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In this work, a new implementation of the finite-difference (FD) modal method (FDMM) based on an iterative approach to calculate the eigenvalues and corresponding eigenfunctions of the Helmholtz equation is presented. Two relevant enhancements that significantly increase the speed and accuracy of the method are introduced. First of all, the solution of the complete eigenvalue problem is avoided in favor of finding only the meaningful part of eigenmodes by using iterative methods. Second, a multigrid algorithm and Richardson extrapolation are implemented. Simultaneous use of these techniques leads to an enhancement in terms of accuracy, which allows a simple method such as the FDMM with a typical three-point difference scheme to be significantly competitive with an analytical modal method.

This paper describes Multi-Modal-Method, a design method for building grammar-based multi modal systems. Multi-Modal-Method defines the procedure which interface designers may follow in developing multi-modal systems, and provides MM-DCG, a grammatical framework for multi-modal input interpretation. Multi-Modal-Method has been inductively defined through several experimental multi-modal interface system developments. A case study of a multi-modal drawing tool development along with Multi-Modal-Method is reported.

A new modal method to derive the response of nonlinear structures in time domain will be presented. The modal capacity method reflects the nonlinear behavior of a structure by one or more nonlinear modes. Therefore a new superposition method was developed. The modal SDOF systems depend not only on the modal parameters (ω, φ,...) but also on the time history of impulse (earthquake, force,...) itself. This very new assumption can be expressed by so called amplification factors. Because of the modal working technique the modal capacity method can use a parallel computer in a very efficient way.

This paper researches on the control laws of synchronised switch damping on inductor technique (SSDI). The SSDI shunt damping is adaptive to the excitation frequency, and no precise tuning of the shunt parameters is necessary. With this property, the SSDI technique is very adept in handling broadband multimodal and random excitation. The triggering of the switch is decided by a decision algorithm, normally called switching control law, which plays an important role in damping performance. In the original control law, the switch is triggered on each extremum deformation of the shunted piezoelement. It is shown that this switching law maximises the dissipated energy only for monomodal excitation, therefore various control laws were proposed for improving the damping performance in the case of complex multimodal excitation. In this paper, all of the proposed control laws are reviewed and classified. Besides, an enhanced switching law base on modal method is presented and highlighted. Measurements are conducted on a clamped-free beam test rig to validate the theoretical results.

The objective of this study was to compare three methods of collecting social class datain general practice. The setting was a rural dispensing practice on the Nottinghamshire/Lincolnshire border. The methods examined were: (a) a self-administered questionnaire to 200 patients to determine their social class based on the occupation of the head of household; (b) members of the practice staff were asked to assign a social class to these households based on their local knowledge; and (c) use of small area statistics from the 1991 census data using modal and weighted methods. It was found that the practice staff were unable reliably to assign a social class to the households. The modal method of using small area statistics to assign social class to households through their postcode and its link to the census data was also inaccurate. While a personal questionnaire will remain the only method for assigning a social class to individual patients for clinical care or most research, the weighted method of small area statistics is shown to be a cost-effective and sufficiently accurate method for health needs assessment in general practice.

Fourier modal method incorporating staircase approximation is used to study tapered crossed subwavelength gratings in this paper. Three intuitive formulations of eigenvalue functions originating from the prototype are presented, and their convergences are compared through numerical calculation. One of them is found to be suitable in modeling the diffraction efficiency of the circular tapered crossed subwavelength gratings without high absorption, and staircase approximation is further proven valid for non-highly-absorption tapered gratings. This approach is used to simulate the "moth-eye" antireflection surface on silicon, and the numerical result agrees well with the experimental one.

Three variants of binary blazed gratings with subwavelength features are considered, which have high first-order efficiencies in the non-paraxial domain for arbitrarily polarized light. A combination of effective medium theory and further parametric optimization with the Fourier modal method are used in design. Experimental demonstration is provided by electron beam lithography on a structure etched in a Si3N4 layer on top of a SiO2 substrate, with period approximately 3.5lambda at lambda = 633 nm. The measured efficiency (81% for TE and 85% for TM polarization) agrees well with the calculated value, 84%.

