Effect of wall thickness on the end corrections of the extended inlet and outlet of a double-tuned expansion chamber

Simple expansion chambers, the simplest of the muffler configurations, have very limited practical application due to the presence of periodic troughs in the transmission loss spectrum which drastically lower the overall transmission loss of the muffler. Tuned extended inlet and outlet can be designed to nullify three-fourths of these troughs, making use of the plane wave theory. These cancellations would not occur unless one altered the geometric lengths for the extended tube in order to incorporate the effect of evanescent higher-order modes (multidimensional effect) through end corrections or lumped inertance approximation at the area discontinuities or junctions. End corrections of the extended inlet and outlet have been studied by several researchers. However the effect of wall thickness of the inlet/outlet duct on end correction has not been studied explicitly. This has significant effect on the tuning of an extended inlet/outlet expansion chamber. It is investigated here experimentally as well as numerically (through use of 3-D FEM software) for stationary medium. Crown Copyright (C) 2010 Published by Elsevier Ltd. All rights reserved.

An optimal parallel algorithm for sparse matrix bandwidth reduction on a linear array

A simple and efficient algorithm for the bandwidth reduction of sparse symmetric matrices is proposed. It involves column-row permutations and is well-suited to map onto the linear array topology of the SIMD architectures. The efficiency of the algorithm is compared with the other existing algorithms. The interconnectivity and the memory requirement of the linear array are discussed and the complexity of its layout area is derived. The parallel version of the algorithm mapped onto the linear array is then introduced and is explained with the help of an example. The optimality of the parallel algorithm is proved by deriving the time complexities of the algorithm on a single processor and the linear array.

Error-free matrix symmetrizers and equivalent symmetric matrices

A symmetrizer of the matrix A is a symmetric solution X that satisfies the matrix equation XA=AprimeX. An exact matrix symmetrizer is computed by obtaining a general algorithm and superimposing a modified multiple modulus residue arithmetic on this algorithm. A procedure based on computing a symmetrizer to obtain a symmetric matrix, called here an equivalent symmetric matrix, whose eigenvalues are the same as those of a given real nonsymmetric matrix is presented.

Electrical Contact Resistance in Thin (<= 0.5 mu m) Gold Plated Contacts: Effect of Gold Plating Thickness

This paper describes the electrical contact resistance (ECR) measurements made on thin gold plated (gold plating of <= 0.5 mu m with a Ni underlayer of similar to 2 mu m) oxygen free high conductivity (OFHC) Cu contacts in vacuum environment. ECR in gold plated OFHC Cu contacts is found to be slightly higher than that in bare OFHC Cu contacts. Even though gold is a softer material than copper, the relatively high ECR values observed in gold plated contacts are mainly due to the higher hardness and electrical resistivity of the underlying Ni layer. It is well known that ECR is directly related to plating factor, which increases with increasing coating thickness when the electrical resistivity of coating material is more than that of substrate. Surprisingly, in the present case it is found that the ECR decreases with increasing gold layer thickness on OFHC Cu substrate (gold has higher electrical resistivity than OFHC Cu). It is analytically demonstrated from the topography and microhardness measurements results that this peculiar behavior is associated with thin gold platings, where the changes in surface roughness and microhardness with increasing layer thickness overshadow the effect of plating factor on ECR.

Processing maps for hot-working of powder metallurgy 1100 Al-10 vol % SiC-particulate metal-matrix composite

The hot-working characteristics of the metal-matrix composite (MMC) Al-10 vol % SiC-particulate (SiCp) powder metallurgy compacts in as-sintered and in hot-extruded conditions were studied using hot compression testing. On the basis of the stress-strain data as a function of temperature and strain rate, processing maps depicting the variation in the efficiency of power dissipation, given by eegr = 2m/(m+1), where m is the strain rate sensitivity of flow stress, have been established and are interpreted on the basis of the dynamic materials model. The as-sintered MMC exhibited a domain of dynamic recrystallization (DRX) with a peak efficiency of about 30% at a temperature of about 500°C and a strain rate of 0.01 s�1. At temperatures below 350°C and in the strain rate range 0.001�0.01 s�1 the MMC exhibited dynamic recovery. The as-sintered MMC was extruded at 500°C using a ram speed of 3 mm s�1 and an extrusion ratio of 10ratio1. A processing map was established on the extruded product, and this map showed that the DRX domain had shifted to lower temperature (450°C) and higher strain rate (1 s�1). The optimum temperature and strain rate combination for powder metallurgy billet conditioning are 500°C and 0.01 s�1, and the secondary metal-working on the extruded product may be done at a higher strain rate of 1 s�1 and a lower temperature of 425°C.

