scholarly journals Crack identification in beam by antiresonant frequencies

2021 ◽  
Vol 43 (4) ◽  
pp. 389-405
Author(s):  
Nguyen Tien Khiem ◽  
Nguyen Minh Tuan ◽  
Pham Thi Ba Lien
Keyword(s):  
Cantilever Beam ◽  
Theoretical Development ◽  
Crack Identification ◽  
Governing Equations ◽  
Scanning Method ◽  
Numerical Examples ◽  
Cracked Beams

The present paper deals with the concept of antiresonance in multiple cracked beams and application for multi-crack identification. First, governing equations for antiresonant frequency are conducted and used for both computing antiresonant frequencies versus crack parameters and measuring-loading colocation and identifying cracks by measured antiresonant frequencies. Then, a procedure is proposed for crack identification in cantilever beam by antiresonant frequencies based on the so-called crack scanning method. Theoretical development is illustrated by numerical examples.

CRACK IDENTIFICATION IN MULTIPLE CRACKED BEAMS MADE OF FUNCTIONALLY GRADED MATERIAL BY USING STATIONARY WAVELET TRANSFORM OF MODE SHAPES

2019 ◽  
Author(s):  
Tran Van Lien ◽  
Ngo Trong Duc
Keyword(s):  
Wavelet Transform ◽  
Functionally Graded Material ◽  
Functionally Graded ◽  
Theoretical Development ◽  
Mode Shapes ◽  
Crack Identification ◽  
Stationary Wavelet Transform ◽  
Graded Material ◽  
Fgm Beam ◽  
Cracked Beams

This paper presents crack identification in multiple cracked beams made of functionally graded material (FGM) by using stationary wavelet transform (SWT) of mode shapes and taking into account influence of Gaussian noise. Mode shapes are obtained from multiple cracked FGM beam element and spring model of cracks. The theoretical development was illustrated and validated by numerical examples. The investigated results show that crack identification method by using SWT of mode shapes is efficient and realizable.

scholarly journals Multiple crack identification in stepped beam by measurements of natural frequencies

2014 ◽  
Vol 36 (2) ◽  
pp. 119-132
Author(s):  
Nguyen Tien Khiem ◽  
Duong The Hung ◽  
Vu Thi An Ninh
Keyword(s):  
Crack Detection ◽  
Natural Frequencies ◽  
Rayleigh Quotient ◽  
Crack Identification ◽  
Multiple Cracks ◽  
Simple Relationship ◽  
Multiple Crack ◽  
Scanning Method ◽  
New Approach ◽  
Efficient Procedure

A new approach is proposed for calculating natural frequencies and crack detection in a stepped cantilever beam with arbitrary number of cracks. This is based an explicit expression of the natural frequencies in term of crack parameter derived in the form similar to the so-called Rayleigh quotient for vibrating beam. The obtained simple relationship between natural frequencies and crack parameters enables not only accurate calculating the natural frequencies but also to develop an efficient procedure for detecting multiple cracks from given natural frequencies. The proposed technique called crack scanning method is illustrated and validated by numerical results.

Kinematics and Dynamics of a Parallel Manipulator With Woven Joints

1993 ◽  
Author(s):  
Hyunsok Pang
Keyword(s):  
Lagrange Multipliers ◽  
Kinematic Analysis ◽  
Inverse Kinematics ◽  
Parallel Manipulator ◽  
Inverse Dynamics ◽  
Numerical Technique ◽  
Vector Analysis ◽  
Kinematics And Dynamics ◽  
Governing Equations ◽  
Numerical Examples

Abstract Presented is an analysis of the kinematics and the inverse dynamics of a proposed three DOF parallel manipulator resembling the Stewart platform in a general form. In the kinematic analysis, the inverse kinematics, velocity and acceleration analyses are performed, respectively, using vector analysis and general homogeneous transformations. An algorithm to solve the inverse dynamics of the proposed parallel manipulator is then presented using a Lagrangin technique. In this case, it is found that one should introduce and subsequently eliminate Lagrange multipliers in order to arrive at the governing equations. Numerical examples are finally carried out to examine the validity of the approach and the accuracy of the numerical technique employed. The trajectory of motion of the manipulator is also performed using a cubic spline.

A Study on Shape Optimization Using Affine Transformation

2001 ◽  
Author(s):  
Satoshi Kitayama ◽  
Hiroshi Yamakawa
Keyword(s):  
Shape Optimization ◽  
Cantilever Beam ◽  
Coordinate Transformation ◽  
Affine Transformation ◽  
Sufficient Conditions ◽  
Optimal Shape ◽  
Design Domain ◽  
Shape Transformation ◽  
Numerical Examples ◽  
Inclined Beam

Abstract This paper presents a new method to determine an optimal shape using affine transformation which is used in the field of Computer Aided Design (CAD), linear programming, and etc. We use affine transformation as coordinate transformation. Affine transformation is a linear transformation, so that shapes transformed must be linearly. Shape optimization of a inclined beam for example, we can deal with in the following manner. We define a simple cantilever beam first in initial design domain, and calculate an optimal shape. Then we use affine transformation remaining with optimal shape calculated in simple design domain and get to an optimal shape of the inclined beam. To compare with an optimal shape obtained by our proposed method, we calculate an optimal shape directly by conventional method in the same design domain after coordinate transformation. We show that affine transformation plays a role as scaling to structural optimization by finite element method and that necessary and sufficient conditions between design variables and shape transformation matrix may exist to get an exact optimal shape. We treat some numerical examples by our proposed method. In numerical examples, we consider shape optimization of inclined cantilever beam for simplicity. We show that some stepwise linear optimal shapes could be expressed from an optimal shape of a simple cantilever beam by using affine transformation. Optimal shape calculated by our method can obtain easily and speedy. Through some numerical examples, we could examine effectiveness of our proposed method.

