Modal Decoupling Research Articles

Coherent versus diffuse surface and volume Reverberation in an ocean wave guide: Reverberation rings, modal decoupling, and possible fish scattering in Geoclutter 2001

Conditions necessary for the field scattered from volume inhomogeneities and surface roughness in a wave guide to become diffuse in nonforward azimuths are derived from Green’s theorem. Diffuse scattering leads to a decorrelation of the wave guide modes that simplifies the expression for the intensity of the total scattered field. When diffuse scattering conditions are not satisfied, seafloor scattering becomes coherent and leads to the formation of ‘‘reverberation rings’’ sometimes observed in high-resolution sonar systems. The formation of these rings will be investigated both analytically and with simulations. The possibility that some prominent clutter events in the Geoclutter 2001 experiment are due to diffuse scattering from fish schools is investigated theoretically and experimentally.

Design of a state feedback controller to achieve minimum eigenvalue differential sensitivity

This paper introduces a new design method using eigenstructure assignment. The differential sensitivity of the eigenvalues of the system is minimized. The method involves minimizing the least-squared error between the achievable and the desired eigenspace to achieve mode decoupling. A global measure of eigenvalue sensitivity for all desired eigenvalues that make the closed-loop system insensitive to perturbations or parameter variations is included in the method. The technique requires the use of a gradient-based algorithm. The method is illustrated by an example, which is intended to show a more flexible approach to eigenstructure assignment.

362 エレメントフリーガラーキン法による任意方向き裂進展解析のためのモード分離法に関する検討(OS24-3 EFGM)(OS24 メッシュレス/粒子法)

362 エレメントフリーガラーキン法による任意方向き裂進展解析のためのモード分離法に関する検討(OS24-3 EFGM)(OS24 メッシュレス/粒子法)

Environmentally adaptive wedge modes

The notion of environmentally adaptive, curvilinear, uncoupled normal modes is developed by writing the Helmholtz equation in curvilinear coordinates. The depth-dependent vertical scaling function provides some coordinate freedom missing from the Cartesian formulation. This freedom permits adaptation of the normal mode approach to variable depth and variable sound-speed problems for environments that change slowly in range. A W.K.B. approximation to the eigenfunctions shows modal decoupling can be realized when the vertical scaling function is chosen equal to the reciprocal of the depth-dependent vertical wave number of the lowest mode. Numerical simulations demonstrate that a requirement for constant inter-modal ratios of the vertical wave number is valid throughout several wedges with different bottom boundary conditions. The horizontal refraction of such modes agrees closely with analytic solutions. For a wide-angle wedge, the acoustic field agrees qualitatively well with the benchmark solution of Dean and Buckingham [J. Acoust. Soc. Am. 93, 1319-1328 (1993)].

Invariant Hybrid Force/Position Control of a Velocity Controlled Robot with Compliant End Effector Using Modal Decoupling

A new method based on modal decoupling is proposed for the hybrid force/position control of a robot during constrained mo tion. The robot is equipped with an internal velocity controller, i.e., the control commands issued by the hybrid force/position controller are desired (joint) velocities. This velocity controller is supposed to be very stiff or of high bandwidth, as is the case for most commercial industrial robots. As a result, the robot dynamics are negligible compared to the contact dynam ics, which have low frequency because passive compliance is concentrated in the robot end effector. The new method incor porates results from the control of flexible robots, to damp out undesired vibrations of the end effector through active control. The contact dynamics during constrained motion are de scribed by a MIMO system: the inputs are the joint velocities; the outputs are the forces and torques measured by the wrist sensor. Using modal decoupling, this MIMO system is decom posed into its vibrational modes, i.e., a set of decoupled SISO systems. These modes are either unconstrained real vibrational modes, or constrained, and hence degenerated modes. Both are easy to control to satisfy the overall requirements of desired contact forces and vibration free motion of the manipulated object. Attention is paid to the invariance of the approach; i.e., the resulting robot behavior is independent of the choice of reference frame and the choice of units. The article contains experimental results of free space and partially constrained motion. Both confirm the theoretical re sults. 2. Usually, forces and torques are measured using strain gauges or dis placement transducers. 3. In practice, the effect of w g can easily be compensated for, by using a gravity model of the MO. 4. Proportional damping is an invariant concept; i.e., α and β are indepen dent of the representation of C, M and K, but few real systems exhibit this characteristic. Nevertheless, the assumption of proportional damp ing is frequently used for the ease of mathematical treatment. Indeed, Caughey (1960) showed that proportional damping is a sufficient—but not a necessary—condition for the existence of real modes. 5. Mathematically, this is easily verified using the positive definiteness of M and K, and the positive semidefiniteness of projection operator JJ †M. 6. In practice, such discontinuities are avoided by proper trajectory genera tion, but here they are deliberately introduced.

