Form Of Transfer Matrix Research Articles

Three-dimensional exact solutions for the electromechanical response of triple-layerpiezoelectric actuators

Actuators consisting of a metallic layer covered symmetrically by two transversely isotropicpiezoelectric layers poled along the thickness direction are analyzed. By recasting the fieldequations of linear piezoelectricity into the transfer-matrix form and using a technique ofexpansion in a small parameter, the coupled electromechanical field in the actuator isexpressed as a closed-form solution in terms of the three orthogonal displacementcomponents on the mid-plane. The displacement components are governed by threetwo-dimensional differential equations, and the associated boundary conditions are specifiedin an average manner as in the classic plate theory. Solving these two-dimensionalequations gives a three-dimensional solution for the piezoelectric actuator. Because theintermediate metallic layer results in some discontinuities in material properties and theelectric displacement, significant physical considerations and analytical complexity arisewhile establishing the three-dimensional analytical method. As an example, theresponse of a cantilevered actuator subjected to an applied voltage is studied,and a significant result is discussed in detail. It is concluded that ignoring theelectromechanical coupling leads to significant underestimation of the deformation of theactuator.

Transfer matrix method for mufflers modeling and experimental verification

Mufflers are very important elements in industry for the attenuation of exhaust noise in vehicles and machinery. Recent advances in modeling procedures, for accurate performance prediction, lead to the development of the transfer matrices method for more practical muffler components appearing in commercial designs. Muffler designers are looking for simple, quick modeling tools, especially in the preliminary evaluation stages of a design. Finite element (FEM) and boundary element (BEM) methods, in spite of giving results in a wide range of frequencies, are still expensive, need very skilled operators, and commercial software is still not user friendly. Plane wave modeling, using the transfer matrix form, offers a cheap and quick method for muffler designers to arrive at an initial prototype solution. In this paper, transmission loss calculations are presented for several practical muffler configurations in explicit formulas and comparison with experimental results are presented.

Pade type model order reduction for multivariable systems using routh approximation

A method of obtaining reduced order models for multivariable systems is described. It is shown that the method has several advantages, e.g. the reduced order models retain the steady-state value and stability of the original system. Irrespective of whether the original multivariable system is described in state space form or in the transfer matrix form, the proposed method yields the reduced order models in state space form. In this method the Routh approximation is used to formulate the common denominator polynomial of a reduced order model. This is used to describe the structure of A r matrix. The matrices B r and C r are chosen appropriately and some of the elements of B r / C r matrices are specified in such a way that after matching time moments/Markov parameters, the resulting equations are linear in the unknown elements of B r and C r matrices. The procedure is illustrated via a numerical example.

Axisymmetric transient solutions of the heat diffusion problem in layered composite media

An analytical/numerical method for solving the problem of non-stationary heat diffusion in multilayered slabs is presented. This is an extension of previous methods that have been used to solve transient heat diffusion problems in one-dimension. In this work, two-dimensional semi-infinite media are considered and double integral transforms are used to obtain the corresponding transfer matrix form from the governing partial differential equations. Numerical techniques are used to compute the overall transfer matrices of the system and to numerically invert them in order to obtain transient results. Difficulties encountered with the numerical operations and ways to circumvent these are presented. The developed methodology has been applied to two-layered configurations.

Perfect space and time focusing ion optics for multiturn time of flight mass spectrometers

Ion optics of multiturn time-of-flight mass spectrometer that satisfy both perfect space and time focusing were investigated. The basic concepts of perfect focusing are explained. It was found that the perfect focusing conditions can be reduced by introducing symmetrical geometries. The conditions are expressed in the transfer matrix form.

Wave propagation in fluids contained in finite-length anisotropic viscoelastic pipes

Wave propagation characteristics are studied of a fluid-filled, finite-length anisotropic viscoelastic pipe—a flexible hydraulic hose. An analytical model in transfer matrix form is developed for relating the pressure and flow ripples at hose upstream and downstream. The anisotropic viscoelasticity of the hose wall, the coupled vibration of the hose and the fluid, and the effect of possible longitudinal resonances of the finite-length hose are considered. The static mechanical properties and frequency-dependent mechanical properties of the hose wall are determined by means of specially designed static expansion method and optimal searching method separately. Experimental confirmation is made over a wide frequency range by using an experimental procedure for measuring the transfer matrix parameters. By comparing the predicted and measured results of the hoses with different lengths, it is shown that the model yields fairly good results in a frequency range of around 0–3 kHz and even may predict the influence of longitudinal resonances of the hose wall on the wave propagation of fluid in the hose. The effectiveness of the experimental methods and procedure proposed here are also verified.

Universality class in the one-dimensional localization problem.

Weak disorder behavior of the Lyapunov exponent is investigated for a one-dimensional disordered system whose band structure and transfer matrix form are manifestly different from the standard ones encountered in tight-binding models. For diagonal disorder, the critical exponents governing the divergence of the localization length at zero disorder are identical with those predicted for tight-binding models. For off-diagonal disorder, a new exponent is found in one of the band edges, indicating a different universality class. The scaling functions near the different band edges are displayed, and their values for zero arguments are not identical at all edges. \textcopyright{} 1996 The American Physical Society.

