The analysis of impact forces in randomly vibrating elastic systems

This work is concerned with the characteristics of the impact force produced when two randomly vibrating elastic bodies collide with each other, or when a single randomly vibrating elastic body collides with a stop. The impact condition includes a non-linear spring, which may represent, for example, a Hertzian contact, and in the case of a single body, closed form approximate expressions are derived for the duration and magnitude of the impact force and for the maximum deceleration at the impact point. For the case of two impacting bodies, a set of algebraic equations are derived which can be solved numerically to yield the quantities of interest. The approach is applied to a beam impacting a stop, a plate impacting a stop, and to two impacting beams, and in each case a comparison is made with detailed numerical simulations. Aspects of the statistics of impact velocity are also considered, including the probability that the impact velocity will exceed a specified value within a certain time.     

Karhunen–Loève decomposition of peripheral blood flow signal

The Karhunen–Loève expansion is applied to scalar signals and the effect of window length (t_w), time lag (τ) and embedding dimension (d) is analysed for periodic signals and for signals modeled by the Lorenz equations. For τ≠k/2f_i (f_i are characteristic frequencies of the signal, k is positive integer), we obtain 2m modes from an m-periodic signal. For a large set of parameters a finite number of modes was not obtained from the Lorenz system. It is further shown that, on the time scale of a minute, the peripheral blood flow signal contains oscillatory modes that occur in pairs thereby confirming that the blood flow through the cardiovascular system is oscillatory. Some of the difficulties of applying Karhunen–Loève expansion to scalar signals are pointed out.     

Smooth decomposition of random fields

The Smooth Decomposition (SD) method was introduced to analyze discrete-time signals and generalized to continuous-time vector-valued random processes. The SD is obtained solving a generalized eigenproblem defined from the covariance matrix of the random process and the covariance matrix of the associated time-derivative random process which defines the decomposition basis. This paper presents a new extension of the SD to continuous-time and continuous-space vector-valued random processes, classically named random fields. This generalization is a major step since one now deals with operators in infinite-dimensional spaces and not matrices. It is shown that in this new context the main properties of the SD are preserved. Applied to the responses of randomly excited continuous mechanical systems, the SD can be considered as an output-only analysis tool. Moreover, two natural orderings are defined to classify the decomposition terms which permit to interpret the SD in terms of modal analysis or in terms of Karhunen–Loève analysis.     

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.     

Synchronization of randomly multiplexed chaotic systems with application to communication

Synchronized chaotic systems have recently been applied to the area of secure communications in a variety of ways. At the same time, there have also been significant advances in deciphering messages masked by chaotic signals. It is important, therefore, to explore more secure approaches to using chaos in communication. We show that multiple chaotic systems can be synchronized through a scalar coupling which carries a stochastic signal generated by random multiplexing of the source systems. This approach, which is a variant of the active-passive decomposition method, promises enhanced security in chaos-based communication.     

Damage detection in discrete vibrating systems

This paper deals with the identification of a single defect in a discrete spring-mass or beam-like system by measurements of damage-induced shifts in resonance frequencies and antiresonance frequencies. For initially uniform discrete systems, it is shown how the measurement of an appropriate set of frequencies and antiresonances permits unique identification of the damage. The theoretical results are confirmed by comparison with numerical and experimental tests.     

功率超声振动系统的研究进展

功率超声振动系统是功率超声技术中的关键部分,其主要部分包括功率超声换能器、超声变幅杆以及超声工具头或超声辐射器。本文就功率超声换能振动系统设计中经常遇到的一些关键问题进行了简要的归纳和总结,目的在于为功率超声换能器的优化设计和性能改善提供一些有用的设计指南和解决措施。同时,对一些新的功率超声振动系统进行了介绍,并简要分析了其发展趋势和应用领域。     

Main-chain smectic liquid-crystalline polymers as randomly disordered systems

We report a high-resolution X-ray lineshape study of main-chain smectic polymers. The results indicate that the layer ordering differs fundamentally from the algebraic decay typical for other smectic liquid-crystalline systems. The lineshapes are best described by broad squared Lorentzians indicating some form of short-range correlations. However, several higher harmonics are observed, which excludes simple liquid-like short-range order. This behaviour is tentatively attributed to a random field of defects associated with entangled hairpins in the main-chain polymer structure.     

