scholarly journals Vibration Analysis and Optimization of a Rectangular Plate with Flanging Hyperellipse Cutout

2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
Wensheng Wang ◽  
Sier Deng ◽  
Song Zhang ◽  
Da Geng
Keyword(s):  
Rectangular Plate ◽  
Vibration Analysis ◽  
Natural Frequencies ◽  
Great Influence ◽  
Optimum Frequency ◽  
Out Of Plane ◽  
Nature Frequency ◽  
Parametric Studies ◽  
The Difference ◽  
Vibration Performance

Vibration analysis and optimization of a rectangular plate with a flanging hyperellipse cutout is investigated in this paper, numerically. In the analysis, finite element method (FEM) is applied to perform parametric studies on various plates in different boundary conditions, addressing the influence of different cutout parameters (area, shape, flanging height, position, and rotation) on the first- and second-order natural frequencies of the rectangular plate and providing references for the optimum frequency design. Then, maximization of frequency or the difference of two consecutive frequencies of the rectangular plate is carried out using Multi-island Genetic Algorithm, aiming to achieve the best dynamic characteristics. The results show that different cutout parameters have great influence on vibration performance of the plate, the existing of the flanging increases the out-of-plane stiffness of the plate. Additionally, the nature frequency of the plate has been improved obviously for different models with the optimal design of the cutout.

scholarly journals Free Vibration Analysis of Rings via Wave Approach

2018 ◽  
Vol 2018 ◽  
pp. 1-14
Author(s):  
Wang Zhipeng ◽  
Liu Wei ◽  
Yuan Yunbo ◽  
Shuai Zhijun ◽  
Guo Yibin ◽  
...  
Keyword(s):  
Free Vibration ◽  
Vibration Analysis ◽  
Natural Frequencies ◽  
Classical Method ◽  
Free Vibration Analysis ◽  
Material Parameters ◽  
Wave Approach ◽  
Out Of Plane ◽  
Vibration Transmissibility ◽  
Ring Structures

Free vibration of rings is presented via wave approach theoretically. Firstly, based on the solutions of out-of-plane vibration, propagation, reflection, and coordination matrices are derived for the case of a fixed boundary at inner surface and a free boundary at outer surface. Then, assembling these matrices, characteristic equation of natural frequency is obtained. Wave approach is employed to study the free vibration of these ring structures. Natural frequencies calculated by wave approach are compared with those obtained by classical method and Finite Element Method (FEM). Afterwards natural frequencies of four type boundaries are calculated. Transverse vibration transmissibility of rings propagating from outer to inner and from inner to outer is investigated. Finally, the effects of structural and material parameters on free vibration are discussed in detail.

Free vibration analysis of a rectangular plate carrying multiple various concentrated elements

2003 ◽  
Vol 217 (2) ◽  
pp. 171-183 ◽  
Author(s):  
J-S Wu ◽  
H-M Chou ◽  
D-W Chen
Keyword(s):  
Finite Element ◽  
Free Vibration ◽  
Boundary Conditions ◽  
Rectangular Plate ◽  
Normal Mode ◽  
Vibration Analysis ◽  
Natural Frequencies ◽  
Free Vibration Analysis ◽  
Equation Of Motion ◽  
Mode Shapes

The dynamic characteristic of a uniform rectangular plate with four boundary conditions and carrying three kinds of multiple concentrated element (rigidly attached point masses, linear springs and elastically mounted point masses) was investigated. Firstly, the closed-form solutions for the natural frequencies and the corresponding normal mode shapes of a rectangular ‘bare’ (or ‘unconstrained’) plate (without any attachments) with the specified boundary conditions were determined analytically. Next, by using these natural frequencies and normal mode shapes incorporated with the expansion theory, the equation of motion of the ‘constrained’ plate (carrying the three kinds of multiple concentrated element) were derived. Finally, numerical methods were used to solve this equation of motion to give the natural frequencies and mode shapes of the ‘constrained’ plate. To confirm the reliability of previous free vibration analysis results, a finite element analysis was also conducted. It was found that the results obtained from the above-mentioned two approaches were in good agreement. Compared with the conventional finite element method (FEM), the approach employed in this paper has the advantages of saving computing time and achieving better accuracy, as can be seen from the existing literature.