TRANSMISSION CHARACTERISTICS OF FLUIDBORNE PRESSURE RIPPLES IN FINITE-LENGTH HYDRAULIC FLEXIBLE HOSES

The paper is concerned with the development of an analytical model for the transmission characteristics of fluidborne pressure ripples in hydraulic flexible hoses with finite length under anchored end conditions, as an extension to the previous researches for the hoses with relatively long length [1, 2]. The model is obtained in transfer matrix form relating the pressure and flow ripples at hose upstream and downstream, by considering the effect of possible longitudinal resonance of the hose in addition to the anisotropic viscoelasticity of the hose wall and the coupled vibration of the hose and the fluid. It is applied to predict the transfer matrix parameters of the hoses with different lengths. By the comparison of the predicted and measured results, it is shown that the model yields fairly good results in a frequency range up to around 3kHz and even may accurately predict what existing models failed to predict, i.e., the influence of longitudinal resonance of the hose wall on the wave propagation of fluid in the hose.

On the generic structure at infinity within the transfer matrix form

Abstract The present paper deals with a graph characterization of some structural properties at infinity for structured systems within the transfer matrix approach. The main properties covered are infinite zeros, essential orders and the row and column properness of a transfer matrix. This structural information is easily expressed in terms of input-output paths on a digraph associated with the structured system.

On “order reduction of linear systems using an error minimization technique”

A method of obtaining reduced order models for multivariable systems is described. It is shown that the method has several advantages, e.g. the reduced order models retain the steady-state value and stability of the original system. Irrespective of whether the original multivariable system is described in state space form or in the transfer matrix form, the proposed method yields the reduced order models in state space form. In this method the Routh approximation is used to formulate the common denominator polynomial of a reduced order model. This is used to describe the structure of Ar matrix. The matrices Br and Cr are chosen appropriately and some of the elements of Br/Cr matrices are specified in such a way that after matching time moments/Markov parameters, the resulting equations are linear in the unknown elements of Br and Cr matrices. The procedure is illustrated via a numerical example.

油圧管路の動特性を利用した遠隔瞬時流量計測手法

Measurement of unsteady flowrate through pipelines and equipment is very important to analyze dynamic characteristics of hydraulic control systems.In this research, we propose two approaches, the remote and quasi-remote measurement method for instantaneous flowrate using hydraulic pipeline dynamics which are well-established in the form of transfer matrix relating to the pressures and flowrates between two cross sections (distance L) of the pipeline.In particular, the remote measurement method of instantaneous flowrate for estimating flowrate through an arbitrary cross section from the measured values of pressure and flowrate at the another remote cross section are investigated in detail.The estimated flowrate waveforms are compared with the measured flowrate waveforms directly by another cylindrical choke type instantaneous flowmeter, which is used for calibration. The excellent agreement obtained between the estimated and directly measured flowrate waveforms illustrates the validity of the proposed method.It is shown that the remote measurement method of instantaneous flowrate proposed here is useful in estimating flowrate through the arbitrary cross section of hydraulic pipeline under unsteady laminar flow.

The role of lossless systems in modern digital signal processing: a tutorial

A self-contained discussion of discrete-time lossless systems and their properties and relevance in digital signal processing is presented. The basic concept of losslessness is introduced, and several algebraic properties of lossless systems are studied. An understanding of these properties is crucial in order to exploit the rich usefulness of lossless systems in digital signal processing. Since lossless systems typically have many input and output terminals, a brief review of multiinput multioutput systems is included. The most general form of a rational lossless transfer matrix is presented along with synthesis procedures for the FIR (finite impulse response) case. Some applications of lossless systems in signal processing are presented. >

On the exact model matching controller design

The problem of designing a static state feedback controller which matches a given multivariable system to a desired ideal system (model) is treated. The system under control is assumed in state space form while the model is assumed in transfer matrix form. An algorithm is developed which separates the conditions which must be satisfied by the system under control and the model to be matched from the equations which must be solved to find the gains of the feedback controller. Two examples are included.

A Modified Computation Scheme for Beam Grid Systems with Intermediate Discontinuities

The presence of rigid supports and releases in intermediate positions in an elastic system of a chain beam topology introduces zero elements and an equal number of complementary discontinuous elements in the complete state vector at the corresponding positions. The rank of the transfer matrix for the beam segment between these discontinuities is reduced by twice the number of these zero elements. The corresponding reduction of the transfer matrix size is executed(1) by choosing a lengthy reduced transfer matrix form arranged in table form. The note suggests a method of reduction depending upon the manipulation of partitioned rectangular matrices, and finally associates each type of discontinuity to a boolean-type matrix, which is easier to handle and adapted to computer programming. The proposed scheme can be used for any n-order problem and for any number of different zero elements in the state vectors of the discontinuities. Special arrangement is suggested for desk calculator operations. The vibration analysis of structures, the analysis of space mechanisms and the analysis of indeterminate structures are applications for which the formulation is helpful.