Natural frequency intervals for vibrating systems with polytopic uncertainty

We consider the problem of locating the natural frequencies of uncertain systems whose describing matrices are functions of an unknown parameter vector which is included in an assigned bounding set. We face what we call the weak frequency interval detection problem of determining the smallest interval which includes all possible frequencies. We show that if the system matrices depend affinely on the parameter vector, whose bounding set is a compact polyhedron, then this problem requires the solution of a finite number of eigenvalue problems associated with the vertices of such a polyhedron. Unfortunately, detecting the intervals associated with all the natural frequencies (strong frequency interval detection problem), cannot rely on this property, so that one must resort to Monte Carlo methods or numerical optimization to find them. We show that the strong version is solvable “exploring the vertices only” under some stronger assumptions. In the case in which the uncertainty bounding set is not defined by linear inequalities, not even the extremal frequencies can be associated with the vertices of the admissibility domain. Then again, numerical approach is necessary unless we accept to merge the original system in a larger one of an “affine nature”. Finally, we present as an application the study of structures with uncertain mass distribution.     

STD-DOSY: A new NMR method to analyze multi-component enzyme/substrate systems

A new approach to analyze multi-component Saturation Transfer Difference (STD) NMR spectra by combining the STD and the DOSY experiment is proposed. The resulting pulse sequence was successfully used to simplify an exemplary multi-component protein/substrate system by means of standard DOSY processing methods. Furthermore, the same experiment could be applied to calculate the ratio of saturated substrate molecules and its saturation rate in the case of competitive interactions. This ratio depends on the strength of this interaction between the substrates and the protein, so that this kind of information could be extracted from the results of our experiment.     

Application of the polar decomposition to light scattering particle systems

We have applied the polar decomposition theorem (PDT) to the scattering matrix of simple systems such as an isolated sphere, either metallic or dielectric. The discrete dipole approximation (DDA) method has been used as an intermediate tool to calculate these matrices. We show how the parameters introduced by the PDT for describing the scattering by a single sphere can be easily interpreted. It is also shown that the PDT provides us with an alternative frame to conventional Mueller matrix analysis, by characterizing the systems by means of a group of independent parameters representing magnitudes of simple (virtual) elements. This step is necessary in order to translate other complex system matrices into manageable information.     

Wave localization in two-dimensional periodic systems with randomly disordered size

The expression of the localization factor in the two-dimensional periodic systems is derived based on the plane-wave expansion, transfer matrix and matrix eigenvalue methods. A comprehensive study is performed for the wave localization in the phononic crystal which is composed of steel cylinders embedded in epoxy matrix with the randomly disordered rod size. From the results, it can be observed that with the increase of the disorder degree, the localization phenomenon is strengthened. Furthermore, the filling fraction has significant effects on the wave localization characteristics.     

Ensemble energy average and energy flow relationships for nonstationary vibrating systems

This paper attempts to introduce a new point of view on energy analysis in structural dynamics with particular emphasis to its link with uncertainty and complexity. A linear, elastic system undergoing free vibrations, is considered. The system is subdivided into two subsystems and their respective energies together with the shared energy flow are analysed.First, the ensemble energy average of the two subsystems, assuming uncertain the natural frequencies, is investigated. It is shown how the energy averages follow a simple law when observing the long-term response of the system, obtained by a suitable asymptotic expansion. The second part of the analysis shows how the ensemble energy average of a set of random samples is representative even of the single case if the system is complex enough.The two previous points, combined, produce a result that applies to the energy sharing between two subsystems even independently of uncertainty: for complex systems, a simple energy sharing law is indeed stated. Moreover, in the case of absence of damping, a nonlinear relation between the energy flow and the energy (weighted) difference between the two subsystems is derived; on the other hand, when damping is present, this relationship becomes linear, including two terms: one is proportional to the energy (weighted) difference between the two subsystems, the other being proportional to its time derivative. Therefore, the approach suggests a way for deriving a general approach to energy sharing in vibration with results that, in some cases, are reminiscent of those met in Statistical Energy Analysis.Finally, computational experiments, performed on systems of increasing complexity, validate the theoretical results.     

Spectral decomposition of expanding probabilistic dynamical systems

We study probabilistic combinations of expanding dynamical systems, which we call expanding probabilistic dynamical systems, in one dimension. If the system is composed by exact endomorphisms we prove that the probabilistic dynamical system is an exact Markov semigroup, and we determine a generalized spectral decomposition of the associated Markov operator on densities for an example of the tent map coupled with the 2-Renyi map.