scholarly journals Damage detection of beam by natural frequencies: General theory and procedure

2006 ◽  
Vol 28 (2) ◽  
pp. 120-132 ◽  
Author(s):  
Nguyen Tien Khiem
Keyword(s):  
Boundary Conditions ◽  
Damage Detection ◽  
Natural Frequencies ◽  
Model Updating ◽  
Measurement Data ◽  
Main Tool ◽  
Frequency Equation ◽  
Geometrical Parameters ◽  
Arbitrary Boundary ◽  
Updating Procedure

The frequency equation of single damaged beam has been established for arbitrary boundary conditions that is the main tool for analysis as well as identification of damaged beam by using measured natural frequencies. A procedure for damage detection problem presented in this paper consists of three steps. First, the modelling error is reduced by a model updating procedure, in which the material, geometrical parameters and boundary conditions are updated. Then, measurement data are corrected based on the updated model. Finally, the damage parameters are identified using updated model and corrected measurement data. Theoretical investigation is illustrated by an example.

scholarly journals Free vibration of functionally graded carbon nanotube-reinforced conical panels integrated with piezoelectric layers subjected to elastically restrained boundary conditions

2017 ◽  
Vol 9 (7) ◽  
pp. 168781401771181 ◽  
Author(s):  
Jianyu Fan ◽  
Jin Huang ◽  
Junbo Ding ◽  
Jie Zhang
Keyword(s):  
Carbon Nanotube ◽  
Free Vibration ◽  
Boundary Conditions ◽  
Natural Frequencies ◽  
Functionally Graded ◽  
Mode Shapes ◽  
Geometrical Parameters ◽  
Arbitrary Boundary ◽  
Piezoelectric Layers ◽  
Elastically Restrained

This article presents the free vibration of piezoelectric functionally graded carbon nanotube-reinforced composite conical panels with elastically restrained boundary conditions. The material properties of carbon nanotube-reinforced composites are assumed to be temperature-dependent and are obtained using the extended rule of mixture. First-order shear deformation theory is adopted to obtain the kinematics of the hybrid panels, and the boundary spring technique is used to implement arbitrary boundary conditions. Meanwhile, two types of electrical boundary conditions, closed circuit and open circuit, are considered for the free surfaces of the piezoelectric layers. The complete sets of electro-mechanically coupled governing equations are obtained using the Rayleigh–Ritz procedure with the Chebyshev polynomial basis functions. The resultant eigenvalue problem is solved to obtain natural frequencies and mode shapes of the hybrid panels. Convergence and comparison studies have been conducted to verify the stability and accuracy of the proposed method. Several numerical examples are examined to reveal the influences of the carbon nanotube volume fractions, carbon nanotube distribution types, boundary conditions, geometrical parameters, and temperatures on the natural frequencies of the hybrid panel. Moreover, the mode shapes of the hybrid panels under various boundary conditions are also presented.

VIBRATION-BASED STRUCTURAL DAMAGE DETECTION UNDER VARYING TEMPERATURE CONDITIONS

2013 ◽  
Vol 13 (05) ◽  
pp. 1250082 ◽  
Author(s):  
XIAO-QING ZHOU ◽  
WEN HUANG
Keyword(s):  
Damage Detection ◽  
Structural Damage ◽  
Natural Frequencies ◽  
Environmental Changes ◽  
Model Updating ◽  
Modal Testing ◽  
Structural Damage Detection ◽  
Vibration Data ◽  
Temperature Conditions ◽  
Vibration Properties

In vibration-based structural damage detection, it is necessary to discriminate the variation of structural properties due to environmental changes from those caused by structural damages. The present paper aims to investigate the temperature effect on vibration-based structural damage detection in which the vibration data are measured under varying temperature conditions. A simply-supported slab was tested in laboratory to extract the vibration properties with modal testing. The slab was then damaged and the modal testing was conducted again, in which the temperature varied. The modal data measured under different temperature conditions were used to detect the damage with a two-stage model updating technique. Some damage was falsely detected if the temperature variation was not considered. Natural frequencies were then corrected to those under the same temperature conditions according to the relation between the temperature and material modulus. It is shown that all of the damaged elements can be accurately identified.