Flow-Induced Vibrations of Heat Exchanger U-Tubes: A Simulation to Study the Effects of Asymmetric Stiffness

1983 ◽  
Vol 105 (1) ◽  
pp. 67-75 ◽  
Author(s):  
D. S. Weaver ◽  
D. Koroyannakis
Keyword(s):  
Heat Exchanger ◽  
Natural Frequencies ◽  
Symmetric Case ◽  
Triangular Array ◽  
Water Tunnel ◽  
Out Of Plane ◽  
Flow Induced Vibrations ◽  
Pitch Ratio ◽  
The Difference

A water tunnel study was conducted to study the effect of asymmetric stiffness on a parallel triangular array of tubes with a pitch ratio of 1.375. The tubes were cantilevered from rectangular support rods so that the stiffness, and hence natural frequencies, were different in directions parallel and transverse to the flow. This arrangement was designed to simulate the difference in in-plane and out-of-plane natural frequencies of curved tubes. A test was conducted with symmetric stiffness for datum purposes and then eight tests were run with differences between streamwise and transverse frequencies ranging from 6.3 to 57 percent. It was found that the critical reduced velocity based on the lower frequency was increased only slightly over the symmetric case. This effect is essentially independent of the difference in frequency and the direction of the lower frequency relative to the flow.

scholarly journals Free vibration analysis of transmission lines based on the dynamic stiffness method

2019 ◽  
Vol 6 (3) ◽  
pp. 181354 ◽  
Author(s):  
Xiaohui Liu ◽  
You Hu ◽  
Mengqi Cai
Keyword(s):  
Transmission Lines ◽  
Vibration Analysis ◽  
Natural Frequencies ◽  
Dynamic Stiffness ◽  
Free Vibration Analysis ◽  
The Finite Element Method ◽  
Damping Parameter ◽  
Inclination Angles ◽  
Parametric Studies ◽  
Coupling Characteristic

An improved mathematical model used to study the coupling characteristic of the multi-span transmission lines is developed. Based on the solution method for single-span cable, an expression for the dynamic stiffness of two-span transmission lines with an arbitrary inclination angle is formulated. The continuity of displacements and forces at a suspension point is used to derive the dynamic stiffness. Interactions between insulator strings and adjacent spans are accommodated. Considering the infinite dynamic stiffness corresponds to the natural frequencies of the transmission lines, the finite-element method (FEM) is employed to assess the validity of the dynamic stiffness. In the numerical investigation, attention is focused on the effect of the inclination angles, Irvine parameter, insulator string length and damping parameter. In addition, the modal function corresponding to the natural frequencies is derived. Then, the results of comprehensive parametric studies are presented and discussed. Special attention is paid to the effect of the Irvine parameter and damping parameter on the in-plane modal shapes. Finally, according to the theoretical model of two-span transmission lines, the generalized dynamic stiffness of transmission lines with an arbitrary number of spans and inclination angles is derived. The method can be used as the basis of the vibration analysis on a wide variety of multi-span transmission lines.

Vibration Analysis and Simulation of Mast Section of Hoist

2012 ◽  
Vol 567 ◽  
pp. 3-9
Author(s):  
Ji Man Luo ◽  
Yang Jiang ◽  
Zhi Hui Xing
Keyword(s):  
Working Conditions ◽  
Vibration Analysis ◽  
Natural Frequencies ◽  
Vibration Mode ◽  
Great Influence ◽  
System Stability ◽  
Analysis Method ◽  
External Excitation ◽  
Excitation Force ◽  
Stiffness Characteristics

In order to avoid the damage of structure caused by the vibration, the natural frequency and vibration mode figure of the stiffness characteristics of the hoist’s structure should be analyzed. Modal analysis method is presented for solving above problem, and the first 6 order natural frequencies in different working conditions have been calculated in this paper. Vibration mode figure of structure system have been simulated corresponding to the first 6 order natural frequencies based on ANSYS. It is shows that the external excitation force have a great influence on the top of the free end when the cage moves to a different location. So, in the actual construction, the stiffness of top free ends connected tie-in device should be strengthened, therefore the system stability will be improved.