The problem of scattering of Rayleigh waves at a rectangular groove is addressed. Grooves are known to excite bulk waves upon scattering and, hence, are potential sources (albeit secondary) in bulk-acoustic-wave (BAW) devices. The groove is formulated as a volume perturbation of the geometry. A modal method is used, and the results of Rayleigh wave reflection as well as bulk wave radiation are obtained and compared with the results available in the literature. The method is compared with the boundary perturbation formulation. The equivalence of the boundary perturbation method and the volume perturbation method is shown. >

This paper details to an electromagnetic modeling of an extreme ultraviolet (EUV) lithography mask. For that purpose, a modal method based on a spline nodal expansion (MMSNE) is presented. The results obtained using first, and second-order splines as basis functions are compared with those obtained using other modal methods, such as modal method by Fourier expansion (MMFE). The agreement between the results obtained using different methods is very good, and a convergence test is also performed. The spline nodal basis function implemented in this paper is the first step toward the realization of a multiresolution scheme that is expected to perform much more efficiently than conventional schemes.

The absorption efficiency for circular or offset double-clad optical fibers is investigated with modal analysis method. First, calculate the number of all the propagating modes approximately using WKB method and derive the analytic formulas for calculating the number of propagating modes that can't be absorbed by active core. Then the absorption efficiency can be obtained analytically. Comparison of modal method with the ray optics method is made and the condition of using both methods is also discussed.

A finite element procedure is presented to solve the problem of dynamic interaction between a train and a bridge. The equations of the motion are derived. A modal method is proposed for the nonlinear equations to obtain the numerical solution efficiently. The sample solutions are given to demonstrate the validity and the effectiveness of the proposed method.

The conventional modal method in structural response analysis converges very slowly with respect to the number of natural modes. The convergent property is improved by using the condensed stiffness and mass matrices of the system. Thus, less natural modes are required and the difficulties of computing high natural modes are avoided. Undamped response due to deterministic and random excitations are discussed and numerical examples are given.

This paper presents a survey of various approaches to the response of flexible spacecraft. It also presents a modal analysis developed recently by this author that permits the derivation of closed-form response of rotating structures in a manner similar to that in which the classical modal analysis permits the derivation of the response of nonrotating structures. The method has important implications in the attitude dynamics and control of flexible spacecraft. As an illustration, the response of a spinning rigid body containing flexible parts is derived. This represents the first time that the response of a flexible gyroscopic system has been derived in closed form.

The spot size of the focus in a very lossy medium is discussed with relevance to creation of local temperature increase in muscle tissue by means of electromagnetic waves. A slot in a cylinder is used as a source for heating a lossy cylinder and the internal fields are analyzed by a modal method and a fast Fourier transform (FFT) method.

The behavior of selected low-rise steel buildings subjected to earthquake base motions has been studied, and recommended techniques for the earthquake resistant design of low-rise buildings have been presented. The seismic response of buildings of practical proportions when subjected to seismic response of buildings of practical proportions when subjected to seismic excitation was determined using inelastic time-history analysis. Practical methods of analysis, specifically the modal method and the quasi-static building code (equivalent lateral force) approach, have been evaluated for use in estimating seismic response. For practical design purposes it is suggested that the quasi-static approach for calculating shear distribution, overturning moments, and displacements be employed. Practical guidelines leading to building design that can resist earthquake base motion with an adequate margin of reserve strength are presented. The study demonstrates that it is possible and desirable to employ modern principles of earthquake engineering for low-rise buildings with simple framing systems.

A new calculation method of the modal unbalance response for general flexible rotors in fluid film bearings has been developed by introducing the concept of modal exciting force vector into the usual complex modal method, and the physical meaning of the damping ratio at a critical speed is discussed. Next, application of this method, that correction weights can be determined in only one trial operation, is reported, and positions to measure vibration and to correct unbalance weight are discussed on the basis of the right eigenvector and the exciting factor mode, respectively. Lastly, it is shown by experiments that the proposed balancing method is of use for actual rotors.

