On the q

Recently Al-Salam and Verma discussed two polynomial sets {Zn(α)(x,k|q)} and {Yn(α)(x,k|q)} which are biorthogonal on (0,∞) with respect to a continuous or discrete distribution function. For the polynomials Yn(α)(x,k|q) the operational formula is derived

Analysis And Experimental Validation Of Structure-Borne Noise From Acoustic Enclosure Of Compressor

Reduction of noise in a compressor is a complex criterion as many factors of machine enclosure contribute its effect on noise. When a panel of enclosure is acoustically excited, its vibrational response comprises both forced vibrational response at the excitation frequencies, and resonant response of all the relevant structural natural frequencies. These are excited due to the interactions of the forced bending waves with the panel boundaries. The non-resonant, forced modes tend to transmit most of the sound at frequencies below the critical frequency. The resonant frequencies below critical frequency are very poor sound transmitters or radiators. Thus, at frequencies below the critical frequency, mass of the panel controls the reduction in sound transmission since the low frequency resonant structural modes do not radiate or transmit sound. Above the critical frequency, it is the resonant modes that transmit most of the sound. The one qualification to the phenomenan discussed here is that the incident sound field has to be diffused – i.e. no acoustic standing waves are present in the fluid medium adjacent to the panel. Each structure exhibits certain low and high frequency response. The response of a panel depends on whether it is mechanically or acoustically excited. In this paper, acoustic enclosure for a compressor model is designed and analysis of the enclosure structure is carried out. A method is presented to reduce noise by structural modifications of enclosure. Efforts have been made to make use of experimental data as input to software and methods to do the validation of output results which matches fairly with the experimental data. In acoustic fluid-structural interactions, the structural dynamics equations were considered along with Navier-Stokes equation of fluid momentum and flow continuity equation. The radiation of sound from body can be formulated in terms of an integral equation involving Green’s functions with an imposed radiation. Green’s functions represent solutions to the wave equation – they can also be considered to be either frequency or impulse response functions between the source and receiver. Modeling of enclosure was done. The material used for panels of the enclosure was made of composite steel. The noise measurements on 10 mounting points where compressor comes in contact with the structure were carried. The results were plotted in both frequency and time domain; i.e. dynamic analysis of structure. The analysis of the structure was carried out in NASTRAN. The measured forces were applied to the enclosure structure at mounting points. Response was then measured at desired points. Authors found that, there were some variations in actual measurement data and the results acquired in software analysis. Guiding phenomenon was implemented to reduce the noise i.e. obstacles to the wave propagation were provided. The points where noise level was maximum than the required, barriers, and ribs were provided, etc. Again noise measurements were done. Numbers of iterations were performed until measured noise data tallies with analysis data in the prescribed limit. This Design approach can be used for similar problems involving structure – borne noise sources

Influence of Nonlinear Fluid Viscous Dampers on Seismic Response of RC Elevated Storage Tanks

The numerical investigation on the seismic response of RC elevated liquid storage tanks installed with viscous dampers is presented. A discrete two-mass model for the liquid and multi-degree of freedom system for staging, installed with the dampers are developed for Reinforced Concrete (RC) elevated liquid storage tanks. The elevated tank is assessed for seismic response reduction when provided with Linear Viscous Damper (LVD) and Nonlinear Viscous Damper (NLVD), installed in the staging. The RC elevated liquid storage tanks are analyzed for two levels of liquid containment in the tank, 100% and 25% of the tank capacity. Three Configurations of placements of dampers viz. dampers at alternate levels (Configuration I and Configuration II) and dampers at all the panels of the staging of the tank (Configuration III) are considered. To study the effect of peak ground acceleration, eight real earthquake time histories with accelerations varying from 0.1 g to 0.93 g are considered. The nonlinearity in the viscous damper is modified by taking force proportional to various velocity exponents. It is found that the nonlinear viscous dampers with lower damping constant result in a comparable reduction in the response of RC elevated liquid storage tank, to that of linear viscous dampers with higher damping constant. A lower damping constant signifies compact the size of the damper. Doi: 10.28991/cej-2020-SP(EMCE)-09 Full Text: PD

Electronic circuit implementation of chaos synchronization

In this paper, an electronic circuit implementation of a robustly chaotic two-dimensional map is presented. Two such electronic circuits are realized. One of the circuits is configured as the driver and the other circuit is configured as the driven system. Synchronization of chaos between the driver and the driven system is demonstrated

A pair of biorthogonal polynomials for the Szegö-Hermite weight function

A pair of polynomial sequences {Snμ(x;k)} and {Tmμ(x;k)} where Snμ(x;k) is of degree n in xk and Tmμ(x;k) is of degree m in x, is constructed. It is shown that this pair is biorthogonal with respect to the Szegö-Hermite weight function |x|2μexp(−x2), (μ>−1/2) over the interval (−∞,∞) in the sense that∫−∞∞|x|2μexp(−x2)Snμ(x;k)Tmμ(x;k)dx=0,   ifm≠n                    ≠0,   ifm=nwhere m,n=0,1,2,… and k is an odd positive integer

Biorthogonal ensembles

One object of interest in random matrix theory is a family of point ensembles (random point configurations) related to various systems of classical orthogonal polynomials. The paper deals with a one--parametric deformation of these ensembles, which is defined in terms of the biorthogonal polynomials of Jacobi, Laguerre and Hermite type. Our main result is a series of explicit expressions for the correlation functions in the scaling limit (as the number of points goes to infinity). As in the classical case, the correlation functions have determinantal form. They are given by certain new kernels which are described in terms of the Wright's generalized Bessel function and can be viewed as a generalization of the well--known sine and Bessel kernels. In contrast to the conventional kernels, the new kernels are non--symmetric. However, they possess other, rather surprising, symmetry properties. Our approach to finding the limit kernel also differs from the conventional one, because of lack of a simple explicit Christoffel--Darboux formula for the biorthogonal polynomials.Comment: AMSTeX, 26 page