scholarly journals Crack identification based on the nonlinear response of plates with variably oriented surface crack.

2018 ◽  
Vol 149 ◽  
pp. 02061
Author(s):  
H. Chouiyakh ◽  
L. Azrar ◽  
K. Alnefaie ◽  
O. Akourri
Keyword(s):  
Hilbert Transform ◽  
Surface Crack ◽  
Structural Integrity ◽  
Plate Theory ◽  
Differential Quadrature Method ◽  
Crack Identification ◽  
Rectangular Plates ◽  
Cracked Plates ◽  
Line Spring Model ◽  
Linear And Nonlinear

In order to secure structural and operational safety of structures, it is important to implement a structural health monitoring (SHM) strategy to issue early warnings on damage or deterioration prior to costly repair or even catastrophic collapse. Developing a SHM strategy for structures enables evaluating structural integrity, durability and reliability of the monitored structure. Hence, the main objective of this work is to develop a damage detection procedure based on a plate’s dynamic response and the Hilbert transform. Rectangular plates are considered and assumed to contain a surface crack which is centrally located, with a depth of h0, a length of 2C and inclined with an angle β. Von Karman plate theory is adopted herein, and the crack is modeled through the line spring model given by fracture mechanics. The plate is assumed to behave nonlinearly due to large deformation. The differential quadrature method is used to investigate the linear and nonlinear dynamic behaviors of cracked plates. The influence of crack’s parameters on modal properties is discussed. The eigenfrequencies of cracked plates with respect to crack half length C and orientation β are performed. For crack characterization, Hilbert transform is applied to the obtained linear and nonlinear time responses. It is shown throughout this paper that identified backbones describe changes in crack orientation.

scholarly journals Buckling and Vibration of Non-Homogeneous Rectangular Plates Subjected to Linearly Varying In-Plane Force

2013 ◽  
Vol 20 (5) ◽  
pp. 879-894 ◽  
Author(s):  
Roshan Lal ◽  
Renu Saini
Keyword(s):  
Differential Equation ◽  
Plate Theory ◽  
Differential Quadrature Method ◽  
Three Dimensional ◽  
Axial Direction ◽  
Mode Shapes ◽  
Rectangular Plates ◽  
Plate Material ◽  
Classical Plate Theory ◽  
Simply Supported

The present work analyses the buckling and vibration behaviour of non-homogeneous rectangular plates of uniform thickness on the basis of classical plate theory when the two opposite edges are simply supported and are subjected to linearly varying in-plane force. For non-homogeneity of the plate material it is assumed that young's modulus and density of the plate material vary exponentially along axial direction. The governing partial differential equation of motion of such plates has been reduced to an ordinary differential equation using the sine function for mode shapes between the simply supported edges. This resulting equation has been solved numerically employing differential quadrature method for three different combinations of clamped, simply supported and free boundary conditions at the other two edges. The effect of various parameters has been studied on the natural frequencies for the first three modes of vibration. Critical buckling loads have been computed. Three dimensional mode shapes have been presented. Comparison has been made with the known results.

Free transverse vibration analysis of thin rectangular plates locally suspended on elastic beam

2012 ◽  
Vol 227 (7) ◽  
pp. 1515-1524 ◽  
Author(s):  
M Golkaram ◽  
MM Aghdam
Keyword(s):  
Transverse Vibration ◽  
Plate Theory ◽  
Rectangular Cross Section ◽  
Differential Quadrature Method ◽  
Differential Quadrature ◽  
Rectangular Plates ◽  
Quadrature Method ◽  
Generalized Differential Quadrature Method ◽  
Free Transverse Vibration ◽  
Generalized Differential

Free transverse vibration of thin rectangular plates locally suspended on deformable beam is presented using generalized differential quadrature method. The plate is completely free at all edges except a local region which is attached to a thin beam with rectangular cross section. The other side of the beam is fixed and the whole system is subjected to free transverse vibrations. According to classical plate theory and Euler–Bernoulli beam assumption, two coupled partial differential equations of the system are obtained. The governing equations and solution domain are discretized based on the generalized differential quadrature method and natural frequencies of the plate attached to the beam are obtained. Accuracy of the predictions is investigated using four simplified cases which show reasonably good agreement. For the general case, however, due to lack of data in the literature, predictions are compared with finite element results, which also demonstrate close agreement.

