Spectral Element Approach to Wave Propagation in Uncertain Composite Beam Structures

2011 ◽  
Vol 133 (5) ◽  
Author(s):  
V. Ajith ◽  
S. Gopalakrishnan
Keyword(s):  
Wave Propagation ◽  
High Frequency ◽  
Composite Beam ◽  
Composite Structures ◽  
Spectral Element ◽  
Frequency Responses ◽  
Propagation Analysis ◽  
Material Uncertainties ◽  
Element Approach ◽  
Spectral Finite Element

This paper presents a study of the wave propagation responses in composite structures in an uncertain environment. Here, the main aim of the work is to quantify the effect of uncertainty in the wave propagation responses at high frequencies. The material properties are considered uncertain and the analysis is performed using Neumann expansion blended with Monte Carlo simulation under the environment of spectral finite element method. The material randomness is included in the conventional wave propagation analysis by different distributions (namely, the normal and the Weibul distribution) and their effect on wave propagation in a composite beam is analyzed. The numerical results presented investigates the effect of material uncertainties on different parameters, namely, wavenumber and group speed, which are relevant in the wave propagation analysis. The effect of the parameters, such as fiber orientation, lay-up sequence, number of layers, and the layer thickness on the uncertain responses due to dynamic impulse load, is thoroughly analyzed. Significant changes are observed in the high frequency responses with the variation in the above parameters, even for a small coefficient of variation. High frequency impact loads are applied and a number of interesting results are presented, which brings out the true effects of uncertainty in the high frequency responses.

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.

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 Wave Propagation Analysis in Composite Laminates Containing a Delamination Using a Three-Dimensional Spectral Element Method

2012 ◽  
Vol 2012 ◽  
pp. 1-19 ◽  
Author(s):  
Fucai Li ◽  
Haikuo Peng ◽  
Xuewei Sun ◽  
Jinfu Wang ◽  
Guang Meng
Keyword(s):  
Wave Propagation ◽  
Lamb Wave ◽  
Composite Laminates ◽  
Composite Structures ◽  
Spectral Element Method ◽  
Three Dimensional ◽  
Spectral Element ◽  
Wave Mode ◽  
Diagonal Form ◽  
Element Method

A three-dimensional spectral element method (SEM) was developed for analysis of Lamb wave propagation in composite laminates containing a delamination. SEM is more efficient in simulating wave propagation in structures than conventional finite element method (FEM) because of its unique diagonal form of the mass matrix. Three types of composite laminates, namely, unidirectional-ply laminates, cross-ply laminates, and angle-ply laminates are modeled using three-dimensional spectral finite elements. Wave propagation characteristics in intact composite laminates are investigated, and the effectiveness of the method is validated by comparison of the simulation results with analytical solutions based on transfer matrix method. Different Lamb wave mode interactions with delamination are evaluated, and it is demonstrated that symmetric Lamb wave mode may be insensitive to delamination at certain interfaces of laminates while the antisymmetric mode is more suited for identification of delamination in composite structures.

A Family of Explicit Dissipative Algorithms for Pseudodynamic Testing

2006 ◽  
Vol 22 (2) ◽  
pp. 145-154 ◽  
Author(s):  
S.- Y. Chang
Keyword(s):  
High Frequency ◽  
Error Propagation ◽  
Numerical Dissipation ◽  
Explicit Method ◽  
High Frequency Response ◽  
Frequency Responses ◽  
Pseudodynamic Test ◽  
Propagation Analysis ◽  
Error Propagation Analysis ◽  
Pseudodynamic Testing

AbstractThe α-function method is a family of second-order explicit methods with controlled numerical dissipation. Thus, it is very promising for the pseudodynamic testing of a system where high frequency responses are of no interest. This is because that favorable numerical dissipation can suppress the spurious growth of high frequency responses, which might arise from numerical and/or experimental errors during a test. Furthermore, the implementation of an explicit method for the pseudodynamic testing is much simpler than for an implicit method. The superiority of using this method in performing a pseudodynamic test was verified both analytically and experimentally. In fact, results of error propagation analysis reveal that the spurious growth of high frequency responses can be suppressed and less error propagation is identified when compared to the Newmark explicit method. Actual tests were conducted pseudodynamically to confirm all the analytical results. It is also illustrated that although the high frequency response is insignificant to the total response it may be significantly amplified and propagated and finally destroys the pseudodynamic test results.

