scholarly journals Variable Thickness in Plates—A Solution for SHM Based on the Topological Derivative

Sensors ◽  
2020 ◽  
Vol 20 (9) ◽  
pp. 2529
Author(s):  
Anxo Martínez ◽  
Alfredo Güemes ◽  
Jose M. Perales ◽  
Jose M. Vega
Keyword(s):  
Health Monitoring ◽  
Variable Thickness ◽  
Guided Waves ◽  
Complex Geometry ◽  
Time Lag ◽  
Topological Derivative ◽  
Dynamic Equations ◽  
Constant Thickness ◽  
Rectangular Plates ◽  
Analyze Case

The topological derivative tool is applied here in structural health monitoring (SHM) problems to locate small defects in a material plate with complex geometry that is subject to permanent multifrequency guided waves excitation. Compared to more standard SHM methods, based in measuring the time-lag between emitted and received propagative pulses plus some postprocessing, the topological derivative somehow compares the measured and computed (solving the full elasto-dynamic equations) response of the damaged plate, instead of relying on only the time of flight of the wave. Thus, the method profits the knowledge behind the physics of the problem and can cope with scenarios in which classical methods give poor results. The authors of this paper have already used the topological derivative in rectangular plates with constant thickness, but with defects consisting simply in both through slits and inclusions of a different material, and actuators/sensors located near the boundary, which makes very difficult to use standard SHM methods. This is an extension of the method, also considering the much more difficult to analyze case of plates with variable thickness and complex (non-rectangular) planform.

Exact solution for free vibration analysis of linearly varying thickness FGM plate using Galerkin-Vlasov’s method

2020 ◽  
pp. 146442072098049
Author(s):  
V Kumar ◽  
SJ Singh ◽  
VH Saran ◽  
SP Harsha
Keyword(s):  
Free Vibration ◽  
Variable Thickness ◽  
Vibration Analysis ◽  
Shear Deformation Theory ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Constant Thickness ◽  
Engineering Structures ◽  
Property Variation ◽  
Varying Thickness

The present paper investigates the free vibration analysis for functionally graded material plates of linearly varying thickness. A non-polynomial higher order shear deformation theory is used, which is based on inverse hyperbolic shape function for the tapered FGM plate. Three different types of material gradation laws, specifically: a power (P-FGM), exponential (E-FGM), and sigmoid law (S-FGM) are used to calculate the property variation in the thickness direction of FGM plate. The variational principle has been applied to derive the governing differential equation for the plates. Non-dimensional frequencies have been evaluated by considering the semi-analytical approach viz. Galerkin-Vlasov’s method. The accuracy of the preceding formulation has been validated through numerical examples consisting of constant thickness and tapered (variable thickness) plates. The findings obtained by this method are found to be in close agreement with the published results. Parametric studies are then explored for different geometric parameters like taper ratio and boundary conditions. It is deduced that the frequency parameter is maximum for S-FGM tapered plate as compared to E- and P-FGM tapered plate. Consequently, it is concluded that the S-FGM tapered plate is suitable for those engineering structures that are subjected to huge excitations to avoid resonance conditions. In addition, it is found that the taper ratio is significantly affected by the type of constraints on the edges of the tapered FGM plate. Some novel results for FGM plate with variable thickness are also computed that can be used as benchmark results for future reference.

scholarly journals Optimization on the Production of Variable Thickness Aluminium Tubes

2010 ◽  
Author(s):  
Reza Bihamta ◽  
Guillaume D’Amours ◽  
Quang-Hien Bui ◽  
Ahmed Rahem ◽  
Michel Guillot ◽  
...  
Keyword(s):  
Variable Thickness ◽  
Constant Thickness ◽  
Outer Diameter ◽  
Minimum Thickness ◽  
Mechanical Parts ◽  
Tube Drawing ◽  
Matlab Code ◽  
Mechanical Assemblies ◽  
Optimization Study ◽  
One Step

The variable thickness tube drawing is a new modification in the tube drawing methods which enables production of axially variable thickness tubes faster and easier in comparison with other similar methods like radial forging or indentation forging. The production of this type of tubes can be used in optimum design of mechanical parts which do not necessarily need constant thickness along the axis of tube and this method can strikingly reduce the overall weight of parts and mechanical assemblies like cars. In this paper, the variable thickness tube drawing were parameterized in a MATLAB code and optimized with the Ls-Opt software as an optimization engine and Ls-Dyna as a FE solver. The final objective of this optimization study is to determine the minimum thickness which can be produced in one step by this method with various tube dimensions (tube thickness and outer diameter). For verification of results, some experiments were performed in the tube drawing machine which was fabricated by this research group and acceptable correspondence was observed between numerical and experimental results.

scholarly journals Experimentation and Adaptive Modeling for Temperature Effect Quantification in PVP Structural Health Monitoring With PWAS

2015 ◽  
Author(s):  
Tuncay Kamas ◽  
Banibrata Poddar ◽  
Bin Lin ◽  
Lingyu Yu ◽  
Victor Giurgiutiu
Keyword(s):  
Elevated Temperature ◽  
Structural Health Monitoring ◽  
Health Monitoring ◽  
Thermal Effects ◽  
Guided Waves ◽  
Substrate Material ◽  
Ultrasonic Waves ◽  
Material Parameters ◽  
Structural Health