SPICE-compatible models for multiconductor transmission lines in Laplace-transform domain

Two models for multiconductor transmission lines are presented that are compatible with SPICE. One model is based on a Thevenin equivalent circuit and the other model is based on mode decoupling. The models contain controlled generators in the Laplace-transform domain and are able to handle lossy lines with frequency-dependent parameters.

Modal Decoupling of Systems Described by Three Linear Operators

Brief Notes Modal Decoupling of Systems Described by Three Linear Operators A. A. Renshaw A. A. Renshaw Department of Mechanical Engineering, Columbia University, 500 West 120th Street, Room 220, New York, NY 10027 Search for other works by this author on: This Site PubMed Google Scholar Author and Article Information A. A. Renshaw Department of Mechanical Engineering, Columbia University, 500 West 120th Street, Room 220, New York, NY 10027 J. Appl. Mech. Mar 1997, 64(1): 238-240 (3 pages) https://doi.org/10.1115/1.2787281 Published Online: March 1, 1997 Article history Received: December 8, 1995 Revised: June 6, 1996 Online: October 25, 2007

Stable Response of Non-Classically Damped Mechanical Systems - II

This review, like its 1987 predecessor, addresses response of a discrete, time-invariant, linear, multiple degree-of-freedom system which exhibits nonclassical damping, including active damping. Unlike a classically damped system, the modes are coupled (or complex). In the intervening decade, stability issues involving nonclassical damping have received attention in applications such as high speed mechanisms, active structural control, vehicle dynamics, and seismic isolation of ground structures. Much of the recent literature has concerned approximate modal decoupling. There have also been contributions to the accurate calculation of the coupled modes, to general stability issues such as gyroscopic stabilization, and to eigenvalue/response bounds. The present article is intended both as a survey of recent literature and as a brief exposition of selected contributions of a general nature.

Optimized feedforward design scheme unifying regulator and command generator tracker

Tracking control law is the control scheme to make the system output follow a nonzero reference command signal. By combining the tracking control law with an eigenstructure assignment and applying it to an advanced aircraft such as control configured vehicles, mode-decoupled command following can be achieved. The tracking control law usually consists of feedback control of output states and feedforward control of reference input. A new design methodology is proposed by utilizing the nonlinear optimization technique to design a useful controller. The proposed algorithm utilizes the eigenstructure assignment and the optimization technique to compute the feedback gain matrix (for aircraft mode decoupling) and feedforward gain matrix, respectively. It is shown that the existing algebraic formula for computing the feedforward gain matrix is the limiting case of the proposed methodology. The design methodology is illustrated by application to an AFTIF-16 aircraft. OR a multi-input/multi-output system, a given set of eigenvalues can be assigned by an infinity of gain matrices. The eigenstructure assignment technique utilizes this extra freedom to assign the closed-loop eigenvectors. The original eigenstructure assignment technique based on the algebraic solution is very useful for aircraft mode decoupling.13 The main drawback of this technique is the lack of stability robustness with respect to parameter variations. To solve this problem, research47 has been performed using optimization46 or the method of inequality. 7 In this paper, we are not very concerned with these feedback methodologies; thus, we just adopt the baseline eigenstructure assignment technique. Sobel and Shapiro2 developed the design methodology for pitch pointing flight control systems by utilizing an eigenstructur e assignment in conjunction with the command generator tracker.8 This methodology computes the feedback gain matrix by eigenstructur e assignment, then the feedforward gain matrix can be obtained by solving an algebraic unsymmetric Lyapunov equation. Therefore, this method does not allow the designer to use his own perspective for computing the feedforward gain matrix during the design process. In this paper, we propose a new design methodology for computing the feedforward gain matrix. The feedforward gains are computed to minimize a performance index, which considers both the error deviation from the prescribed model dynamics and steadystate error. By selecting the design parameters, the feedforward gain matrix will yield various tracking performances. We prove that the perfect model following control scheme is one of the limiting case of the proposed design methodology. The proposed design schemes are illustrated by application to an AFTI F-16 aircraft for pitch pointing control.

Viscosity of chalcogenide glass-forming liquids: an anomaly in the ‘strong’ and ‘fragile’ classification

High purity chalcogenide glasses with an average coordination number, 〈r〉, between 2 and 2.8 were prepared by vacuum melting of pre-distilled samples in the GeSe binary and GeSbSe ternary systems. Viscometry and scanning calorimetry were performed to understand the nature of the property thresholds observed with respect to 〈r〉 in these glass-forming systems. There is a lack of correlation between viscosity-based and heat capacity-based classifications of strong and fragile liquids in the overconstrained region of these glass-forming systems. An argument based on Adam-Gibbs equation and mode decoupling is put forward for the observation of the anomaly.

