Detecting cracks in a longitudinally vibrating beam with dissipative boundary conditions

This paper focuses on detecting a small open crack in an axially vibrating beam with viscous boundary conditions by using non-destructive dynamical measurements. The damage is simulated by an equivalent linear elastic spring. It is shown that the measurement of the changes in a suitable pair of eigenvalues leads to the solution of the diagnostic problem, namely identification of crack location and severity. Results apply to uniform beams under various sets of boundary conditions.     

Measurements of velocity distributions in the deformation zone in cold rolling by a scanning LDV

Experimental determination of the velocity distribution in the deformation zone is of significant importance to investigate the metal flow in both conventional and asymmetrical rolling processes. In this paper, a scanning laser Doppler velocimetry (LDV) system, designed for measuring the velocity distributions in the deformation zone in plate rolling is reported. The LDV used for the rolling process is briefly described and then the scanning mechanism based on beam displacement by a rotating transparent plate is introduced. The relationship among the scanning distance, the beam-cross angle of the LDV system and the rotating angle of the plate is established. The scanning LDV was first tested with a rotating disk and then applied in the rolling process. The test results have demonstrated the feasibility of the scanning LDV.     

Detecting fuzzy community structures in complex networks with a Potts model

A fast community detection algorithm based on a q-state Potts model is presented. Communities (groups of densely interconnected nodes that are only loosely connected to the rest of the network) are found to coincide with the domains of equal spin value in the minima of a modified Potts spin glass Hamiltonian. Comparing global and local minima of the Hamiltonian allows for the detection of overlapping ("fuzzy") communities and quantifying the association of nodes with multiple communities as well as the robustness of a community. No prior knowledge of the number of communities has to be assumed.     

Smoothed frequency responses for matrix-characterized vibrating structures

A method for predicting smoothed frequency responses for matrix-characterized structures is shown to be practical. Smoothed frequency responses are the same as conventional responses for real mobility versus frequency, except for the removal of resonant-antiresonant detail consisting of peaks and notches. A family of smoothed frequency responses, with varying disregard of resonant-antiresonant detail, depends on a series expansion in Tchebyshev orthogonal polynomial functions of a matrix A, namely, φ₀(ω)f₀(A) + φ₁(ω)f₁(A) + φ₂(ω)f₂(A) + … (in equation (1)), where A is derived from the matrices of stiffness coefficients and masses. The smoothed frequency responses are shown to be connected with modal density, and, depending on the number of terms which are takem in the expansion, are capable of exhibiting influences of point of excitation, point of response, and participation of the various modes of vibration. Illustrations are given for the example of a theoretical seven-element clamped-clamped uniform beam. Some possible advantages of using smoothed frequency responses are briefly considered. These include reduced arithmetic and the possibility of predicting low-degree (very approximate) smoothed frequency responses for incompletely characterized structures. The present connection between modal density and the smoothed real mobilities is a matrix formulation of a known result, but introduces a treatment of modal density as the smoothed product of an orthogonal polynomial fit (rather than an average taken over bands of modes, such as used in Statistical Energy Analysis).     

On linear modeling of interface damping in vibrating structures

Dissipation of mechanical vibration energy at contact interfaces in a structure, commonly referred to as interface damping, is an important source of vibration damping in built-up structures and its modeling is the focus of the present study. The approach taken uses interface forces which are linearly dependent on the relative vibration displacements at the contact interfaces.The main objective is to demonstrate a straightforward technique for simulation of interface damping in built-up structures using FE modeling and simple, distributed, damping forces localized to interfaces where the damping occurs.As an illustration of the resulting damping the dissipated power is used for evaluation purposes. This is calculated from surface integrals over the contact interfaces and allows for explicit assessment of the effect of simulated interface forces for different cases and frequencies. The resulting loss factor at resonance is explicitly evaluated and, using linear simulations, it is demonstrated that high damping levels may arise even though the displacement differences between contacting surfaces at damped interfaces may be very small.     

Computation of acoustic radiation from vibrating structures in motion

The noises from a vibrating structure in motion are often encountered in engineering practice, for example, tire noise and pass-by noise of moving vehicles. Consequently, research on the radiation characteristics of moving acoustic source is of significance. In this paper, a new computational method based on the wave superposition approach is developed for the acoustic field from a vibrating structure in motion. It inherits the advantages of the wave superposition approach in the acoustic computation, and in which a method of moving simple sources is used to eliminate the influence of the Doppler effect. By the proposed method, the acoustic radiation from the moving vibrating structure can be calculated easily with the same implementation process as the conventional wave superposition approach performed in the stationary acoustic field. Finally, the validity and feasibility of the proposed method are verified by the numerical results.     

