the non - linear deflection curve of the large deflected flexible plate. The thin curved plate is modeled by using the finite element method with a four-node quadrilateral element. Three different aspect ratios are used to examine the effect of crack. The effect of crack and its location on the natural frequency parameter is given in tables and graphs. Also, the natural frequency parameters of the present model are compared with the finite element software results to verify the reliability and validity of the present model. This study shows that the different mode shapes are occurred due to the change of load parameter, and these different mode shapes cause a change in the effect of crack.

Vibration-based delamination evaluation in GFRP composite beams using ANN

2021 ◽  
pp. 096739112110033
Author(s):  
TG Sreekanth ◽  
M Senthilkumar ◽  
S Manikanta Reddy
Keyword(s):  
Finite Element ◽  
Natural Frequency ◽  
Composite Structures ◽  
Composite Beams ◽  
Vibration Characteristics ◽  
Mode Shapes ◽  
Aviation Industry ◽  
Frequency Data ◽  
Fiber Reinforced ◽  
Back Propagation Algorithm

Delamination is definitely an important topic in the area of composite structures as it progressively worsens the mechanical performance of fiber-reinforced polymer composite structures in its service period. The detection and severity analysis of delaminations in engineering areas like the aviation industry is vital for safety and economic considerations. The existence of delaminations varies the vibration characteristics such as natural frequencies, mode shapes, etc. of composites and hence this indication can be effectively used for locating and quantifying the delaminations. The changes in vibration characteristics are considered as inputs for the inverse problem to determine the location and size of delaminations. In this paper Artificial Neural Network (ANN) is used for delamination evaluationof glass fiber-reinforced composite beams using natural frequency as typical vibration parameter. The Finite Element Analysis is used for generating the required dataset for ANN. The frequency-based delamination prediction technique is validated by finite element models and experimental modal analysis. The results indicate that the ANN-based back propagation algorithm can predict the location and size of delaminations in composites with good accuracy for numerical natural frequency data but the accuracy is comparitivelyless for experimental natural frequency data.

Dynamic characteristics of horizontally curved bridges

2017 ◽  
Vol 24 (19) ◽  
pp. 4465-4483 ◽  
Author(s):  
Mohsen Amjadian ◽  
Anil K Agrawal
Keyword(s):  
Free Vibration ◽  
Dynamic Characteristics ◽  
Natural Frequencies ◽  
Response Spectrum ◽  
Translational Motion ◽  
Free Vibration Analysis ◽  
Mode Shapes ◽  
Curved Bridges ◽  
Horizontally Curved ◽  
Horizontally Curved Bridges

Horizontally curved bridges have complicated dynamic characteristics because of their irregular geometry and nonuniform mass and stiffness distributions. This paper aims to develop a simplified and practical method for the calculation of the natural frequencies and mode shapes of horizontally curved bridges that would be of interest to bridge engineers for the estimation of the seismic response of these types of bridges. For this purpose, a simple three-degree-of-freedom (3DOF) dynamic model for free vibration equation of this type of bridge has been developed. It is shown that the translational motion of the deck of horizontally curved bridges in the direction that is perpendicular to their axis of symmetry is always coupled with the rotational motion of the deck, regardless of the location of the stiffness center. The model is further exploited to develop closed-form formulas for the estimation of the maximum displacements of the corners of the deck of one-way asymmetric horizontally curved bridges. The accuracy of the model is verified by finite-element model of a horizontally curved bridge prototype in OpenSEES. Finally, the model is utilized to study the influence of the location of the stiffness center with respect to the deck curvature center on the natural frequency and the maximum displacements of the corners of the deck for different curvatures of the deck. The results of free vibration analysis show that the natural frequencies of one-way asymmetric horizontally curved bridges, in general, increase with the increase of the subtended angle of the deck. The results of earthquake response spectrum analysis show that the increase in the subtended angle of one-way asymmetric horizontally curved bridges decreases the radial displacements of the corners of the deck but increases the azimuthal displacement. These two responses both increase with the increase in the distance between the stiffness center and the curvature center.

