Two inequalities involving Hadamard products of positive semi-definite Hermitian matrices

We extend two inequalities involving Hadamard products of positive definite Hermitian matrices to positive semi-definite Hermitian matrices. Simultaneously, we also show the sufficient conditions for equalities to hold. Moreover, some other matrix inequalities are also obtained. Our results and methods are different from those which are obtained by S. Liu in [J. Math. Anal. Appl. 243:458–463(2000)] and B.-Y. Wang et al. in [Lin. Alg. Appl. 302–303: 163–172(1999)].     

Double-layer structural-acoustic coupling for cylindrical shell by using a combination of WDA and BIE

This work formulates the double-layer structural-acoustic coupling problem for cylindrical shell by using a combination of the wave-number domain approach (WDA) and the boundary integral equation (BIE). Expressions for the spectral radial velocity of the outer surface of a finite fluid-filled/submerged (FFS) cylindrical thin shell are formulated by means of the transfer matrix equation in wave-number domain. It is shown that the spectral variables on the inner surface of the shell are related to those on the outer surface of the shell. The far field sound radiation from this kind of shell is numerically evaluated for various fluid cases. An experimental verification is performed, and a good correlation between the theoretical results and the experimental results shows that the theoretical study work in this paper is correct.     

AERODYNAMIC DAMPING OF RANDOMLY EXCITED PLATES IN STATIONARY AND MOVING AIR

An experimental study of the aerodynamic damping of oscillating plates has been undertaken. Plates of various shapes were placed into an air flow normal to the plate and excited to oscillate parallel to the flow direction by electromagnetic forces of equal amplitudes and random frequencies. The aerodynamic damping of oscillating plates, evaluated in terms of a quality Q-factor from a frequency response resonance curve, was found to vary linearly with the absolute pressure in stationary surrounding air and with the air flow velocity in moving air. The flow velocity was also found to affect the aerodynamic damping more than the absolute pressure. A simple empirical model has been developed to predict the variation of the aerodynamic damping with the flow velocity.     

约束层对激光驱动冲击波压力影响机理的理论研究

针对刚性约束层、柔性约束层以及液体约束层，从激光诱导冲击波阵面状态、汽化物(包括气体和等离子体)扩散以及冲击波的反射进行分析，发现对于脉宽小于冲击波通过汽化物层的时间间隔的短脉冲激光，约束层并不能直接提高冲击波的冲量，而对于脉宽大于冲击波通过汽化层时间间隔的激光，其增强冲击效果是通过约束汽化物的扩散，提高压力幅值和由于冲击波在约束层与工件表面的多次反射而延长对工件的作用时间来实现的.刚性约束层能最大地增加冲击冲量，而柔性约束层和液体约束层的主要优点是其形状可与非平面形工件表面符合. 关键词： 激光 约束层 扩散 反射波     

Case-study evaluations of the acoustical designs of renovated university classrooms

The acoustical characteristics of 14 university classrooms at the University of British Columbia were measured before and after renovation—seven of these are discussed in detail here. From these measurements, and theoretical considerations, values of quantities used to assess each classroom configuration were predicted, and used to evaluate renovation quality. Information on each renovation was determined with the help of the university campus-planning office and/or the project acoustical consultant. These were related to the evaluation results in order to determine the relationship between design and acoustical quality. The criteria focused on the quality of verbal communication in the classrooms. Room-average Speech Intelligibility (SI) and its physical correlate, Speech Transmission Index (STI), were used to quantify verbal-communication quality. A simplified STI-calculation procedure was applied. The results indicate that some renovations were beneficial, others were not. Verbal-communication quality varied from ‘poor’ to ‘good’. The effect of a renovation depends on a complex interplay between changes in the reverberation and changes in the signal-to-noise level difference, as affected by sound absorption and the source outputs. Renovations which reduce noise are beneficial unless signal-to-noise level differences remain optimal. Renovations often put too much emphasis on adding sound absorption to control reverberation, at the expense of lower speech levels, particularly at the backs of classrooms. The absorption and noise contributed by room occupants has apparently often been neglected.     

Time-domain numerical computation of noise reduction by diffraction and finite impedance of barriers

A new time-domain numerical method is presented for the estimation of noise reduction by the diffraction and finite impedance of barriers. High order finite difference schemes conventionally used for computational aeroacoustics, and time-domain impedance boundary conditions are utilized for the development of the time-domain method. Compared with other methods, this method can be applied more easily to the problems related to nonlinear noise propagation such as impulsive noise and broadband noise. Linearized Euler equations in Cartesian co-ordinates are considered and solved numerically. Straight and T-shaped barriers with and without surface admittance are calculated. In order to assess the accuracy of this time-domain method, comparison with the results of SYSNOISE software (Ver. 5.3) are made. There are very good agreements between the results of the present time-domain numerical method and the boundary element method of the SYSNOISE software.     

Equilibrium point damage prognosis models for structural health monitoring

Most structural dynamic systems are of high order; however, they often exhibit phenomena that can be dealt with effectively using low order models. This paper presents a method for describing certain kinds of damage evolution in mechanical systems. The method relies on a simple principle that as damage evolves in a structural dynamic system, the damage indicator (i.e., diagnostic feature) behaves like a stable quasi-stationary equilibrium point in a subsidiary non-linear bifurcating system within the so-called damage center manifold. It is shown that just as linear normal modes govern the behavior of linear structures with idealized damping, so too do non-linear normal forms govern the evolution of damage within structures in many instances. The method is justified with citations from the literature on certain types of mechanical failure and then applied in an experimental case involving reversible damage in a bolted fastener. Off-line experiments on a rotorcraft fuselage show that the evolution of damage is sensitive to both temporal and spatial bifurcation parameters. A diagnostic sensing strategy whereby output-only transmissibility features are used to decrease the order of high order structural dynamic measurements is also described.     

Using enclosing ellipsoids in multiaxial fatigue strength criteria

We propose in this paper a scalar measure for the amplitude of shear stress variations based on the definition of an enclosing hyper-ellipsoid of minimum Frobenius norm. This equivalent shear amplitude is combined with the maximal mean stress, in both linear and quadratic functions, leading to two alternative fatigue criteria. The predictions of these criteria are compared with experimental data in order to validate the proposed shear amplitude measure. The crucial issue concerning the feasibility of the computation of the minimum norm ellipsoid is discussed and a practical algorithm is proposed and demonstrated.     

Oscillating viscoelastic flow in a curved duct—Exact analytical and numerical solution

The analytical solution of the equations of motion is presented for a fully developed laminar flow in a curved channel with circular walls, when an oscillating circumferential pressure gradient is imposed (finite gap oscillating Dean flow). The fluid studied, is a viscoelastic (Jeffrey) fluid. The validity of the solution is verified by a finite difference numerical method.     

Investigation of closure approximations for fiber orientation distribution in contracting turbulent flow

We have investigated the orientation state of a dilute fiber suspension flow in a planar contraction at high Reynolds numbers in turbulent flow. High speed imaging is used to directly measure the orientation distribution function at different downstream positions along the contraction centerline. The results from the direct measurement of the orientation distribution are used to evaluate the existing closure models. The results show that the fitted orthotropic and natural closure approximations give almost identical results with the best agreement to the orientation distribution in the contraction flow considered here.