A Hermite Spline Layerwise Time Domain Spectral Finite Element for Guided Wave Prediction in Laminated Composite and Sandwich Plates

2017 ◽  
Vol 139 (3) ◽  
Author(s):  
C. S. Rekatsinas ◽  
D. A. Saravanos
Keyword(s):  
Finite Element ◽  
Time Domain ◽  
Guided Waves ◽  
Mass Matrix ◽  
Time Integration ◽  
Laminated Composite ◽  
Guided Wave ◽  
Sandwich Plates ◽  
Transverse Displacement ◽  
Lumped Mass

A new time domain spectral plate finite element (FE) is developed to provide fast numerical calculations of guided waves and transient phenomena in laminated composite and sandwich plates. A new multifield layerwise laminate theory provides the basis for the FE, which incorporates cubic Hermite polynomial splines for the approximation of the in-plane and transverse displacement fields through the thickness of the plate, enabling the modeling of symmetric and antisymmetric wave modes. The time domain spectral FE with multi-degrees-of-freedom (DOF) per node is subsequently formulated, which uses integration points collocated with the nodes to yield consistent diagonal lumped mass matrix which expedites the explicit time integration process. Numerical simulations of wave propagation in aluminum, laminated carbon/epoxy and thick sandwich plates are presented and validated with an analytical solution and a three-dimensional (3D) solid element; moreover, the capability to accurately and rapidly predict antisymmetric and symmetric guided waves is demonstrated.

CALCULATION OF DISPERSION CURVES FOR ARBITRARY WAVEGUIDES USING FINITE ELEMENT METHOD

2014 ◽  
Vol 06 (05) ◽  
pp. 1450059 ◽  
Author(s):  
KAIGE ZHU ◽  
DAINING FANG
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Guided Waves ◽  
Dispersion Curves ◽  
Guided Wave ◽  
Sandwich Plates ◽  
Multilayered Structures ◽  
Finite Element Software ◽  
Honeycomb Sandwich ◽  
Element Method

Dispersion curves for waveguide structures are an important prerequisite for the implementation of guided wave-based nondestructive evaluation (NDE) approach. Although many methods exist, each method is only applicable to a certain type of structures, and also requires complex programming. A Bloch theorem-based finite element method (FEM) is proposed to obtain dispersion curves for arbitrary waveguides using commercial finite element software in this paper Dispersion curves can be obtained for a variety of structures, such as homogeneous plates, multilayered structures, finite cross section rods and honeycomb sandwiches. The propagation of guided waves in honeycomb sandwich plates and beams are discussed in detail. Then, dispersion curves for honeycomb sandwich beams are verified by experiments.

scholarly journals Time-Domain Hybrid Global-Local Prediction of Guided Waves Interaction with Damage

2013 ◽  
Vol 558 ◽  
pp. 116-127 ◽  
Author(s):  
Matthieu Gresil ◽  
Victor Giurgiutiu
Keyword(s):  
Finite Element ◽  
Wave Propagation ◽  
Time Domain ◽  
Guided Waves ◽  
Lamb Waves ◽  
Mode Conversion ◽  
Wave Interaction ◽  
Guided Wave ◽  
Element Mesh ◽  
The Time Domain

This paper presents a hybrid finite element and analytical method to predict the 1-D guided wave propagation interaction with damage for nondestructive evaluation (NDE) and structural health monitoring (SHM) application. The finite element mesh is used to describe the region around the damage (defects or flaws). In contrast to other hybrid models developed elsewhere, the interaction between Lamb waves and defects is computed in the time domain using the explicit solver of the commercial finite element method (FEM) software ABAQUS. Analytical methods can perform efficient modeling of wave propagation but are limited to simple geometries. Realistic structures with complicated geometries are usually modeled with the FEM. However, to obtain an accurate wave propagation solution at ultrasonic frequencies is computationally intensive and may become prohibitive for realistic structures. In response to today's complex cases not covered by the simulation tools available, we aim to develop an efficient and accessible tool for SHM applications. This tool will be based on a hybrid coupling between analytical solutions and time domain numerical codes. Lamb wave interaction with a notch is investigated by using this method, and the results obtained are with respect to transmission, reflection and mode conversion. Because of the symmetric mode shape, S0 is more sensitive to the shallow notch than A0. By making use of the fact that the reflection increases with increase in notch depth and mode conversion are maximized when the notch is around half through the thickness of the plate, the reflection and conversion coefficients can be used to characterize the depth of the notch.