Semilocal Convergence of a Seventh-Order Method in Banach Spaces Under Hölder Continuity Condition

2020 ◽  
Vol 87 (1-2) ◽  
pp. 56
Author(s):  
Neha Gupta ◽  
J. P. Jaiswal
Keyword(s):  
Banach Spaces ◽  
Error Bound ◽  
Order Of Convergence ◽  
Nonlinear Operator ◽  
Lipschitz Continuity ◽  
Semilocal Convergence ◽  
Continuity Condition ◽  
Theoretical Development ◽  
Numerical Examples ◽  
Seventh Order

The motive of this article is to analyze the semilocal convergence of a well existing iterative method in the Banach spaces to get the solution of nonlinear equations. The condition, we assume that the nonlinear operator fulfills the Hölder continuity condition which is softer than the Lipschitz continuity and works on the problems in which either second order Frèchet derivative of the nonlinear operator is challenging to calculate or does not hold the Lipschitz condition. In the convergence theorem, the existence of the solution x<sup>*</sup> and its uniqueness along with prior error bound are established. Also, the <em>R</em>-order of convergence for this method is proved to be at least 4+3q. Two numerical examples are discussed to justify the included theoretical development followed by an error bound expression.

scholarly journals Curved Nanotube Structures under Mechanical Loading

2015 ◽  
Vol 2015 ◽  
pp. 1-11
Author(s):  
Hamidreza Yazdani Sarvestani ◽  
Ali Naghashpour
Keyword(s):  
Carbon Nanotube ◽  
Theoretical Study ◽  
Nonlocal Parameter ◽  
Bending Moment ◽  
Theoretical Development ◽  
Governing Equations ◽  
Nonlocal Continuum ◽  
The Subject ◽  
Displacement Based ◽  
Displacement Approach

Configuration of carbon nanotube (CNT) has been the subject of research to perform theoretical development for analyzing nanocomposites. A new theoretical solution is developed to study curved nanotube structures subjected to mechanical loadings. A curved nanotube structure is considered. A nonlocal displacement-based solution is proposed by using a displacement approach of Toroidal Elasticity based on Eringen’s theory of nonlocal continuum mechanics. The governing equations of curved nanotube structures are developed in toroidal coordinate system. The method of successive approximation is used to discretize the displacement-based governing equations and find the general solution subjected to bending moment. The numerical results show that all displacement components increase with increasing the nonlocal parameter. The present theoretical study highlights the significance of the geometry and nonlocal parameter effects on mechanical behavior of nanotube structures.

A New Reactive Hybrid Membership Function in Fuzzy Approach for Identification of Inclined Edge Crack in Cantilever Beam Using Vibration Signatures

2014 ◽  
Vol 592-594 ◽  
pp. 1996-2000 ◽  
Author(s):  
K.B. Ranjan ◽  
Sasmita Sahu ◽  
R. Parhi Dayal
Keyword(s):  
Cantilever Beam ◽  
Edge Crack ◽  
Fuzzy Controller ◽  
Experimental Results ◽  
Mode Shapes ◽  
Crack Identification ◽  
Hybrid Technique ◽  
Membership Functions ◽  
Inclined Edge Crack ◽  
Vibration Signatures

In this paper, the crack identification using smart technique (by several hybrid membership functions in a fuzzy controller) has been developed for inverse analysis of the vibration signatures (like modal frequencies, mode shapes) and crack parameters (like crack depth, crack location and crack inclination) of an inclined edge crack cantilever beam. The modal frequencies are obtained from finite element (using ANSYS) and experimental analysis which are used as inputs to the hybrid fuzzy controller. The hybrid fuzzy system is designed by taking different types of membership functions (MF) to determine the crack parameters. The calculated first three modal frequencies are used to create number of fuzzy rules with the three output crack parameters. Finally, the proposed hybrid technique is validated by comparing the results obtained from trapezoidal and Gaussian fuzzy controllers, FEA and experimental results. The outcomes obtained from hybrid fuzzy controller are in good agreement with experimental results. Nomenclature

Acceleration Strategies Based on an Improved Bubble Packing Method

2014 ◽  
Vol 16 (1) ◽  
pp. 115-135 ◽  
Author(s):  
Nan Qi ◽  
Yufeng Nie ◽  
Weiwei Zhang
Keyword(s):  
Delaunay Triangulation ◽  
Viscosity Coefficient ◽  
Stable System ◽  
Governing Equations ◽  
High Quality ◽  
Numerical Examples ◽  
Ongoing Effort ◽  
System Equilibrium ◽  
The Cost ◽  
Packing Method

AbstractThe bubble packing method can generate high-quality node sets in simple and complex domains. However, its efficiency remains to be improved. This study is a part of an ongoing effort to introduce several acceleration schemes to reduce the cost of simulation. Firstly, allow the viscosity coefficient c in the bubble governing equations to change according the coordinate of the bubble which are defined separately as odd and normal bubbles, and meanwhile with the saw-shape relationship with time or iterations. Then, in order to relieve the over crowded initial bubble placement, two coefficients w1 and w2 are introduced to modify the insertion criterion. The range of those two coefficients are discussed to be w1 = 1, w2 ∈ [0.5,0.8]. Finally, a self-adaptive termination condition is logically set when the stable system equilibrium is achieved. Numerical examples illustrate that the computing cost can significantly decrease by roughly 80% via adopting various combination of proper schemes (except the uniform placement example), and the average qualities of corresponding Delaunay triangulation substantially exceed 0.9. It shows that those strategies are efficient and can generate a node set with high quality.

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