Fundamental Understanding of Wave Propagation in a Beam Using PZT Actuators and Sensors

2013 ◽  
Author(s):  
Vishnu Prasad Venugopal ◽  
Gang Wang
Keyword(s):  
Finite Element ◽  
Wave Propagation ◽  
Finite Elements ◽  
Timoshenko Beam ◽  
High Frequency ◽  
Beam Structure ◽  
Frequency Wave ◽  
Coupled Equations ◽  
High Frequency Wave ◽  
Spectral Finite Element

Embedded smart actuators/sensors, such as piezoelectric types, have been used to conduct wave transmission and reception, pulse-echo, pitch-catch, and phased array functions in order to achieve in-situ nondestructive evaluation for different structures. By comparing to baseline signatures, the damage location, amount, and type can be determined. Typically, this methodology does not require analytical structural models and interrogation algorithm is carefully designed with little wave propagation knowledge of the structure. However, the wave excitation frequency, waveform, and other signal characteristics must be comprehensively considered to effectively conduct diagnosis of incipient forms of damage. Accurate prediction of high frequency wave response requires a prohibitively large number of conventional finite elements in the structural model. A new high fidelity approach is needed to capture high frequency wave propagations in a structure. In this paper, a spectral finite element method (SFEM) is proposed to characterize wave propagations in a beam structure under piezoelectric material (i.e., PZT) actuation/sensing. Mathematical models are developed to account for both Uni-morph and bi-morph configurations, in which PZT layers are modeled as either an actuator or a sensor. The Timoshenko beam theory is adopted to accommodate high frequency wave propagations, i.e., 20–200 KHz. The PZT layer is modeled as a Timoshenko beam as well. Corresponding displacement compatibility conditions are applied at interfaces. Finally, a set of fully coupled governing equations and associated boundary conditions are obtained when applying the Hamilton’s principle. These electro-mechanical coupled equations are solved in the frequency domain. Then, analytical solutions are used to formulate the spectral finite element model. Very few spectral finite elements are required to accurately capture the wave propagation in the beam because the shape functions are duplicated from exact solutions. Both symmetric and antisymmetric mode of lamb waves can be generated using bimorph or uni-morph actuation. Comprehensive simulations are conducted to determine the beam wave propagation responses. It is shown that the PZT sensor can pick up the reflected waves from beam boundaries and damages. Parametric studies are conducted as well to determine the optimal actuation frequency and sensor sensitivity. Such information helps us to fundamentally understand wave propagations in a beam structure under PZT actuation and sensing. Our SFEM predictions are validated by the results in the literature.

Wave Propagation Analysis of Piping Structures

2009 ◽  
Author(s):  
Akemi Nishida
Keyword(s):  
Wave Propagation ◽  
Dynamic Behavior ◽  
Nuclear Power ◽  
Power Plants ◽  
Three Dimensional ◽  
Beam Theory ◽  
Spectral Element ◽  
Analysis Tool ◽  
Propagation Analysis ◽  
Piping Systems

It is becoming important to carry out detailed modeling procedures and analyses to better understand the actual phenomena. Because some accidents caused by high-frequency vibrations of piping have been recently reported, the clarification of the dynamic behavior of the piping structure during operation is imperative in order to avoid such accidents. The aim of our research is to develop detailed analysis tools and to determine the dynamic behavior of piping systems in nuclear power plants, which are complicated assemblages of different parts. In this study, a three-dimensional dynamic frame analysis tool for wave propagation analysis is developed by using the spectral element method (SEM) based on the Timoshenko beam theory. Further, a multi-connected structure is analyzed and compared with the experimental results. Consequently, the applicability of the SEM is shown.

Sign in / Sign up

Export Citation Format

Share Document