TE and TM modes in cylindrical metallic structures filled with bianisotropic material

Modal propagation is studied for metallic circular waveguides, coaxial cables and sectoral waveguides filled with linear bianisotropic material. By representing the material constitutive tensors in cylindrical coordinates, the conditions under which TE and TM modal decoupling occurs are obtained, and second-order differential equations for the longitudinal field components are derived. Though the TE and TM longitudinal field components are expressible in terms of hypergeometric functions, a complete numerical solution scheme is, in general, more convenient. Conventional application of finite elements renders the differential problem numerically equivalent to a generalized eigenvalue matrix problem, whose solution yields the dispersion relation and cutoff frequencies of the waveguides together with the eigenfields expression. The effects one can obtain by varying the various coefficients of the constitutive tensors are illustrated by several numerical results.

A simplified real frequency independent modal transformation for overhead line switching transient computations

AbstractModal transformation technique is a common tool for transmission line transient computations. A simplified modal decomposition of overhead transmission lines, suitable for time‐domain switching (up to 105 Hz) transient computations, is proposed. By neglecting residual terms in the ZY matrix, transformation matrices are approximated as real and frequency independent. The resulting propagation constants remain unaffected from the line being transposed or not, although the existing asymmetries affect transformation matrices. The method can be extended for double circuit lines, provided they have the same configuration. Propagation characteristics, mode decoupling and travelling‐wave transmission effects have been investigated. Results are compared with those obtained from other methods in use.

Examination, clarification, and simplification of modal decoupling method for multiconductor transmission lines

In the application of the modal decoupling method, questions arise as to why the nonnormal matrices LC and CL are diagonalizable. Is the definition of the characteristic impedance matrix Z/sub c/ unique? Is it possible to normalize current and voltage eigenvectors simultaneously, yet assure the correct construction of the Z/sub c/ matrix? Under what conditions do M/sub i//sup t/M/sub u/=I and Z/sub c/=M/sub u/M/sub i//sup -1/? In this paper, these questions are thoroughly addressed. We prove the diagonalizability of matrices LC and CL for lossless transmission lines (though the diagonalizability of their complex analogues, ZY and YZ matrices, is not guaranteed for lossy lines), and demonstrate the properties of their eigenvalues. We have developed an algorithm to decouple one type of matrix differential equation, and to construct the characteristic impedance matrix Z/sub c/ explicitly and efficiently. Based on this work, the congruence and similarity transformations, which have caused considerable confusion and not a few errors in the decoupling and solution of the matrix telegrapher's equations, are analyzed and summarized. In addition, we also demonstrate that under certain conditions, the diagonalization of two or more matrices by means of the congruence or similarity transformations may lead to coordinate system mismatch and introduce erroneous results. >

Multirate Control System Design Using Eigenstructure Assignment

This paper describes the application of eigenstructure assignment to the multirate control systems design. It is shown that eigenstructure assignment can be used to design state feedback control to ensure that the closed-loop system has less modal interaction and hence reduced intersample oscillation. Modal decoupling also provides good eigenvalue insensitivity with respect to perturbations in the nominal system dynamics. Multirate sampling provides extra design freedom for assigning the desired eigenstructure. However, this often results in a high gain norm which, in turn leads to unreasonably large control effort. Hence, an optimal eigenstructure assignment approach is used to achieve an acceptable compromise between control effort minimization and assignment of a prescribed modal structure. An example is used to illustrate the approach taken in the paper

A finite volume Navier‐Stokes algorithm for adaptive grids

AbstractA compact, finite volume, time‐marching scheme for the two‐dimensional Navier‐Stokes equations of viscous fluid flow is presented. The scheme is designed for unstructured (locally refined) quadrilateral meshes. An earlier inviscid equation (Euler) scheme is employed for the convective terms and the emphasis is on treatment of the viscous terms. An essential feature of the algorithm is that all necessary operations are restricted to within each cell, which is very important when dealing with unstructured grids. Numerical issues which have to be addressed when developing a Navier‐Stokes scheme are investigated. These issues are not limited to the particular Navier‐Stokes scheme developed in the present work but are general problems. Specifically, the extent of the numerical molecule, which is related to the compactness of the scheme and to its suitability for unstructured grids, is examined. An approach which considers suppression of odd‐even mode decoupling of the solution when designing a scheme is presented. In addition, accuracy issues related to grid stretching as well as boundary layer solution contamination due to artificial dissipation are addressed. Although the above issues are investigated with respect to the specific scheme presented, the conclusions are valid for an entire class of finite volume algorithms. The Navier‐Stokes solver is validated through test cases which involve comparisons with analytical, numerical and experimental results. The solver is coupled to an adaptive algorithm for high‐Reynolds‐number aerofoil flow computations.

