scholarly journals Guided Waves in Thin-Walled Structural Members

2001 ◽  
Vol 123 (3) ◽  
pp. 376-382 ◽  
Author(s):  
A. H. Shah ◽  
W. Zhuang ◽  
N. Popplewell ◽  
J. B. C. Rogers
Keyword(s):  
Finite Element ◽  
Guided Waves ◽  
Polynomial Interpolation ◽  
Axial Direction ◽  
Thin Plates ◽  
Infinite Length ◽  
Structural Members ◽  
Cross Sectional ◽  
Frequency Spectra ◽  
Thin Walled

A semi-analytical finite element (SAFE) formulation is proposed to study the wave propagation characteristics of thin-walled members with an infinite length in the longitudinal (axial) direction. Common structural members are considered as an assemblage of thin plates. The ratio of the thickness of the plate to the wavelength in the axial direction is assumed to be small so that the plane-stress assumption is valid. Employing a finite element modeling in the transverse direction circumvents difficulties associated with the cross-sectional profile of the member. The dynamic behavior is approximated by dividing the plates into several line (one-dimensional) segments and representing the generalized displacement distribution through the segment by polynomial interpolation functions. By applying Hamilton’s principle, the dispersion equation is obtained as a standard algebraic eigenvalue problem. The reasonably good accuracy of the method is demonstrated for the lowest modes by comparing, where feasible, the results with analytical solutions. To demonstrate the method’s versatility, frequency spectra are also presented for I and L shaped cross sections.

scholarly journals Guided Waves in Thin-Walled Structural Members

1999 ◽  
Author(s):  
J. B. C. Rogers ◽  
W. Zhuang ◽  
A. H. Shah ◽  
N. Popplewell
Keyword(s):  
Finite Element ◽  
Guided Waves ◽  
Polynomial Interpolation ◽  
Fatigue Cracks ◽  
Axial Direction ◽  
Ultrasonic Waves ◽  
Thin Plates ◽  
Structural Members ◽  
Cross Sectional ◽  
Thin Walled

Abstract Infrastructures are deteriorating and billions of dollars are spent to rehabilitate them. Civil structures usually comprise of pavements and bridge decks (plates), pipelines (cylinders), and structural members having, say, I, L, etc. cross sections. The deterioration of these structures causes flaws arising from factors such as the severity of the weather, aging, corrosion, fatigue cracks, etc... The flaws degrade the stiffness (material properties) of a structure and severe conditions eventually can result in a catastrophic failure. Thus, the detection and characterization of the flaws is important in evaluating and monitoring the integrity of existing structures and determining the viability of their continued use or a change in use. Therefore, it is necessary to employ a reliable and effective, quantitative nondestructive evaluation (QNDE) to characterize the mechanical properties and identify defects in the structures. Ultrasonic waves provide such a technique but a knowledge of guided elastic waves is required. Considerable information is available for waves in plates and cylinders but very little work has been reported in the literature on the waves in thin-walled, structural members. In this paper, a semi-analytical finite element (SAFE) formulation is proposed to study the wave propagation characteristics of thin-walled members. Common structural members are considered as an assemblage of thin plates. The members are assumed to be infinitely long in the longitudinal (axial) direction. The ratio of the thickness of the plate to the wavelength in the axial direction is assumed to be small so that the plane-stress assumption is valid. Employing a finite element modeling in the transverse direction circumvents difficulties associated with the cross-sectional profile of the member. The dynamic behavior is approximated by dividing the plates into several line (one-dimensional) segments and representing the generalized displacement distribution through the segment by polynomial interpolation functions. By applying Hamilton’s principle, the dispersion equationis obtained as a standard algebraic eigenvalue problem. The accuracy of the proposed method is demonstrated by comparing the results with analytical solutions. Detailed numerical results are presented for an I shaped cross section.

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.

Investigation of Effective Bending and Shear Stiffness of Thin-Walled Girders Related to Ship Hull Vibration Analysis

1989 ◽  
Vol 33 (04) ◽  
pp. 298-309
Author(s):  
Ivo Senjanovic ◽  
Ying Fan
Keyword(s):  
Finite Element ◽  
Frequency Domain ◽  
Vibration Analysis ◽  
Ship Hull ◽  
Moment Of Inertia ◽  
Cross Sectional ◽  
Simply Supported ◽  
Thin Walled ◽  
Beam Parameters ◽  
Shear Area

Application of beam theory in flexural vibration analysis of thin-walled girders is extended for the high-frequency domain by introducing the concept of effective values of beam parameters, that is, cross-sectional moment of inertia, shear area, mass, and mass moment of inertia. Formulation of these parameters is based on equivalence of deformation energy and inertia work, respectively, for a considered structure and its beam model, resulting in the same values of their natural frequencies. For illustration, the natural vertical vibration of a simply supported pontoon has been considered, where it was possible to obtain the analytical solution due to sinusoidal mode shapes. The effective values of cross-sectional moment of inertia and shear area show significant variation in frequency domain. Transfer of effective values of beam parameters, determined for simply supported structure, in the case of other boundary conditions is suggested, based on equal mode wavelengths, and checked for the free pontoon. The results show very low discrepancies compared with a three-dimensional finite-element model solution, so this procedure may be applied generally, as well as to the problem of ship hull vibration. In conclusion, the possibility of calculating the values of effective parameters for multicell ship cross sections, utilizing the theory of folded structure and the finite-element method, is pointed out.