Mode shapes and frequencies of thin rectangular plates with arbitrarily varying non-homogeneity along two concurrent edges

2016 ◽  
Vol 23 (17) ◽  
pp. 2841-2865 ◽  
Author(s):  
Roshan Lal ◽  
Renu Saini
Keyword(s):  
Eigenvalue Problems ◽  
Plate Theory ◽  
Differential Quadrature Method ◽  
Three Dimensional ◽  
Mode Shapes ◽  
Rectangular Plates ◽  
Simply Supported ◽  
Transverse Vibrations ◽  
Modes Of Vibration ◽  
Generalized Differential

Analysis and numerical results are presented for free transverse vibrations of isotropic rectangular plates having arbitrarily varying non-homogeneity with the in-plane coordinates along the two concurrent edges on the basis of Kirchhoff plate theory. For the non-homogeneity, a general type of variation for Young’s modulus and density of the plate material has been assumed. Generalized differential quadrature method has been used to obtain the eigenvalue problem for such model of plates for four different combinations of boundary conditions at the edges namely, (i) fully clamped, (ii) two opposite edges are clamped and other two are simply supported, (iii) two opposite edges are clamped and other two are free, and (iv) two opposite edges are simply supported and other two are free. By solving these eigenvalue problems using software MATLAB, the lowest three eigenvalues have been reported as the first three natural frequencies for the first three modes of vibration. The effect of various plate parameters on the vibration characteristics has been analysed. Three dimensional mode shapes have been plotted. A comparison of results with those available in literature has been presented.

VIBRATION ANALYSES OF CRACKED PLATES BY THE RITZ METHOD WITH MOVING LEAST-SQUARES INTERPOLATION FUNCTIONS

2014 ◽  
Vol 14 (02) ◽  
pp. 1350060 ◽  
Author(s):  
C. S. HUANG ◽  
C. W. CHAN
Keyword(s):  
Least Squares ◽  
Plate Theory ◽  
Ritz Method ◽  
Thin Plates ◽  
Mode Shapes ◽  
Moving Least Squares ◽  
Rectangular Plates ◽  
Classical Plate Theory ◽  
Cracked Plates ◽  
Admissible Functions

The solutions for the vibrations of cracked thin plates are obtained by the Ritz method with admissible functions. Based on the classical plate theory, the basis functions comprising polynomials and crack functions are adopted to generate the admissible functions by the moving least-squares approach for a set of nodes randomly distributed in the domain. The crack functions account for the singular behaviors of stress resultants at crack tip(s), which are discontinuous in displacement and slope across the crack. The present solutions are validated through convergence tests of frequencies and by comparison with the published results for simply-supported cracked rectangular plates. The solutions are further employed to determine the natural frequencies of cantilevered skewed rhombic and isosceles triangular plates and completely free circular plates, each with a crack of varying length, location and orientation. The numerical results are tabulated and some corresponding mode shapes are also presented, by means of nodal patterns. Most of the results shown here are new to the literature.