Experimental modal analysis of a multi-degree-of-freedom system with random parametric excitation and non-linear damping

Though there are many non-linear systems in use, the experimental modal analysis techniques are based on the linear system. In this paper, an experimental modal analysis technique for a multi-degree-of-freedom system with random parametric excitation and non-linear damping being proportional to the squared velocity is proposed. This technique is developed from examining a stability condition for the covariance of response given by applying the perturbation technique to a stochastic differential equation, which is derived by the mode decoupling, the statistical linearization and other assumptions. Additionally, experiments were carried out to identify the modal parameters with the aid of the proposed technique, the technique was confirmed with analytical solutions.

Scattering from partial bodies of revolution

The electromagnetic scattering from classes of partial bodies of revolution formed by the presence of perfectly electrically or magnetically conducting (PEC or PMC) planes is investigated. It is found that when the Galerkin technique is used with a harmonic circumferential expansion, there is a modal decoupling of the integral operators. The choice of these expansions is determined by the angle subtended by the intersecting planes and by whether these planes are PEC, PMC, or a combination of the two. In this analysis, the partial bodies can be either PEC or penetrable. Examples illustrating this formulation are given for conducting and dielectric hemispherical geometries and for a modified corner reflector. Measured and calculated data are compared for the case of a half-cylinder on a finite ground plane. >

Parametric output feedback control with response insensitivity

A recent parameterization of the class of linear output-feedback controllers that assign a set of desired self-conjugate eigenvalues to the closed-loop system is used to formulate and solve a fundamental response insensitivity problem. It is established to what extent output-feedback control can be used to render the closed-loop system response insensitive to possibly many not necessarily small parameter variations in the open-loop state space model. A non-conservative sequential design procedure is developed for making as many of the closed-loop system eigenmodes as possible totally insensitive while retaining arbitrary assignment of the maximum number of closed-loop eigenvalues. The main result is a class of desensitizing fixed-gain output-feedback controllers explicitly specified by a set of free parameters which may be chosen to satisfy additional design requirements. Conditions are given for total modal decoupling insensitivity to possibly many not necessarily small parameter variations in the open-loop state model. The mechanism of modal decoupling insensitivity for a given mode is interpreted in terms of the insensitivity of the corresponding left eigenmode. A parametric approach to output feedback design for modal decoupling insensitivity is discussed.

Electromagnetic scattering from ducts with irregular edges. I. Circular case

A formulation is developed for electromagnetic scattering from finite circular ducts terminated with irregular edges. The analysis is based on the solution of the electric field integral equation using an entire-domain Galerkin expansion for both the axial and the circumferential variation of the currents, defined in terms of an edge-slope-dependent vector field that provides simplifying symmetry properties for the method-of-moments system matrix. Comparisons are made with edge-slope-independent formulations. The analysis is general and applicable for cases in which the functional variation of the edge irregularities is specified by either a deterministic or a random process. Circumferential modal decoupling occurs when the irregularities are specified by a stationary stochastic process having a periodic correlation function. Numerical results are given for edge irregularities governed by a Gaussian random process and are compared for various limiting cases with results for right circular cylindrical ducts.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Modal decoupling methods for fluid-structure interaction in piping systems

A simple model for fluid-structure interaction in piping systems is considered, using beam elements for the structure and assuming the propagation of planar pressure waves in the fluid. The forces, exerted, on the structure at the ‘singular’ points of the piping system due to the change of the fluid momentum, are treated in a natural and straightforward way. The model is shown to behave quite well in the low frequency range, provided that certain corrections are made to the structure inertia, to the structure flexibility at the ‘singular’ points (elbows, tees, etc) and to the fluid sound speed. Recent advances concerning the general ‘acoustoelastic’ fluid structure model—symmetrisation procedures, modal decoupling methods—are applied to the model. The modal methods start with the solution of the ‘in vacuum’ and of the ‘acoustic’ eigenproblems and lead to the solution, not only of the ‘full’ eigenproblem, but also of several ‘limit case’ eigenproblems, such as the ‘incompressible’ fluid. These methods are not simply an efficient analytical tools, since they can be implemented utilizing ‘standard black box’ beam analysis codes, but they can also provide the designer with useful indications with respect to the effect of several individual structure or fluid parameters on the coupled system.