Detecting spatially localized excitons in InGaN quantum well structures with a micro-photoluminescence technique

Spatially localized excitons are observed in InGaN quantum well structures at 4 K by using a micro-photoluminescence (PL) technique. By combining PL and nano-lithographic techniques, we are able to detect PL signals with a 0.2 μm spatial resolution. A sharp PL line (linewidth of <0.4 meV) is clearly obtained, which originates from a single localized exciton induced by a quantum dot like a local potential minimum position. Sharp PL spectra detected in three QWs with different indium compositions confirm that there are exciton localization effects in quantum wells in the blue-green (about 2.60 eV, 477 nm) to purple (about 3.05 eV, 406 nm) regions.     

Singular optimal control problems in the design of vibrating structures

It is shown that several recent publications dealing with the design of vibrating structures by optimal control theory have problem formulations corresponding to singular control problems. For such problems, the conditions of neither the maximum principle nor the classical variational theory provide adequate tests for optimality of the solution. The singular control formulation of these publications is acknowledged here for the first time and the optimality of the solutions is examined by using supplementary necessary conditions.     

Detecting coherent structures using braids

The detection of coherent structures is an important problem in fluid dynamics, particularly in geophysical applications. For instance, knowledge of how regions of fluid are isolated from each other allows prediction of the ultimate fate of oil spills. Existing methods detect Lagrangian coherent structures, which are barriers to transport, by examining the stretching field as given by finite-time Lyapunov exponents. These methods are very effective when the velocity field is well-determined, but in many applications only a small number of flow trajectories are known, for example when dealing with oceanic float data. We introduce a topological method for detecting invariant regions based on a small set of trajectories. In this method, we regard the two-dimensional trajectory data as a braid in three dimensions, with time being the third coordinate. Invariant regions then correspond to trajectories that travel together and do not entangle other trajectories. We detect these regions by examining the growth of hypothetical loops surrounding sets of trajectories, and searching for loops that show negligible growth.     

Chaos in vibrating systems with a limited power-supply

New models and properties of forced oscillations of the various physical systems (pendulum and piezoceramic transducer) due to the interaction with the excitation device of limited power-supply are investigated in details. Using an analysis of the largest Lyapunov exponent for a complicated system-vibrating subsystem and exciter-the regions for three steady state regimes are determined, namely: stationary, periodic and chaotic.     

Excitation and sensing of multiple vibrating traveling waves in one-dimensional structures

Lightly damped vibrating structures normally exhibit vibration patterns that are a combination of standing waves, i.e. mode shapes. Traveling waves, on the other hand, occur only under special circumstances. In this work, the theoretical conditions under which traveling waves prevail in finite structure are investigated. These conditions are highly sensitive to the geometrical and material parameters of the structure and in particular the vibration pattern is sensitive to the boundary conditions. There are several combinations under which traveling waves cannot be formed and these ill-posed cases are analyzed in some detail. To overcome the unavoidable uncertainties in a model, a tuning process based on identification and optimization of the excitation is suggested. The identification process uses a parametric algorithm to estimate the wavenumbers of the measured vibrations. Then, the waves are decomposed into traveling and standing parts and the external excitation is tuned until a pure traveling wave is formed.     

Lau phase interferometry with a vibrating object

In this paper, we have demonstrated experimentally the vibration analysis of a reflecting object in a time-averaged mode using Lau phase interferometry. Experimental results provide information about the tilt at every point of a vibrating plate. The Lau phase interferometry is robust and simple. Experimental results are compared with conventional shadow-moiré method.     

Talbot interferometry with a vibrating phase object

We describe a Talbot interferometer for measuring a vibrating phase object. The time-average fringes are moiré patterns modulated by the zeroth-order Bessel function. They provide information about the tilt at every point of a vibrating plate, for example. The Talbot interferometer is robust (common path) and cheap (printers grids as beam-splitters). The experiments can be performed with laser illumination or with a collimated beam of white light. Some experimental results are shown.     

Dynamic testing of nonlinear vibrating structures using nonlinear normal modes

Modal testing and analysis is well-established for linear systems. The objective of this paper is to progress toward a practical experimental modal analysis (EMA) methodology of nonlinear mechanical structures. In this context, nonlinear normal modes (NNMs) offer a solid theoretical and mathematical tool for interpreting a wide class of nonlinear dynamical phenomena, yet they have a clear and simple conceptual relation to the classical linear normal modes (LNMs). A nonlinear extension of force appropriation techniques is developed in this study in order to isolate one single NNM during the experiments. With the help of time-frequency analysis, the energy dependence of NNM modal curves and their frequencies of oscillation are then extracted from the time series. The proposed methodology is demonstrated using two numerical benchmarks, a two-degree-of-freedom system and a planar cantilever beam with a cubic spring at its free end.     

