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.

A Spectral Finite Element Model for Wave Propagation Analysis in Laminated Composite Plate

2006 ◽  
Vol 128 (4) ◽  
pp. 477-488 ◽  
Author(s):  
A. Chakraborty ◽  
S. Gopalakrishnan
Keyword(s):  
Finite Element ◽  
Wave Propagation ◽  
Shear Deformation ◽  
Mechanical Response ◽  
Laminated Composite ◽  
Wave Number ◽  
Single Element ◽  
Element Formulation ◽  
Frequency Wave ◽  
Spectral Finite Element

A new spectral plate element (SPE) is developed to analyze wave propagation in anisotropic laminated composite media. The element is based on the first-order laminated plate theory, which takes shear deformation into consideration. The element is formulated using the recently developed methodology of spectral finite element formulation based on the solution of a polynomial eigenvalue problem. By virtue of its frequency-wave number domain formulation, single element is sufficient to model large structures, where conventional finite element method will incur heavy cost of computation. The variation of the wave numbers with frequency is shown, which illustrates the inhomogeneous nature of the wave. The element is used to demonstrate the nature of the wave propagating in laminated composite due to mechanical impact and the effect of shear deformation on the mechanical response is demonstrated. The element is also upgraded to an active spectral plate clement for modeling open and closed loop vibration control of plate structures. Further, delamination is introduced in the SPE and scattered wave is captured for both broadband and modulated pulse loading.

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