A Sensitivity-Enhancing Control Approach for Structural Model Updating

2007 ◽  
Author(s):  
L. J. Jiang ◽  
K. W. Wang ◽  
J. Tang
Keyword(s):  
Closed Loop ◽  
Structural Model ◽  
Natural Frequencies ◽  
Model Updating ◽  
Measurement Data ◽  
Frequency Measurement ◽  
Physical Parameters ◽  
Fe Model ◽  
Initial Model ◽  
Closed Loop Systems

Model updating plays an important role in structural design and dynamic analysis. The process of model updating aims to produce an improved mathematical model by correlating the initial model with the experimentally measured data. There are a variety of techniques available for model updating using dynamic and static measurements of the structure’s behavior. This paper focuses on the model updating methods using the measured natural frequencies of the structure. The practice of model updating using only the natural frequencies encounters two well-known limitations: deficiency of frequency measurement data, and low sensitivity of measured natural frequencies with respect to the physical parameters that need to be updated. To overcome these limitations, a novel model updating method is presented in this paper. First, closed-loop control is applied to the structure to enhance the sensitivity of natural frequencies to the updating parameters. Second, by including the natural frequencies based on a series of sensitivity-enhanced closed-loop systems, we can significantly enrich the frequency measurement data available for model updating. Using the natural frequencies of these sensitivity-enhanced closed-loop systems, an iterative process is utilized to update the physical parameters in the initial model. To demonstrate and verify the proposed method, case studies are carried out using a cantilevered beam structure. The natural frequencies of a series of sensitivity-enhanced closed-loop systems are utilized to update the mass and stiffness parameters in the initial FE model. Results show that the modeling errors in the mass and stiffness parameters can be accurately identified by using the proposed model updating method.

Vibro-Acoustic Analysis and Topology Optimization of Anti-Tetra Chiral Auxetic Lattices Driven by Different Colored Noises

2020 ◽  
Vol 20 (11) ◽  
pp. 2050113
Author(s):  
A. Hosseinkhani ◽  
D. Younesian ◽  
M. Ranjbar
Keyword(s):  
Boundary Conditions ◽  
Natural Frequencies ◽  
Acoustic Analysis ◽  
Honeycomb Structure ◽  
Geometrical Parameters ◽  
Acoustic Behavior ◽  
The Finite Element Method ◽  
Load Spectrum ◽  
The Core ◽  
Radiated Sound

In this paper, we study vibro-acoustic behavior of auxetic sandwich panels subjected to different excitations and boundary conditions. The core of this panel has the auxetic feature (with negative Poisson’s ratio or NPR) with anti-tetrachiral honeycomb structure. Mechanical behavior of the core is formulated using theoretical relations presented for this kind of auxetic. Using the Finite Element Method, the modal analysis and spectral analysis of the structure are accomplished. Different random colored noises are applied as the system excitation. First, a parametric study is performed; and some interesting results are observed from investigating the effects of geometric parameters, boundary conditions, and noise color on the vibro-acoustic behavior of the structure. These parameters affect the natural frequencies, level of radiated sound, and mass of the structure. An optimization algorithm is applied to the geometrical parameters in order to simultaneously reduce the level of radiated sound and preserve the amount of total mass. By the use of the Genetic Algorithm (GA), we could achieve a remarkable noise attenuation gain. It is shown that the GA choses different optimized parameters for the structure according to the location of the load and frequency content of the load spectrum.

scholarly journals Wave Based Method for Free Vibration Analysis of Ring Stiffened Cylindrical Shell with Intermediate Large Frame Ribs

2013 ◽  
Vol 20 (3) ◽  
pp. 459-479 ◽  
Author(s):  
Meixia Chen ◽  
Jianhui Wei ◽  
Kun Xie ◽  
Naiqi Deng ◽  
Guoxiang Hou
Keyword(s):  
Cylindrical Shell ◽  
Free Vibration ◽  
Boundary Conditions ◽  
Natural Frequencies ◽  
Free Vibration Analysis ◽  
Structure Type ◽  
Vibration Characteristics ◽  
Mode Shapes ◽  
Arbitrary Boundary ◽  
Stiffened Cylindrical Shell

Wave based method which can be recognized as a semi-analytical and semi-numerical method is presented to analyze the free vibration characteristics of ring stiffened cylindrical shell with intermediate large frame ribs for arbitrary boundary conditions. According to the structure type and the positions of discontinuities, the model is divided into different substructures whose vibration field is expanded by wave functions which are exactly analytical solutions to the governing equations of the motions of corresponding structure type. Boundary conditions and continuity equations between different substructures are used to form the final matrix to be solved. Natural frequencies and vibration mode shapes are calculated by wave based method and the results show good agreement with finite element method for clamped-clamped, shear diaphragm – shear diaphragm and free-free boundary conditions. Free vibration characteristics of ring stiffened cylindrical shells with intermediate large frame ribs are compared with those with bulkheads and those with all ordinary ribs. Effects of the size, the number and the distribution of intermediate large frame rib are investigated. The frame rib which is large enough is playing a role as bulkhead, which can be considered imposing simply supported and clamped constraints at one end of the cabin and dividing the cylindrical shell into several cabins vibrating separately at their own natural frequencies.