Relationship Between The Impedance Matrix And The Transfer Matrix With Specific Reference To Symmetrical, Reciprocal And Conservative Systems

Impedance matrix and transfer matrix methods are often used in the analysis of linear dynamical systems. In this paper, general relationships between these matrices are derived. The properties of the impedance matrix and the transfer matrix of symmetrical systems, reciprocal systems and conservative systems are investigated. In the process, the following observations are made: (a) symmetrical systems are not a subset of reciprocal systems, as is often misunderstood; (b) the cascading of reciprocal systems again results in a reciprocal system, whereas cascading of symmetrical systems does not necessarily result in a symmetrical system; (c) the determinant of the transfer matrix, being ±1, is a property of both symmetrical systems and reciprocal systems, but this condition, however, is not sufficient to establish either the reciprocity or the symmetry of the system; (d) the impedance matrix of a conservative system is skew-Hermitian.

The superheating of Pb embedded in a Zn matrix the role of interface melting

Evidence of a shape-dependent superheating of entrained nanosized Pb particles in a Zn matrix has been presented. It is shown that size dependence and pressure effects cannot explain the observed differences in melting points. The importance of crystallography and morphology at the microlevel at the interphase interface in controlling interfacial melting has been emphasized in order to explain the melting of entrained particles.

Heterogeneous nucleation of pb particles embedded in a Zn matrix

Zinc-10 and 20 wt pct Pb alloys have been rapidly solidified by melt spinning to obtain a very fine scale dispersion of nanometer-sized Pb particles embedded in Zn matrix. The microstructure and crystallography of the Pb particles have been studied using transmission electron microscopy (TEM). Each embedded Pb particle is a single crystal, with a truncated hexagonal biprism shape with the 6/mmm Zn matrix point group symmetry surrounded by and { 0001 á },\text { \text10[`\text1] \text0 },\text and { \text10[`\text1] \text1 }0001 1010 and 1011 facets. The Pb particles solidify with a well-defined orientation relationship with the Zn matrix of ( 0001 )Zn ||(111)Pb\text and\text [ \text11[`\text2] \text0 ]Zn| ||[ 1[`1] 0 ]Pb 0001Zn(111)Pb and 1120Zn110Pb . The melting and solidification behavior of the Pb particle have been studied using differential scanning calorimetry (DSC). The Pb particles solidify with an undercooling of approximately 30 K, by heterogeneous nucleation on the {0001} facets of the surrounding Zn matrix, with an apparent contact angle of 23 deg.

Characteristics of superplasticity domain in the processing map for hot working of an Al alloy 2014---20vol.%Al2O3 metal matrix composite

The processing map for hot working of Al alloy 2014-20vol.%Al2O3 particulate-reinforced cast-plus-extruded composite material has been generated covering the temperature range 300-500 degrees C and the strain rate range 0.001-10 s(-1) based on the dynamic materials model. The efficiency eta of power dissipation given by 2m/(m + 1), where m is the strain rate sensitivity, is plotted as a function of temperature and strain rate to obtain a processing map. A domain of superplasticity has been identified, with a peak efficiency of 62% occurring at 500 degrees C and 0.001 s(-1). The characteristics of this domain have been studied with the help of microstructural evaluation and hot-ductility measurements. Microstructural instability is predicted at higher strain rates above (ls(-1)) and lower temperatures (less than 350 degrees C).

Concise row-pruning algorithm to invert a matrix

Presented here, in a vector formulation, is an O(mn2) direct concise algorithm that prunes/identifies the linearly dependent (ld) rows of an arbitrary m X n matrix A and computes its reflexive type minimum norm inverse A(mr)-, which will be the true inverse A-1 if A is nonsingular and the Moore-Penrose inverse A+ if A is full row-rank. The algorithm, without any additional computation, produces the projection operator P = (I - A(mr)- A) that provides a means to compute any of the solutions of the consistent linear equation Ax = b since the general solution may be expressed as x = A(mr)+b + Pz, where z is an arbitrary vector. The rank r of A will also be produced in the process. Some of the salient features of this algorithm are that (i) the algorithm is concise, (ii) the minimum norm least squares solution for consistent/inconsistent equations is readily computable when A is full row-rank (else, a minimum norm solution for consistent equations is obtainable), (iii) the algorithm identifies ld rows, if any, and reduces concerned computation and improves accuracy of the result, (iv) error-bounds for the inverse as well as the solution x for Ax = b are readily computable, (v) error-free computation of the inverse, solution vector, rank, and projection operator and its inherent parallel implementation are straightforward, (vi) it is suitable for vector (pipeline) machines, and (vii) the inverse produced by the algorithm can be used to solve under-/overdetermined linear systems.