Design for Desired Mode Shapes: Preliminary Results

1998 ◽  
Author(s):  
Elizabeth K. Lai ◽  
G. K. Ananthasuresh
Keyword(s):  
Finite Element ◽  
Feasibility Study ◽  
Mode Shape ◽  
Longitudinal Axis ◽  
Mode Shapes ◽  
Future Research ◽  
Structural Members ◽  
Element Analysis ◽  
Cross Sectional ◽  
Made In

Abstract This paper is concerned with the shape optimization of structures to attain prescribed normal mode shapes. Optimizing structural members in order to have desired mode shapes, besides the desired natural frequencies, is of interest in some applications at both macro and micro scales. After reviewing the relevant past work on the “inverse mode shape” problem, a feasibility study using the lumped spring-mass models and finite element models of an axially vibrating bar is presented. Based on the observations made in the feasibility study with bars, a meaningful optimization problem is formulated and solved. Using finite element analysis and numerical optimization, a method for designing beam-like structures for prescribed mode shapes is developed. The method is demonstrated with an example of designing the cross-sectional area profile of a beam along its longitudinal axis to get a desired fundamental mode shape. The nonuniqueness of the solution is noted and avenues for future research are identified.

Dual Representation Methods for Efficient and Automatable Analysis of 3D Plates

2010 ◽  
Vol 10 (4) ◽  
Author(s):  
Vikalp Mishra ◽  
Krishnan Suresh
Keyword(s):  
Finite Element ◽  
Computer Aided Design ◽  
Dimensional Space ◽  
Reduction Process ◽  
Thin Plates ◽  
Design Environment ◽  
Element Analysis ◽  
Cross Sectional ◽  
Dual Representation ◽  
3D Finite Element

It is well recognized that 3D finite element analysis is inappropriate for analyzing thin structures such as plates and shells. Instead, a variety of highly efficient and specialized 2D methods have been developed for analyzing such structures. However, 2D methods pose serious automation challenges in today’s 3D design environment. Specifically, analysts must manually extract cross-sectional properties from a 3D computer aided design (CAD) model and import them into a 2D environment for analysis. In this paper, we propose two efficient yet easily automatable dual representation methods for analyzing thin plates. The first method exploits standard off-the-shelf 3D finite element packages and achieves high computational efficiency through an algebraic reduction process. In the reduction process, a 3D plate bending stiffness matrix is constructed from a 3D mesh and then projected onto a lower-dimensional space by appealing to standard 2D plate theories. In the second method, the analysis is carried out by integrating 2D shape functions over the boundary of the 3D plate. Both methods do not entail extraction of the cross-sectional properties of the plate. However, the user must identify the plate or thickness direction. The proposed methodologies are substantiated through numerical experiments.

Modeling Large Deformation Impact Dynamics for Legged Microrobot Locomotion: A Preliminary Formulation

2018 ◽  
Author(s):  
Nikhil Potu Surya Prakash ◽  
Kenn Oldham
Keyword(s):  
Finite Element ◽  
Large Deformation ◽  
Axial Direction ◽  
Small Scale ◽  
Uniform Density ◽  
Element Analysis ◽  
Cross Sectional ◽  
Micro Robot ◽  
Impact Events ◽  
Prior Analysis

A finite element dynamic model is developed to better understand impact events during large amplitude dynamics of a compliant, elastic-legged small-scale robot. The proposed motion of the robot would be achieved as a result of impulse forces generated from the forced collision of piezoelectrically-actuated, beam-like legs with the ground. The nominal robot leg is a prismatic continuous structure with uniform density, cross-sectional area and moment of inertia. Dynamic modeling in this work attempts to manage the non-negligible motion of the actuated beam tip in its axial direction at impact when large bending deformations are excited, which complicates prior analysis methods. For the micro-robot, this motion is proposed to be exploited as a means to produce locomotion in the horizontal direction, and hence must be accounted for. Finite element analysis approaches are adapted for the micro-robotic circumstances. Preliminary results are presented for the scenario of large deformation, unforced dynamics with impact, tested using centimeter-scale mock-ups for future thin-film based micro-robots. Needs and opportunities for further validation are briefly discussed.

Cross-Section Deformation Effects in the Vibration of Thin-Walled Beams of Arc Section

1965 ◽  
Vol 7 (3) ◽  
pp. 292-299 ◽  
Author(s):  
S. A. Hasan ◽  
A. D. S. Barr
Keyword(s):  
Cross Section ◽  
Reasonable Agreement ◽  
Natural Frequencies ◽  
Characteristic Functions ◽  
Curved Beam ◽  
Cross Sectional ◽  
Frequency Spectra ◽  
Circular Arc ◽  
Beam Geometry ◽  
Thin Walled

Differential equations describing the coupling of ordinary bending motion with cross-sectional distortion are obtained for thin-walled beams of circular-arc cross-section using Hamilton's principle. In deriving the theory the cross-sectional deformation is assumed to take the form of the characteristic functions of a curved beam of the shape of the section. The variation with wavelength of the frequency spectra which result from the coupling is obtained. Experimental results showing the effects of the variation of the parameters of the beam geometry on the natural frequencies are in reasonable agreement with the theory.

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