SPECTRAL-ELEMENT-BASED SOLUTIONS FOR WAVE PROPAGATION ANALYSIS OF MULTIPLY CONNECTED UNSYMMETRIC LAMINATED COMPOSITE BEAMS

2000 ◽  
Vol 237 (5) ◽  
pp. 819-836 ◽  
Author(s):  
D. ROY MAHAPATRA ◽  
S. GOPALAKRISHNAN ◽  
T.S. SANKAR
Keyword(s):  
Wave Propagation ◽  
Laminated Composite ◽  
Spectral Element ◽  
Composite Beams ◽  
Multiply Connected ◽  
Propagation Analysis ◽  
Laminated Composite Beams

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.

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.

Spectral Element Model for the PZT-Bonded Laminated Composite Beams

2012 ◽  
Vol 249-250 ◽  
pp. 838-841 ◽  
Author(s):  
Usik Lee ◽  
Il Wook Park ◽  
In Joon Jang
Keyword(s):  
Frequency Domain ◽  
Dynamic Stiffness ◽  
Laminated Composite ◽  
Element Model ◽  
Spectral Element ◽  
Composite Beams ◽  
Dft Theory ◽  
Shape Functions ◽  
Laminated Composite Beams ◽  
Dynamic Shape

This paper presents a spectral element model for the laminated composite beams with a surface-bonded PZT layer. The spectral element model represented by exact dynamic stiffness matrix is derived in the frequency-domain by using the frequency-dependent dynamic shape functions which are formulated from the free wave solutions satisfying the governing differential equations transformed into the frequency-domain by using the DFT theory. The performance of the present spectral element model is then evaluated by comparing its solutions with those obtained by using the conventional finite element model

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