A balancing procedure utilizing the Complex Modal Method is presented for linear flexible rotor dynamic systems including the effect of residual shaft bow. The method does not require trial runs; however, a valid mathematical model of the system dynamics is required to obtain the system's modal parameters, which are used to relate the balance corrections to measured responses. Several balancing strategies based on the extension of previous work are suggested for single-speed balancing. Two applications are presented: 1) a gas turbine system with computergenerated response data, and 2) an operating steam turbine-generator system.

In order to find the sound pressure field in a rectangular room, the classical modal method may be applied. However, it does not apply to polyhedric rooms of any shape, to which, however, the image sources method may be applied. The two methods are compared for several geometric shapes: two parallel planes (a layer), a rectangular wave guide and a rectangular enclosure. It is shown under what conditions the image sources method can give accurate enough results. A comparison of theoretical and experimental results is presented.

Methods used for analyzing both long and short term transients for Heavy Water Organic Cooled Reactor (HWOCR) designs are discussed. Along with the conventional point kinetics methods, a one-dimensional space-time method was employed for short term transients, and a one-dimensional modal method as well as a two-dimensional finite difference method was used for studying xenon-induced spatial power oscillations.

A coupled modal method has been developed for analyzing the problem of dynamic interaction between flexible rotary machines and their elastic supporting structures. A special feature of the method considered here is that the structure modes are derived from a dynamic model which contains the rotary machines as rigid mass lumps; therefore, the customary component mode synthesis methods dealing with the assemblage of distinct components are not directly applicable. The present approach combines these types of structure modes directly with the free-free flexible modes of the rotary machines. An example problem is solved for the case under harmonic excitation produced by some interior source in the rotary machine, and the amplitude amplifications are determined for the supporting member loads. Interaction effects, including the influence of gyroscopic coupling, are investigated and discussed.

International audience; The cooling loads of a building and the comfort its induces, depend on the local micro climate, the building, ist occupancy and its shape. The thermophysical and geometrical properties of a building can be described with static and dynamic parameters. These parameters represent the filter effect a building has between the environment and the occupant. The static parameters give an insight of the thermal state of a building in steady state conditions, the climate driving forces being constant. The other parameters are the dynamic ones as they represent the dynamic response of a building to variable driving forces. The modal form of the model for the thermal behaviour enables one to distinguish clearly the intrinsic dynamic parameters which are eigen modes and their corresponding eigenvalue. These parameters are independant of the nature of the outputs and inputs which are applied to the building. the thermal inertia of a building is therefore the physical entity defined as the set of all the eigenmodes and eigenvalues. The number of eigen modes in not a propoerty of the building; this number is related to the precision of the model (it is of the order of the nodes of the grid for finite difference method and is strictly infinite for a model continuous in space). However, simplified assumptions had to be done when elaborating physical and mathematical models. A coherent level of precision with these assumptions will make the best of an important reduction of the eigenmodes describing the interia. As a conslusion, the modal method allows one to strictly define the thermal inertia and it also provides tools for its analysis. Such an analysis will be roughly performed on a particulur example described later.

The influence of the lattice geometry to the band spacings and crosspolarisation of single layer tripole arrays is investigated. A modal method of analysing cascaded FSS with arbitrary element and lattice geometries has been developed and the performance of double 1ayer arrays is described.

The purpose of this paper is to compare the efficiency and robustness of policies obtained using alternative system dynamics support methods. The comparison shows the need for creating new methods which combine the efficiency of the optimization methods with the robustness of the modal methods. One of these hybrid methods is the recently developed reference approach which exhibits the best efficiency and robustness.