A Note on the Lowest Natural Frequency of a Square Plate Point-Supported at the Corners

1962 ◽  
Vol 66 (616) ◽  
pp. 240-241 ◽  
Author(s):  
C. L. Kirk
Keyword(s):  
Natural Frequency ◽  
Natural Frequencies ◽  
Present Note ◽  
Flexural Vibration ◽  
Approximate Solutions ◽  
Mode Shapes ◽  
Electronic Digital Computer ◽  
Isotropic Plates ◽  
Four Corners ◽  
Square Plate

Recently Cox and Boxer determined natural frequencies and mode shapes of flexural vibration of uniform rectangular isotropic plates, that have free edges and pinpoint supports at the four corners. In their analysis, they obtain approximate solutions of the differential equation through the use of finite difference expressions and an electronic digital computer. In the present note, the frequency expression and mode shape for a square plate, vibrating at the lowest natural frequency, are determined by considerations of energy. The values obtained are compared with those given in reference.

Free Vibration Analysis of a Carbon Nanotube Reinforced Composite Beam

2014 ◽  
Vol 592-594 ◽  
pp. 2041-2045 ◽  
Author(s):  
B. Naresh ◽  
A. Ananda Babu ◽  
P. Edwin Sudhagar ◽  
A. Anisa Thaslim ◽  
R. Vasudevan
Keyword(s):  
Carbon Nanotube ◽  
Free Vibration ◽  
Composite Beam ◽  
Natural Frequencies ◽  
Equations Of Motion ◽  
Free Vibration Analysis ◽  
Mode Shapes ◽  
Element Formulation ◽  
Reinforced Composite ◽  
Vibration Responses

In this study, free vibration responses of a carbon nanotube reinforced composite beam are investigated. The governing differential equations of motion of a carbon nanotube (CNT) reinforced composite beam are presented in finite element formulation. The validity of the developed formulation is demonstrated by comparing the natural frequencies evaluated using present FEM with those of available literature. Various parametric studies are also performed to investigate the effect of aspect ratio and percentage of CNT content and boundary conditions on natural frequencies and mode shapes of a carbon nanotube reinforced composite beam. It is shown that the addition of carbon nanotube in fiber reinforced composite beam increases the stiffness of the structure and consequently increases the natural frequencies and alter the mode shapes.

scholarly journals Phononic Band Gap and Free Vibration Analysis of Fluid-Conveying Pipes with Periodically Varying Cross-Section

2021 ◽  
Vol 11 (21) ◽  
pp. 10485
Author(s):  
Hao Yu ◽  
Feng Liang ◽  
Yu Qian ◽  
Jun-Jie Gong ◽  
Yao Chen ◽  
...  
Keyword(s):  
Free Vibration ◽  
Band Gap ◽  
Cross Section ◽  
Natural Frequencies ◽  
Free Vibration Analysis ◽  
Critical Parameters ◽  
Mode Shapes ◽  
Beam Model ◽  
The Impact ◽  
Fluid Conveying Pipes

Phononic crystals (PCs) are a novel class of artificial periodic structure, and their band gap (BG) attributes provide a new technical approach for vibration reduction in piping systems. In this paper, the vibration suppression performance and natural properties of fluid-conveying pipes with periodically varying cross-section are investigated. The flexural wave equation of substructure pipes is established based on the classical beam model and traveling wave property. The spectral element method (SEM) is developed for semi-analytical solutions, the accuracy of which is confirmed by comparison with the available literature and the widely used transfer matrix method (TMM). The BG distribution and frequency response of the periodic pipe are attained, and the natural frequencies and mode shapes are also obtained. The effects of some critical parameters are discussed. It is revealed that the BG of the present pipe system is fundamentally induced by the geometrical difference of the substructure cross-section, and it is also related to the substructure length and fluid–structure interaction (FSI). The number of cells does not contribute to the BG region, while it has significant effects on the amplitude attenuation, higher order natural frequencies and mode shapes. The impact of FSI is more evident for the pipes with smaller numbers of cells. Moreover, compared with the conventional TMM, the present SEM is demonstrated more effective for comprehensive analysis of BG characteristics and free vibration of PC dynamical structures.

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