The thermal effects at elevated temperatures mostly exist for pressure vessel and pipe (PVP) applications. The technologies for diagnosis and prognosis of PVP systems need to take the thermal effect into account and compensate it on sensing and monitoring of PVP structures. One of the extensively employed sensor technologies has been permanently installed piezoelectric wafer active sensor (PWAS) for in-situ continuous structural health monitoring (SHM). Using the transduction of ultrasonic elastic waves into voltage and vice versa, PWAS has been emerged as one of the major SHM sensing technologies. However, the dynamic characteristics of PWAS need to be explored prior its installation for in-situ SHM. Electro-mechanical impedance spectroscopy (EMIS) method has been utilized as a dynamic descriptor of PWAS and as a high frequency local modal sensing technique by applying standing waves to indicate the response of the PWAS resonator by determining the resonance and anti-resonance frequencies. Another SHM technology utilizing PWAS is guided wave propagation (GWP) as a far-field transient sensing technique by transducing the traveling guided ultrasonic waves (GUW) into substrate structure. The paper first presents EMIS method that qualifies and quantifies circular PWAS resonators under traction-free boundary condition and in an ambience with increasing temperature. The piezoelectric material degradation was investigated by introducing the temperature effects on the material parameters that are obtained from experimental observations as well as from related work in literature. GWP technique is also presented by inclusion of the thermal effects on the substrate material. The MATLAB GUI under the name of Wave Form Revealer (WFR) was adapted for prediction of the thermal effects on coupled guided waves and dynamic structural change in the substrate material at elevated temperature. The WFR software allows for the analysis of multimodal guided waves in the structure with affected material parameters in an ambience with elevated temperature.

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.

An Analytical Solution for Transversely Isotropic Simply Supported Thick Rectangular Plates Using Displacement Potential Functions

2011 ◽  
Vol 46 (2) ◽  
pp. 121-142 ◽  
Author(s):  
M Nematzadeh ◽  
M Eskandari-Ghadi ◽  
B Navayi Neya
Keyword(s):  
Isotropic Material ◽  
Transversely Isotropic ◽  
Numerical Results ◽  
Potential Functions ◽  
Constant Thickness ◽  
Rectangular Plates ◽  
Displacement Potential ◽  
Simply Supported ◽  
Axial Forces ◽  
Internal Forces

Using a complete set of displacement potential functions, the exact solution of three-dimensional elasticity equations of a simply supported rectangular plates with constant thickness consisting of a transversely isotropic linearly elastic material subjected to an arbitrary static load is presented. The governing partial differential equations for the potential functions are solved through the use of the Fourier method, which results in exponential and trigonometric expression along the plate thickness and the other two lengths respectively. The displacements, stresses, and internal forces are determined through the potential functions at any point of the body. To prove the validity of this approach, the analytical solutions developed in this paper are degenerated for the simpler case of plates containing isotropic material and compared with the existing solution. In addition, the numerical results obtained from this study are compared with those reported in other researches for the isotropic material, where excellent agreement is achieved for both thin and thick plates. The results show that increasing the thickness ratios of the plate causes compressive axial forces and central shear forces inside the plate. Finally, the internal forces and displacement components are calculated numerically for several kinds of transversely isotropic materials with different anisotropies and are compared with a finite element (FE) solution obtained from the ANSYS software, where the high accuracy of the present method is demonstrated. The effects of the material anisotropy are clearly revealed in the numerical results presented.

RELATIONSHIP OF MAXIMUM DEFLECTIONS AND NATURAL FREQUENCIES VIBRATIONS OF ISOTROPIC CIRCULAR PLATES WITH INHOMOGENEOUS RESISTANCE CONDITIONS ON THE OUTER AND INNER CONTOUR

2021 ◽  
Vol 98 (6) ◽  
pp. 36-42
Author(s):  
A.V. TURKOV ◽  
◽  
S.I. POLESHKO ◽  
E.A. FINADEEVA ◽  
K.V. MARFIN ◽  
...  
Keyword(s):  
Variable Thickness ◽  
Constant Thickness ◽  
Circular Plates ◽  
Outer Contour ◽  
Numerical Studies ◽  
The Difference ◽  
Relationship Of ◽  
The Relationship ◽  
Hinged Support ◽  
Natural Transverse

The relationship between the maximum deflections from a static uniformly distributed load W0 and the fundamental frequency of natural transverse vibrations of a round isotropic plate of linearly variable thickness with thickening to the edge under homogeneous conditions of support along the outer contour, depending on the ratio of the thickness of the plate in the center to the thickness along the edge, is considered. According to the results of the study, graphs of the dependence of the maximum deflection and the frequency of natural vibrations of the plate on the ratio t1 / t2 are constructed. It is shown that for round plates of linearly variable thickness at t1/t2<1.1 coefficient K with an accuracy of 5.9% coincides with the analytical coefficient for round plates of constant thickness. Numerical studies shows that when the ratio of the thicknesses on the contour and in the center is equal to two, the difference in the coefficient K, which depends on the relationship between the static and dynamic characteristics of the platinum, is about 25% for hinged support along the contour and up to 37% for rigid support. This indicates a more significant effect of uneven mass distribution for such boundary conditions.

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