scholarly journals Modeling Structural Dynamics Using FE-Meshfree QUAD4 Element with Radial-Polynomial Basis Functions

Materials ◽  
2021 ◽  
Vol 14 (9) ◽  
pp. 2288
Author(s):  
Hongming Luo ◽  
Guanhua Sun
Keyword(s):  
Structural Dynamics ◽  
Interpolation Method ◽  
Mass Matrix ◽  
Time Integration ◽  
Partition Of Unity ◽  
Implicit Time ◽  
Lumped Mass ◽  
Point Interpolation Method ◽  
Point Interpolation ◽  
Consistent Mass Matrix

The PU (partition-of-unity) based FE-RPIM QUAD4 (4-node quadrilateral) element was proposed for statics problems. In this element, hybrid shape functions are constructed through multiplying QUAD4 shape function with radial point interpolation method (RPIM). In the present work, the FE-RPIM QUAD4 element is further applied for structural dynamics. Numerical examples regarding to free and forced vibration analyses are presented. The numerical results show that: (1) If CMM (consistent mass matrix) is employed, the FE-RPIM QUAD4 element has better performance than QUAD4 element under both regular and distorted meshes; (2) The DLMM (diagonally lumped mass matrix) can supersede the CMM in the context of the FE-RPIM QUAD4 element even for the scheme of implicit time integration.

scholarly journals Longitudinal Guided Wave Inspection of Small-Diameter Elbowed Steel Tubes with a Novel Squirrel-Cage Magnetostrictive Sensor

2019 ◽  
Vol 2019 ◽  
pp. 1-9
Author(s):  
Yao Liu ◽  
Xiucheng Liu ◽  
Chehua Yang ◽  
Wenxin Guo ◽  
Bin Wu ◽  
...  
Keyword(s):  
Finite Element ◽  
Guided Waves ◽  
Mode Conversion ◽  
Small Diameter ◽  
Longitudinal Mode ◽  
Guided Wave ◽  
Wall Defect ◽  
Squirrel Cage ◽  
Simulation Results ◽  
Magnetostrictive Sensor

In the study, ultrasonic longitudinal mode guided waves were employed to detect defects in elbowed tubes (without welds) with a diameter of 10 mm. Finite element simulation results highlighted that the emitted L(0,1) mode guided waves experienced strong reflection and mode conversion at the elbow region to generate F(1,1) mode, followed by slow and weak F(2,1) mode. The guided wave reflected from the elbow with a through-wall defect was manifested as two overlapped wave packets, which were good indicators of a defective elbow. To conduct L(0,1) mode guided waves inspection on the small-diameter elbowed tubes, a novel tailored squirrel-cage magnetostrictive sensor was employed in the experiment. The new sensor employed the configuration of segmental iron-cobalt strips and small-size permanent magnet arrays. The entire sensor is composed of two identical C-shaped sensor elements and can be recycled and installed conveniently. Experimental results obtained from healthy and defective tubes were consistent with the conclusions obtained from finite element simulations. An artificial through-wall defect at the elbow and a notch defect at the straight part of the tube could be simultaneously detected by L(0,1) mode guided waves through comparing experimental signals with simulation results.

Guided Wave Focusing Mechanics in Pipe

2003 ◽  
Author(s):  
Takahiro Hayashi ◽  
Koichiro Kawashima ◽  
Zongqi Sun ◽  
Joseph L. Rose
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Guided Waves ◽  
Wave Structure ◽  
Guided Wave ◽  
Pipe Inspection ◽  
Specific Point ◽  
Wave Focusing ◽  
Beam Focusing ◽  
Subsequent Time

Guided waves can be used in pipe inspection over long distances. Presented in this paper is a beam focusing technique to improve the S/N ratio of the reflection from a tiny defect. Focusing is accomplished by using non-axisymmetric waveforms and subsequent time delayed superposition at a specific point in a pipe. A semi-analytical finite element method is used to present wave structure in the pipe. Focusing potential is also studied with various modes and frequencies.

