Wavelet based spectral finite element modelling and detection of de-lamination in composite beams

2006 ◽  
Vol 462 (2070) ◽  
pp. 1721-1740 ◽  
Author(s):  
M Mitra ◽  
S Gopalakrishnan
Keyword(s):  
Finite Element ◽  
Wave Propagation ◽  
Damage Detection ◽  
Function Approximation ◽  
Scaling Function ◽  
Narrow Band ◽  
Broad Band ◽  
Propagation Characteristics ◽  
Propagation Analysis ◽  
Spectral Finite Element

In this paper, a model for composite beam with embedded de-lamination is developed using the wavelet based spectral finite element (WSFE) method particularly for damage detection using wave propagation analysis. The simulated responses are used as surrogate experimental results for the inverse problem of detection of damage using wavelet filtering. The WSFE technique is very similar to the fast fourier transform (FFT) based spectral finite element (FSFE) except that it uses compactly supported Daubechies scaling function approximation in time. Unlike FSFE formulation with periodicity assumption, the wavelet-based method allows imposition of initial values and thus is free from wrap around problems. This helps in analysis of finite length undamped structures, where the FSFE method fails to simulate accurate response. First, numerical experiments are performed to study the effect of de-lamination on the wave propagation characteristics. The responses are simulated for different de-lamination configurations for both broad-band and narrow-band excitations. Next, simulated responses are used for damage detection using wavelet analysis.

Wave Propagation Analysis in Anisotropic Plate Using Wavelet Spectral Element Approach

2008 ◽  
Vol 75 (1) ◽  
Author(s):  
Mira Mitra ◽  
S. Gopalakrishnan
Keyword(s):  
Finite Element ◽  
Wave Propagation ◽  
Differential Equations ◽  
Laminated Composite ◽  
Composite Plates ◽  
Spectral Element ◽  
Wave Number ◽  
Frequency Wave ◽  
Propagation Analysis ◽  
Spectral Finite Element

In this paper, a 2D wavelet-based spectral finite element (WSFE) is developed for a anisotropic laminated composite plate to study wave propagation. Spectral element model captures the exact inertial distribution as the governing partial differential equations (PDEs) are solved exactly in the transformed frequency-wave-number domain. Thus, the method results in large computational savings compared to conventional finite element (FE) modeling, particularly for wave propagation analysis. In this approach, first, Daubechies scaling function approximation is used in both time and one spatial dimensions to reduce the coupled PDEs to a set of ordinary differential equations (ODEs). Similar to the conventional fast Fourier transform (FFT) based spectral finite element (FSFE), the frequency-dependent wave characteristics can also be extracted directly from the present formulation. However, most importantly, the use of localized basis functions in the present 2D WSFE method circumvents several limitations of the corresponding 2D FSFE technique. Here, the formulated element is used to study wave propagation in laminated composite plates with different ply orientations, both in time and frequency domains.

scholarly journals A novel formulation of 3D spectral element for wave propagation in reinforced concrete

2017 ◽  
Vol 65 (6) ◽  
pp. 805-813 ◽  
Author(s):  
M. Rucka ◽  
W. Witkowski ◽  
J. Chróścielewski ◽  
S. Burzyński ◽  
K. Wilde
Keyword(s):  
Finite Element ◽  
Wave Propagation ◽  
Reinforced Concrete ◽  
Damage Detection ◽  
Numerical Simulations ◽  
Spectral Element ◽  
Steel Bars ◽  
Degradation Models ◽  
Spectral Finite Element ◽  
3D Solid

AbstractThe paper deals with numerical simulations of wave propagation in reinforced concrete for damage detection purposes. A novel formulation of a 3D spectral element was proposed. The reinforcement modelled as the truss spectral element was embedded in the 3D solid spectral finite element. Numerical simulations have been conducted on cuboid concrete specimens reinforced with two steel bars. Different degradation models were considered to study the real behaviour of bended beams.

Spectral finite element method for wave propagation analysis in smart composite beams containing delamination

2020 ◽  
Vol 92 (3) ◽  
pp. 440-451
Author(s):  
Namita Nanda
Keyword(s):  
Finite Element ◽  
Wave Propagation ◽  
Composite Beam ◽  
Spectral Element ◽  
Equation Of Motion ◽  
Composite Beams ◽  
Piezoelectric Composite ◽  
Content Type ◽  
Propagation Analysis ◽  
Spectral Finite Element

Purpose The purpose of the study is to present a frequency domain spectral finite element model (SFEM) based on fast Fourier transform (FFT) for wave propagation analysis of smart laminated composite beams with embedded delamination. For generating and sensing high-frequency elastic waves in composite beams, piezoelectric materials such as lead zirconate titanate (PZT) are used because they can act as both actuators and sensors. The present model is used to investigate the effects of parametric variation of delamination configuration on the propagation of fundamental anti-symmetric wave mode in piezoelectric composite beams. Design/methodology/approach The spectral element is derived from the exact solution of the governing equation of motion in frequency domain, obtained through fast Fourier transformation of the time domain equation. The beam is divided into two sublaminates (delamination region) and two base laminates (integral regions). The delamination region is modeled by assuming constant and continuous cross-sectional rotation at the interfaces between the base laminate and sublaminates. The governing differential equation of motion for delaminated composite beam with piezoelectric lamina is obtained using Hamilton’s principle by introducing an electrical potential function. Findings A detailed study of the wave response at the sensor shows that the A0 mode can be used for delamination detection in a wide region and is more suitable for detecting small delamination. It is observed that the amplitude and time of arrival of the reflected A0 wave from a delamination are strongly dependent on the size, position of the delamination and the stacking sequence. The degraded material properties because of the loss of stiffness and density in damaged area differently alter the S0 and A0 wave response and the group speed. The present method provides a potential technique for researchers to accurately model delaminations in piezoelectric composite beam structures. The delamination position can be identified if the time of flight of a reflected wave from delamination and the wave propagation speed of A0 (or S0) mode is known. Originality/value Spectral finite element modeling of delaminated composite beams with piezoelectric layers has not been reported in the literature yet. The spectral element developed is validated by comparing the present results with those available in the literature. The spectral element developed is then used to investigate the wave propagation characteristics and interaction with delamination in the piezoelectric composite beam.

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