Matrix method for eigenstructure assignment - The multi-input case with application

The eigenvalue and eigenstructure assignment procedure has found application in a wide variety of control problems. In this paper a method for assigning eigenstructure to a linear time invariant multi-input system is proposed. The algorithm determines a matrix that has eigenvalues and eigenvectors at the desired locations. It is obtained from the knowledge of the open-loop system and the desired eigenstructure. Solution of the matrix equation, involving unknown controller gams, open-loop system matrices, and desired eigenvalues and eigenvectors, results hi the state feedback controller. The proposed algorithm requires the closed-loop eigenvalues to be different from those of the open-loop case. This apparent constraint can easily be overcome by a negligible shift in the values. Application of the procedure is illustrated through the offset control of a satellite supported, from an orbiting platform, by a flexible tether.

Matrix method for eigenvalue assignment: The single input case

The eigenvalue assignment/pole placement procedure has found application in a wide variety of control problems. The associated literature is rather extensive with a number of techniques discussed to that end. In this paper a method for assigning eigenvalues to a Linear Time Invariant (LTI) single input system is proposed. The algorithm determines a matrix, which has eigenvalues at the desired locations. It is obtained from the knowledge of the open-loop system and the desired eigenvalues. Solution of the matrix equation, involving unknown controller gains, open-loop system matrices and desired eigenvalues, results in the state feedback controller. The proposed algorithm requires the closed-loop eigenvalues to be different from those of the open-loop case. This apparent constraint is easily overcome by a negligible shift in the values. Two examples are considered to verify the proposed algorithm. The first one pertains to the in-plane libration of a Tethered Satellite System (TSS) while the second is concerned with control of the short period dynamics of a flexible airplane. Finally, the method is extended to determine the Controllability Grammian, corresponding to the specified closed-loop eigenvalues, without computing the controller gains.

Matrix method for eigenstructure assignment - The multi-input case with application

The eigenvalue and eigenstructure assignment procedure has found application in a wide variety of control problems. In this paper a method for assigning eigenstructure to a Linear time invariant multi-input system is proposed. The algorithm determines a matrix that has eigenvalues and eigenvectors at the desired locations. It is obtained from the knowledge of the open-loop system and the desired eigenstructure. solution of the matrix equation, involving unknown controller gains, open-loop system matrices, and desired eigenvalues and eigenvectors, results in the state feedback controller. The proposed algorithm requires the closed-loop eigenvalues to be different from those of the open-loop case. This apparent constraint can easily be overcome by a negligible shift in the values. Application of the procedure is illustrated through the offset control of a satellite supported, from an orbiting platform, by a flexible tether,

Matrix method for eigenvalue assignment: The single input case

The eigenvalue assignment/pole placement procedure has found application in a wide variety of control problems. The associated literature is rather extensive with a number of techniques discussed to that end. In this paper a method for assigning eigenvalues to a Linear Time Invariant (LTI) single input system is proposed. The algorithm determines a matrix, which has eigenvalues at the desired locations. It is obtained from the knowledge of the open-loop system and the desired eigenvalues. Solution of the matrix equation, involving unknown controller gains, open-loop system matrices and desired eigenvalues, results in the state feedback controller. The proposed algorithm requires the closed-loop eigenvalues to be different from those of the open-loop case. This apparent constraint is easily overcome by a negligible shift in the values. Two examples are considered to verify the proposed algorithm. The first one pertains to the in-plane libration of a Tethered Satellite System (TSS) while the second is concerned with control of the short period dynamics of a flexible airplane. Finally, the method is extended to determine the Controllability Grammian, corresponding to the specified closed-loop eigenvalues, without computing the controller gains.

A study of microstructure and wear behaviour of TiB2/Al metal matrix composites

The present paper deals with the study of microstructure and wear characteristics of TiB2 reinforced aluminium metal matrix composites (MMCs). Matrix alloys with 5, 10 and 15% of TiB2 were made using stir casting technique. Effect of sliding velocity on the wear behaviour and tribo-chemistry of the worn surfaces of both matrix and composites sliding against a EN24 steel disc has been investigated under dry conditions. A pin-on-disc wear testing machine was used to find the wear rate, in which EN24 steel disc was used as the counter face, loads of 10-60N in steps of 10N and speeds of 100, 200, 300, 400 and 500 rpm were employed. The results showed that the wear rate was increased with an increase in load and sliding speed for both the materials. However, a lower wear rate was obtained for MMCs when compared to the matrix alloys. The wear transition from slight to severe was presented at the critical applied loads. The transition loads for the MMCs were much higher than that of the matrix alloy. The transition loads were increased with increase in TiB2 and the same was decreased with the increase of sliding speeds. The SEM and EDS analyses were undertaken to demonstrate the effect of TiB2 particles on the wear mechanism for each conditions.