The Unified Balancing Approach has been designed to incorporate the advantages of both the influence coefficient and modal balancing methods, while eliminating the disadvantages of both methods. That is, the Unified Balancing Approach uses a modal method of applying correction masses in modal sets using data derived in an empirical manner and requiring a minimum of prior knowledge of the dynamics of the rotor. Essentially, the technique involves the calculation of modal trial mass sets. Generally, these modal trial mass sets are determined such that they affect the mode of interest while not having any effect on the lower modes that have already been balanced. However, using the appropriate data, if available from previous tests, a modal trial mass set can be constructed that will have no effect on any general set of modes (hereafter referred to as the unaffected modes), which can include modes above and below the mode being excited. In general, the number of planes required for the modal trial mass set is one more than the number of modes which must not be affected. In addition, the Unified Balancing Approach is not restricted to planar modes. In this chapter, the theoretical development of the Unified Balancing Approach is presented along with the step-by-step procedure required for its implementation.

In a machine with short bunches of high peak currents, such as the SLAC collider, one needs to know the longitudinal wake potential, for the higher mode losses, and the transverse wake potential, since, for bunches passing slightly off axis, the induced transverse forces will tend to cause beam break up. The longitudinal and transverse wakes of the SLAC structure presented here, were calculated by computer using the modal method, and including an analytic extension for higher modes.

International audience; The computation time needed to compute modes remains the main drawback of modal methods. This computation time can be reduced by using the sub structuring modal method. First of all, the model is divided into elementary entities, and modes of each entity are independently computed. In order to solve the original problem, only specific modes are chosen to couple sub-structures together: the Steklov modes. This method is applied to an electronic card witch supports eighteen components. The Printed Circuit Board is accurately modeled considering local thermal properties (like local copper tracks). The reduced model recovers the maximum temperature of critical component for a dynamic scenario and various boundary conditions reducing the solver time by 500.

We describe a modal method to find the intervening sound‐speed profile from propagated acoustic field data. The method uses the Fourier‐Bessel representation for the propagated acoustic field. For a purely depth‐dependent profile, the depth solution can be represented exactly as the solution of an integral equation whose kernel contains the correction to an assumed initial guess of the profile. This solution is treated in Born approximation and written using a travel length coordinate. The result expresses the data as a linear transform over the profile correction. Using asymptotics, the transform kernel can be evaluated and, for some simple cases, the transform can be inverted. An example is presented with a bilinear profile as the first guess with accompanying inversion in either frequency or depth. The former corresponds to fixed source, fixed receiver broadband experimental situations and the latter to single frequency multireceiver experiments. We also include some remarks on range‐dependent profiles. [Work supported by ONR.]

'Likins, P.W., "Attitude Stability Criteria for Dual-Spin Spacecraft," Journal of Spacecraft and Rockets, Vol. 4, April 1967, pp. 1638-1643. Mingori, D.L., "Effects of Energy Dissipation on the Attitude Stability of Dual-Spin Satellites," AIAA Journal, Vol. 7, Jan. 1969, pp. 20-26. Pringle, R., Jr., "Stability of the Force-Free Motions of a DualSpin Spacecraft," AIAA Journal, Vol. 7, June 1969, pp. 1054-1063. Gale, A.H. and Likins, P.W., "Influence of Flexible Appendages on Dual-Spin Spacecraft Dynamics and Control," Journal of Spacecraft and Rockets, Vol. 7, Sept. 1970, pp. 1049-1056. Meirovitch, L., "A New Method of Solution of the Eigenvalue Problem for Gyroscopic Systems," AIAA Journal, Vol. 12, Oct. 1974, pp. 1337-1342. Meirovitch, L., "A New Modal Method for the Response of Structures Rotating in Space," presented as paper 74-002 at the 25th International Aeronautical Congress of the I.A.F., Amsterdam, The Netherlands, Sept. 30-Oct. 5, 1974, to be published in Acta Astronautica. Meirovitch, L., "On the Reduction of the Eigenvalue Problem for Spinning Axisymmetric Structures," AIAA Paper 75-159, Pasadena, Calif., Jan. 1975, to be published in AIAA Journal.