Experimental Observations of Nonlinear Nonplanar Oscillations of a Cantilever Beam

2007 ◽  
Author(s):  
Haider N. Arafat ◽  
Ali H. Nayfeh ◽  
Bashar K. Hammad
Keyword(s):  
Cantilever Beam ◽  
Natural Frequencies ◽  
Excitation Frequency ◽  
Low Frequency ◽  
Harmonic Load ◽  
Bending Vibrations ◽  
Out Of Plane ◽  
Frequency Components ◽  
Plane Bending ◽  
The Difference

The dynamics of a thin cantilever beam undergoing combined torsion and bending vibrations are examined experimentally. The beam’s fundamental natural frequencies in the two orthogonal bending motions and in torsion are fv1 = 5.719 Hz, fw1 = 189.730 Hz, and fφ1 = 138.938 Hz, respectively. A base-excitation shaker imparts a harmonic load that acts parallel to the width of the beam. First, the response of the beam is examined when the excitation frequency is equal to the fundamental torsion natural frequency (i.e., f = 138.9 Hz). For low levels of excitation, the motion consists mainly of hardly noticeable twisting vibrations. For high levels of excitation, the energy of the first torsion mode excites the first out-of-plane bending mode. In this case, the beam responses exhibit modulated vibrations containing both high-frequency and low-frequency components. Second, the beam is excited at the frequency f = 132.0 Hz, which is in the neighborhood the difference of these two natural frequencies. For large excitation levels, the beam vibrates with large-amplitude out-of-plane bending motions that exhibit chaotically intermittent behaviors.

Vibration Analysis of Curved Pipes Conveying Fluid

2014 ◽  
Author(s):  
Gongmin Liu ◽  
Shuaijun Li ◽  
Bryan W. Karney
Keyword(s):  
Vibration Analysis ◽  
Natural Frequencies ◽  
Fluid Pressure ◽  
The Finite Element Method ◽  
Curved Pipe ◽  
Geometrical Properties ◽  
Curved Pipes ◽  
Resonance Frequencies ◽  
Out Of Plane ◽  
And Migration

The partial differential equations for curved pipes with fluid structure interaction, including the effects of fluid pressure and Coriolis force, Centrifugal force and migration force caused by flow velocity, etc., were derived. These equations were then solved numerically utilizing the transfer matrix method (TMM) in the frequency domain because of its computational efficiency. The results were compared with those predicted by the finite element method and a discrete model. It is demonstrated that the TMM has high precision in the vibration analysis of fluid-filled curved pipes. Furthermore, the influence laws of geometrical properties on the natural frequencies and frequency responses of pipeline are discussed, which show that the natural frequencies of the fluid do not change with the varying of curvature angle when curved pipe filled with steam. But the resonance frequencies of the out-of-plane vibration and vibration amplitudes of the fluid pressure waves are strongly influenced by the variation of curvature angle.