Frequency Equations for Vibration Analysis of Fuel Rod

2005 ◽  
Author(s):  
Hyeong Koo Kim ◽  
Jae Ik Kim ◽  
Kyu Tae Kim ◽  
Moon Saeng Kim
Keyword(s):  
Boundary Conditions ◽  
Natural Frequencies ◽  
Frequency Equation ◽  
Sine Series ◽  
Various Boundary Conditions ◽  
Fuel Rod ◽  
Conventional Analysis ◽  
Fourier Sine Series ◽  
Fuel Design ◽  
Parametric Analyses

In this study, the frequency equations for calculating the natural frequencies of the beams with generally restrained boundary conditions by both translational and rotational springs are derived in matrix form using Fourier sine series. In order to show the validation of the solution, numerical results for two degenerate cases are compared with existing results for natural frequency obtained by the conventional analysis. And as a specific application, the natural frequencies of fuel rod for KSNP (Korean Standard Nuclear Plant) fuel assembly are calculated and compared with the external excitations. As a result, the frequency equation derived by present paper seems to be very useful to evaluate the natural frequencies of the double span beams with various boundary conditions. Especially, when some parametric analyses are needed to modify fuel design, the equation can be applied very easily.

Development of a Structural Health Monitoring Benchmark Problem for High-Rise Slender Structures

2008 ◽  
Vol 56 ◽  
pp. 489-494 ◽  
Author(s):  
Yong Xia ◽  
Yi Qing Ni ◽  
Jan Ming Ko ◽  
Hua Bin Chen
Keyword(s):  
Structural Health Monitoring ◽  
Damage Detection ◽  
Health Monitoring ◽  
Model Updating ◽  
Measurement Data ◽  
Benchmark Problem ◽  
Test Bed ◽  
Structural Health ◽  
High Rise ◽  
Slender Structures

Under the auspices of the Asian-Pacific Network of Centers for Research in Smart Structures Technology (ANCRiSST) and the International Society for Structural Health Monitoring of Intelligent Infrastructure (ISHMII), a structural health monitoring benchmark problem for highrise slender structures is being developed by taking the instrumented Guangzhou New Television Tower as a test bed. The benchmark problem consists of the following four tasks: (i) output-only modal identification and finite element model updating, (ii) damage detection using simulated data, (iii) optimal sensor placement for structural health monitoring, and (iv) damage detection using field measurement data. This paper will address some key issues related to the development of this first benchmark problem for high-rise structures. More details of the study can be found in the website: http://www.cse.polyu.edu.hk/benchmark/index.htm

An Extended Separation-of-Variable Method for Free Vibration of Rectangular Mindlin Plates

2021 ◽  
pp. 2150154
Author(s):  
Gen Li ◽  
Yufeng Xing ◽  
Zekun Wang
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Closed Form ◽  
Natural Frequencies ◽  
Mode Shapes ◽  
Arbitrary Boundary ◽  
Unknown Variable ◽  
Closed Form Solutions ◽  
Solution Methods ◽  
Separation Of Variable

For rectangular thick plates with non-Levy boundary conditions, it is important to explore analytical free vibration solutions because the classical inverse and semi-inverse exact solution methods are not applicable to this category of problems. This work is to develop an extended separation-of-variable (SOV) method to find closed-form analytical solutions for the free vibration of rectangular Mindlin plates with arbitrary homogeneous boundary conditions. In the extended SOV method, characteristic differential equations and boundary conditions in two directions are obtained by employing the Rayleigh principle and the assumption that the mode functions are in the SOV form, and two transcendental eigenvalue equations are achieved through boundary conditions. But these two eigenvalue equations cannot be solved simultaneously since there are two equations and only the natural frequency is the unknown variable. Considering this, the second assumption in this method is that the natural frequencies corresponding to two-direction mode functions are independent of each other in the mathematical sense, thus there are two unknowns in two transcendental eigenvalue equations, and the closed-form solutions for plates with arbitrary boundary conditions can be obtained non-iteratively. From the physical sense, the natural frequencies pertaining to different direction mode functions should be the same, and this conclusion is validated analytically and numerically. The present natural frequencies and mode shapes agree well with those obtained by other analytical and numerical methods. Especially, for the plates with at least two opposite sides simply supported, the present solutions are exact.

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