Dynamical Behaviors of Sinusoidal Nanocomposite Plates Subjected to Thermomechanical Loads

2021 ◽  
Author(s):  
Vu Ngoc Viet Hoang ◽  
Dinh Gia Ninh
Keyword(s):  
Thermal Environment ◽  
Plate Theory ◽  
Micromechanical Model ◽  
Functionally Graded ◽  
Geometrical Parameters ◽  
Rectangular Plates ◽  
Sine Function ◽  
Classical Plate Theory ◽  
Wolfram Mathematica ◽  
Number Of Cycles

In this paper, a new plate structure has been found with the change of profile according to the sine function which we temporarily call as the sinusoidal plate. The classical plate theory and Galerkin’s technique have been utilized in estimating the nonlinear vibration behavior of the new non-rectangular plates reinforced by functionally graded (FG) graphene nanoplatelets (GNPs) resting on the Kerr foundation. The FG-GNP plates were assumed to have two horizontal variable edges according to the sine function. Four different configurations of the FG-GNP plates based on the number of cycles of sine function were analyzed. The material characteristics of the GNPs were evaluated in terms of two models called the Halpin–Tsai micromechanical model and the rule of mixtures. First, to verify this method, the natural frequencies of new non-rectangular plates made of metal were compared with those obtained by the Finite Element Method (FEM). Then, the numerical outcomes are validated by comparing with the previous papers for rectangular FGM/GNP plates — a special case of this structure. Furthermore, the impacts of the thermal environment, geometrical parameters, and the elastic foundation on the dynamical responses are scrutinized by the 2D/3D graphical results and coded in Wolfram-Mathematica. The results of this work proved that the introduced approach has the advantages of being fast, having high accuracy, and involving uncomplicated calculation.

J and CTOD Based Tensile Strain Capacity Prediction for Pipelines with a Surface Crack in Girth Weld

2021 ◽  
Author(s):  
Youn-Young Jang ◽  
Nam-Su Huh ◽  
Ik-Joong Kim ◽  
Young-Pyo Kim
Keyword(s):  
Crack Initiation ◽  
Internal Pressure ◽  
Surface Crack ◽  
Driving Force ◽  
Tensile Strain ◽  
Structural Integrity ◽  
Accurate Estimation ◽  
Long Distance ◽  
Crack Driving Force ◽  
Girth Welding

Abstract Long-distance pipelines for the transport of oil and natural gas to onshore facilities are mainly fabricated by girth welding, which has been considered as a weak location for cracking. Pipeline rupture due to crack initiation and propagation in girth welding is one of the main issues of structural integrity for a stable supply of energy resources. The crack assessment should be performed by comparing the crack driving force with fracture toughness to determine the critical point of fracture. For this reason, accurate estimation of the crack driving force for pipelines with a crack in girth weld is highly required. This paper gives the newly developed J-integral and crack-tip opening displacement (CTOD) estimation in a strain-based scheme for pipelines with an internal surface crack in girth weld under axial displacement and internal pressure. For this purpose, parametric finite element analyses have been systematically carried out for a set of pipe thicknesses, crack sizes, strain hardening, overmatch and internal pressure conditions. Using the proposed solutions, tensile strain capacities (TSCs) were quantified by performing crack assessment based on crack initiation and ductile instability and compared with TSCs from curved wide plate tests to confirm their validity.

scholarly journals Nonlinear Dynamic Analysis for Rectangular FGM Plates with Variable Thickness Subjected to Mechanical Load

2019 ◽  
Vol 35 (3) ◽  
Author(s):  
Khuc Van Phu ◽  
Le Xuan Doan ◽  
Nguyen Van Thanh
Keyword(s):  
Variable Thickness ◽  
Nonlinear Dynamic ◽  
Volume Fraction ◽  
Mechanical Load ◽  
Plate Theory ◽  
Geometrical Nonlinearity ◽  
Nonlinear Dynamic Analysis ◽  
Dynamic Responses ◽  
Rectangular Plates ◽  
Classical Plate Theory

 In this paper, the governing equations of rectangular plates with variable thickness subjected to mechanical load are established by using the classical plate theory, the geometrical nonlinearity in von Karman-Donnell sense. Solutions of the problem are derived according to Galerkin method. Nonlinear dynamic responses, critical dynamic loads are obtained by using Runge-Kutta method and the Budiansky–Roth criterion. Effect of volume-fraction index k and some geometric factors are considered and presented in numerical results.

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