State space coupling is a new approach for handling computational fluid–structure interaction problems in the low to medium frequency range. The method is based on standard boundary element (BEM) and finite element (FEM) discretizations of the acoustic and structural domains, respectively. The implicit frequency dependence of a traditional acoustic impedance matrix is made explicit through a power series expansion on circular frequency and considering time harmonic motion. Once expanded, the acoustic energy of the fluid is directly coupled to that of the structure via Hamilton’s principle. The coupled system is then recast in a canonical state space form which is also in the form of a standard eigenvalue problem. Solution of this system produces a series of complex eigenvalues and eigenvectors which represent a modal decomposition of the fluid-loaded structure. Biorthogonality properties of the state space eigensystem allow for an uncoupled, modal solution of the forced problem. Results for a submerged spherical shell and a finite plate in an infinite ridged baffle are given to illustrate the state space approach.
This study demonstrated that the emphatic sensitivity in paraprofessionals could be increased as a result of training and examined the maintenance of such changes 6-14 months after training was completed. Also explored is the relationship of verbal intelligence to changes in students' empathic sensitivity. Forty-seven students who were enrolled in an associate degree mental health/ human service program participated. Each of these students completed a 10week training course in one of four different groups. Each was given the Recognition Assessment Empathy (RA-E) on completion of the course (posttest) and again 6-14 months later (follow-up). Students in two of the groups were also pretested on the RA-E. Empathic sensitivity did increase after completion of the course, confirming previous research. More important, changes in empathic sensitivity were not only maintained but increased over time to a level comparable with a normative group of experienced clinicians. Mortality and selection effects were judged to be minimal. Finally, as predicted, no significant relationship emerged between verbal intelligence and empathic sensitivity either before or after training.
The use of relatively quiet engines and electric motors on lawn mowers has shifted much of the emphasis on noise reduction to the under deck flow-induced noise sources. However, the environment under an operating mower deck makes it difficult to either model or directly measure the pressure field. This presentation will detail a rather simple scheme which was used to first measure, then animate the pressure field in a plane directly below an operating deck, using an inertial frame of reference. Time synchronous averaging was employed to collect the data at discrete sample points. Individual data planes were then reconstructed representing all the sample points at specific blade locations. The measurement planes were contoured and used as separate frames in a slow-motion animation of the pressure field.
In this experiment, a dramatic reduction in the total radiated power of an extended radiator is achieved via active control through optimization of the secondary source strengths. A box-shaped, acoustic radiator has a single panel that is driven in a structural mode. The four corners of the panel are cut out and contain loudspeakers that are used as the secondary sources. An acoustic boundary element program is used as the basis for determining the active source strengths that minimize the total radiated power. The program, which allows the active sources to be modeled at any position on the acoustic radiator, provides the magnitude and phase at which to drive the active sources for a prescribed frequency and normal velocity distribution on the radiator. A computer, which generates and monitors the driving signals to the panel shaker and loudspeakers, provides precise control of the active sources during power measurements. The numerically predicted reduction in radiated power compared favorably to measurements that were performed in a hemi-anechoic chamber.
A numerical scheme is presented wherein the structural equations for an elastic structure are coupled to the acoustic radiation equations and recast in canonical form. The acoustic impedance matrix, which may be found via boundary element methods or by the superposition method, is expanded in a power series on angular frequency prior to coupling it with the structural matrices. The resulting system of equations is then decomposed to find an orthogonal basis set which uncouples the original equations. Once the basis set has been determined, the structural response and acoustic radiation spectra may be easily reconstructed for any arbitrary forcing function on the structure. Results will be given for two water-loaded examples, a finite plate in an infinite rigid baffle and a spherical shell.
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