OUT-OF-PLANE FREE VIBRATIONS OF CIRCULAR STRIPS WITH VARIABLE BREADTH

2007 ◽  
Vol 07 (03) ◽  
pp. 403-423 ◽  
Author(s):  
BYOUNG KOO LEE ◽  
TAE EUN LEE ◽  
ATHOL J. CARR ◽  
SANG JIN OH
Keyword(s):  
Differential Equations ◽  
Natural Frequencies ◽  
Slenderness Ratio ◽  
Free Vibrations ◽  
Mode Shapes ◽  
The Finite Element Method ◽  
Out Of Plane ◽  
Angle Section ◽  
Parametric Studies ◽  
Experimental Validations

This paper deals with the out-of-plane free vibrations of circular strips with linearly varying breadth. In deriving the differential equations for such strips, the effects of the rotatory and torsional inertias and shear deformation are considered. The differential equations are numerically solved to calculate the natural frequencies and mode shapes. In the numerical examples, three end constraints, i.e. clamped–clamped, clamped-hinged and hinged–hinged ends, are considered. The five lowest frequency parameters and mode shapes are presented. The effects of the rotatory and torsional inertias, and shear parameter on the natural frequencies are evaluated. Parametric studies are carried out for the influence of following parameters of the strip on the natural frequencies: subtended angle, section ratio, thickness ratio, and slenderness ratio. Also presented are the experimental validations of the seven lowest predicted natural frequencies. The natural frequencies obtained by this study agree well with those by the finite element method for both the flexural and torsional modes.

Elimination of outlier measurements for damage detection of structures under changing environmental conditions

2021 ◽  
pp. 147592172199847
Author(s):  
William Soo Lon Wah ◽  
Yining Xia
Keyword(s):  
Damage Detection ◽  
Multiple Regression ◽  
Natural Frequencies ◽  
Detection Method ◽  
Detection Methods ◽  
Structure Model ◽  
Bridge Structure ◽  
Beam Structure ◽  
Dependent Variables ◽  
The Difference

Damage detection methods developed in the literature are affected by the presence of outlier measurements. These measurements can prevent small levels of damage to be detected. Therefore, a method to eliminate the effects of outlier measurements is proposed in this article. The method uses the difference in fits to examine how deleting an observation affects the predicted value of a model. This allows the observations that have a large influence on the model created, to be identified. These observations are the outlier measurements and they are eliminated from the database before the application of damage detection methods. Eliminating the outliers before the application of damage detection methods allows the normal procedures to detect damage, to be implemented. A multiple-regression-based damage detection method, which uses the natural frequencies as both the independent and dependent variables, is also developed in this article. A beam structure model and an experimental wooden bridge structure are analysed using the multiple-regression-based damage detection method with and without the application of the method proposed to eliminate the effects of outliers. The results obtained demonstrate that smaller levels of damage can be detected when the effects of outlier measurements are eliminated using the method proposed in this article.

scholarly journals Out-of-Plane Vibration of Curved Uniform and Tapered Beams with Additional Mass

2017 ◽  
Vol 2017 ◽  
pp. 1-8 ◽  
Author(s):  
Hamdi Alper Özyiğit ◽  
Mehmet Yetmez ◽  
Utku Uzun
Keyword(s):  
Finite Element ◽  
Free Vibration ◽  
Boundary Conditions ◽  
Natural Frequencies ◽  
Variable Cross ◽  
Additional Mass ◽  
Inertia Effects ◽  
Tapered Beam ◽  
Out Of Plane ◽  
Good Agreement

As there is a gap in literature about out-of-plane vibrations of curved and variable cross-sectioned beams, the aim of this study is to analyze the free out-of-plane vibrations of curved beams which are symmetrically and nonsymmetrically tapered. Out-of-plane free vibration of curved uniform and tapered beams with additional mass is also investigated. Finite element method is used for all analyses. Curvature type is assumed to be circular. For the different boundary conditions, natural frequencies of both symmetrical and unsymmetrical tapered beams are given together with that of uniform tapered beam. Bending, torsional, and rotary inertia effects are considered with respect to no-shear effect. Variations of natural frequencies with additional mass and the mass location are examined. Results are given in tabular form. It is concluded that (i) for the uniform tapered beam there is a good agreement between the results of this study and that of literature and (ii) for the symmetrical curved tapered beam there is also a good agreement between the results of this study and that of a finite element model by using MSC.Marc. Results of out-of-plane free vibration of symmetrically tapered beams for specified boundary conditions are addressed.

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