Statistical damage identification of structures with frequency changes

Model updating methods based on structural vibration data have being rapidly developed and applied to detect structural damage in civil engineering. But uncertainties existing in the structural model and measured vibration data might lead to unreliable damage detection. In this paper a statistical damage identification algorithm based on frequency changes is developed to account for the effects of random noise in both the vibration data and finite element model. The structural stiffness parameters in the intact state and damaged state are, respectively, derived with a two-stage model updating process. The statistics of the parameters are estimated by the perturbation method and verified by Monte Carlo technique. The probability of damage existence is then estimated based on the probability density functions of the parameters in the two states. A higher probability statistically implies a more likelihood of damage occurrence. The presented technique is applied to detect damages in a numerical cantilever beam and a laboratory tested steel cantilever plate. The effects of using different number of modal frequencies, noise level and damage level on damage identification results are also discussed.     

PIV and LDV evidence of hydrodynamic instability over a liner in a duct with flow

The acoustical behavior and the flow in a rectangular lined channel with grazing flow have been investigated. The liner consists of a ceramic structure of parallel square channels and is locally reacting. In the absence of flow, the liner has a classical behavior: the acoustic transmission coefficient has a minimum at the resonance frequency of the resonators. When the Mach number of the grazing flow increases, the material behavior becomes unclassical in the sense that its acoustic transmission increases strongly around the resonance frequency. To connect this behavior with flow features, the flow itself in the vicinity of a liner has been measured by means of laser velocimetry. Periodic structures have been observed along the liner that are phase-locked with the incident sound wave. The axial and transverse velocity of these structures bear the typical features of an instability. In particular, the wavelength, convection speed, and growth rate are given. This is the first time that an aeroacoustic instability resulting from the interaction of flow and sound over a liner is measured.     

Sound radiation from a vibrating plate with uncertainty

Sound radiation into open space from a vibrating structure has been investigated since Rayleigh. On the other hand the sound power transferring into neighboring reverberant subsystems has also been rigorously studied using statistical energy analysis, particularly for the high frequency range. Falling between the two well-known problems, pressure and intensity fields from the sound radiation have not yet been widely studied using statistical methods. In this paper, the sound radiation from a vibrating thin plate having uncertain dynamic properties is investigated. Estimates are developed for the reverberant vibration field in the uncertain plate subjected to a point-excitation, and for the ensemble average of pressure from the direct field and from the reverberant field, leading to an estimate of the average sound intensity. The power radiated from the plate and the radiation efficiency is also derived. Monte Carlo simulations are conducted with an ensemble of plates with randomly-distributed point masses, and the simulation results compare well with the estimates.     

Model for continuously scanning ultrasound vibrometer sensing displacements of randomly rough vibrating surfaces

An analytic model is developed for the time-dependent ultrasound field reflected off a randomly rough vibrating surface for a continuously scanning ultrasound vibrometer system in bistatic configuration. Kirchhoff's approximation to Green's theorem is applied to model the three-dimensional scattering interaction of the ultrasound wave field with the vibrating rough surface. The model incorporates the beam patterns of both the transmitting and receiving ultrasound transducers and the statistical properties of the rough surface. Two methods are applied to the ultrasound system for estimating displacement and velocity amplitudes of an oscillating surface: incoherent Doppler shift spectra and coherent interferometry. Motion of the vibrometer over the randomly rough surface leads to time-dependent scattering noise that causes a randomization of the received signal spectrum. Simulations with the model indicate that surface displacement and velocity estimation are highly dependent upon the scan velocity and projected wavelength of the ultrasound vibrometer relative to the roughness height standard deviation and correlation length scales of the rough surface. The model is applied to determine limiting scan speeds for ultrasound vibrometer measuring ground displacements arising from acoustic or seismic excitation to be used in acoustic landmine confirmation sensing.     

Effects of scanning speed on the laser beam profile measurements by vibrating wire

For measuring laser beam profiles, a vibrating wire monitor (VWM) has been introduced. The measurements were carried out at different speeds of scan. Preliminary estimates were made for the calculation of the VWM response times with respect to the thermal losses along the wire, and radiative and convective losses. These estimates, however, do not determine the difference between the beam profile and the frequency response of the VWM for a given scan rate. To evaluate the reliability of the frequency response of the VWM, comparisons between forward and reverse beam scans at different speeds have been used. The results of these scans are used to correct the thermal inertia in the frequency response of the VWM.