Contribution of Lamb wave modes in the formation of higher order modes cluster (HOMC) guided waves

2021 ◽  
pp. 095440622110424
Author(s):  
Z Abbasi ◽  
F Honarvar
Keyword(s):  
Finite Element ◽  
Wave Packet ◽  
Lamb Wave ◽  
Guided Waves ◽  
Element Model ◽  
Higher Order ◽  
Guided Wave ◽  
Cross Sectional ◽  
Higher Order Modes ◽  
Wave Modes

In recent years, Higher Order Modes Cluster (HOMC) guided waves have been considered for ultrasonic testing of plates and pipes. HOMC guided waves consist of higher order Lamb wave modes that travel together as a single nondispersive wave packet. The objective of this paper is to investigate the effect of frequency-thickness value on the contribution of Lamb wave modes in an HOMC guided wave. This is an important issue that has not been thoroughly investigated before. The contribution of each Lamb wave mode in an HOMC guided wave is studied by using a two-dimensional finite element model. The level of contribution of various Lamb wave modes to the wave cluster is verified by using a 2D FFT analysis. The results show that by increasing the frequency-thickness value, the order of contributing modes in the HOMC wave packet increases. The number of modes that comprise a cluster also increases up to a specific frequency-thickness value and then it starts to decrease. Plotting of the cross-sectional displacement patterns along the HOMC guided wave paths confirms the shifting of dominant modes from lower to higher order modes with increase of frequency-thickness value. Experimental measurements conducted on a mild steel plate are used to verify the finite element simulations. The experimental results are found to be in good agreement with simulations and confirm the changes observed in the level of contribution of Lamb wave modes in a wave cluster by changing the frequency-thickness value.

Finite-Element Modeling of Time-Domain Controlled-Source Electromagnetic Survey with Weighted Laguerre Polynomials

Geophysics ◽  
2021 ◽  
pp. 1-43
Author(s):  
Qingtao Sun ◽  
Runren Zhang ◽  
Yunyun Hu
Keyword(s):  
Finite Element ◽  
Time Domain ◽  
Laguerre Polynomials ◽  
Time Integration ◽  
Sampling Interval ◽  
Controlled Source ◽  
Time Integration Method ◽  
Transient Electromagnetic ◽  
Backward Euler ◽  
Land Survey

To facilitate the modeling of time-domain controlled-source electromagnetic survey, we propose an efficient finite-element method with weighted Laguerre polynomials, which shows a much lower computational complexity than conventional time integration methods. The proposed method allows sampling the field at arbitrary time steps and also its accuracy is determined by the number of polynomials, instead of the time sampling interval. Analysis is given regarding the optimization of the polynomial number to be used and the criterion of selecting the time scale factor. Two numerical examples in marine and land survey environments are included to demonstrate the superiority of the proposed method over the existing backward Euler time integration method. The proposed method is expected to facilitate the modeling of transient electromagnetic surveys in the geophysical regime.

Nonlinear finite element analysis of smart laminated composite sandwich plates

2014 ◽  
Vol 14 (03) ◽  
pp. 1350075 ◽  
Author(s):  
S. K. Sarangi ◽  
B. Basa
Keyword(s):  
Finite Element ◽  
Fiber Composite ◽  
Orientation Angle ◽  
Shear Deformation Theory ◽  
Laminated Composite ◽  
Numerical Results ◽  
Sandwich Plates ◽  
Fe Model ◽  
Composite Sandwich ◽  
Composite Sandwich Plates

This paper deals with the nonlinear dynamic analysis of smart laminated composite sandwich plates. A three dimensional energy based finite element (FE) model has been developed for the composite sandwich plates integrated with the patches of active constrained layer damping (ACLD) treatment. Von Kármán type nonlinear strain–displacement relations and the first-order shear deformation theory (FSDT) are adopted individually for each layer of the sandwich plate in developing the FE model. The constraining layer of the ACLD treatment is considered to be made of active fiber composite (AFC) material. The Golla–Hughes–McTavish (GHM) method is used to model the constrained viscoelastic layer of the ACLD treatment in the time domain. Sandwich plates with symmetric and antisymmetric laminated faces separated by HEREX core are considered for evaluation of the numerical results. The numerical results indicate that the ACLD patches significantly improve the damping characteristics of the composite sandwich plates for suppressing their geometrically nonlinear transient vibrations. The effect of variation of piezoelectric fiber orientation angle in the AFC material on the control authority of the ACLD patches is also investigated.

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