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Paper presents an effective technique for developing reduced-order models to predict the dynamic responses of systems using the receptance coupling and frequency-based substructuring (RCFBS) method. The proposed approach is particularly suited for reconfigurable dynamic systems across various applications, like cars, robots, mechanical machineries, and aerospace structures. The methodology focuses on determining the overall system receptance matrix by coupling the receptance matrices (FRFs) of individual subsystems in a disassembled configuration. Two case studies, one with distributed parameters and the other with lumped parameters, are used to illustrate the application of this approach. The first case involves coupling three substructures with flexible components under fixed–fixed boundary conditions, while the second case examines the coupling of subsystems characterized by multiple masses, springs, and dampers, with various internal and connection degrees of freedom. The accuracy of the proposed method is validated against a numerical finite element analysis (FEA), direct methods, and a modal analysis. The results demonstrate the reliability of RCFBS in predicting dynamic responses for reconfigurable systems, offering an efficient framework for reduced-order modeling by focusing on critical points of interest without the need to account for detailed modeling with numerous degrees of freedom. [ABSTRACT FROM AUTHOR]

Elements of powerful steam turbines are subjected to significant unsteady loads, in particular the rotor blades of the last stages. These loads, in some cases, can cause self-excited oscillations, which are extremely dangerous and have a negative impact on the efficiency and service life of the blade cascade. Therefore, when designing new or modernizing existing steam turbine stages, it is recommended to study the aeroelastic characteristics of the blades. The conditions for the occurrence of self-excited oscillations are influenced by both the geometric characteristics and the alloy from which the blade is made. To determine the effect of the blade material on the aeroelastic behaviour, a numerical analysis of the aeroelastic characteristics of the last stage blades made of steel and titanium alloy was performed. For the analysis, the method of simultaneous modeling of unsteady gas flow through the blade cascades and elastic vibrations of the blades (coupled problem) was used, which allows obtaining the amplitude-frequency spectrum of the interaction of unsteady loads and blade vibrations. The paper presents the results of numerical analysis for harmonic oscillations with a given amplitude and a given inter-blade phase angle, as well as for the regime of coupled vibration of blades under the action of unsteady aerodynamic forces. The dependences of the aerodamping coefficient on the inter-blade phase angle and the distribution of the coefficient along the blade are presented. The results of modeling the coupled vibration of the blades for the first six natural forms are presented in the form of a time-evolving displacement of the blade peripheral section, as well as forces and moments acting on the peripheral section. The corresponding amplitude-frequency spectra of displacements and loads in the peripheral section are also presented. The analysis of the results showed an insignificant difference in the characteristics of the proposed blade materials. For the first natural form of blade oscillations, the possibility of self-excited oscillations was found, and for the second form, there are conditions for the appearance of stable self-oscillations.

Paper presents an effective technique for developing reduced-order models to predict the dynamic responses of systems using the receptance coupling and frequency-based substructuring (RCFBS) method. The proposed approach is particularly suited for reconfigurable dynamic systems across various applications, like cars, robots, mechanical machineries, and aerospace structures. The methodology focuses on determining the overall system receptance matrix by coupling the receptance matrices (FRFs) of individual subsystems in a disassembled configuration. Two case studies, one with distributed parameters and the other with lumped parameters, are used to illustrate the application of this approach. The first case involves coupling three substructures with flexible components under fixed–fixed boundary conditions, while the second case examines the coupling of subsystems characterized by multiple masses, springs, and dampers, with various internal and connection degrees of freedom. The accuracy of the proposed method is validated against a numerical finite element analysis (FEA), direct methods, and a modal analysis. The results demonstrate the reliability of RCFBS in predicting dynamic responses for reconfigurable systems, offering an efficient framework for reduced-order modeling by focusing on critical points of interest without the need to account for detailed modeling with numerous degrees of freedom.

Previous works have demonstrated that a parallel plate waveguide, equipped at the end with a tip, can be used to initiate an "electromagnetic jet (Ej)" (this name generalizes the photonic jet (Pj) phenomenon regardless of the wavelength). In addition to being easy to manufacture, a rectangular shape improves energy concentration, however concurrently the full-width at half maximum (FWHM) is slightly degraded. This article aims to introduce tips with multi-rectangular sections reducing the drawbacks previously mentioned. This article proposes the use of Aperiodic Polynomial Modal Method (A-PMM) as an efficient yet robust method to model and optimize an outgoing Ej, equipped with this kind of dielectric tips. Thus, a three rectangular sections tip can improve energy concentration and can reduce the FWHM beyond the diffraction limit compared to a single section tip. [ABSTRACT FROM AUTHOR]

The finite element method is widely used to solve the problem of flexible bodies with contact-impact. To express the high-frequency and high-transient characteristics of the impact process and the high stress distribution of the local contact region, the amount of the node coordinates will be very large, which brings great burden to the dynamic simulation. It is particularly important to reduce the degrees of freedom of the system in the contact-impact problem. However, as the impact itself is a strong nonlinear problem, the linear model reduction techniques cannot be used directly. The partition method is presented to solve this problem, in which the deformation of the contact region is described by finite element node coordinates to preserve the local nonlinear characteristic while the deformation of the non-contact region is described by the reduced elastic coordinates. Different model reduction techniques including modal truncation method and Krylov subspace method are used to reduce the degrees of freedom of the non-contact region of an experimental rod-plate impact case, and the results are compared with that of the finite element method and the experiment. The simulation results show that the partition method can effectively reduce the degrees of freedom of the system and maintain good accuracy. Moreover, the Krylov subspace method has an advantage over the modal method in the model reduction of contact-impact problem. [ABSTRACT FROM AUTHOR]

A method is proposed for solving non-stationary dynamic problems with complex elastic moduli or stiffness matrices, which makes it possible to take into account the local dissipative properties of structural elements. It is shown that in synthesized structures, even with significantly different dissipative properties, the dynamic behavior and loading parameters at resonant frequencies are determined by single integral logarithmic decrements obtained by mass-energy averaging of the dissipative properties of structures. Two concepts for estimating the integral quality factors and logarithmic vibration decrements of structures with different dissipative properties are proposed, one of which is based on the physical features of resonant phenomena in mechanical systems, and the second is based on the analysis of the behavior of damped fundamental solutions of the corresponding homogeneous equations. The coincidence of the integral logarithmic decrements obtained on the basis of different concepts makes it possible to solve non-stationary problems for structures with different dissipative properties by expanding the kinematic parameters in terms of natural vibration modes (modal method). The results of calculations of the dynamic behavior of structures with different dissipative properties are demonstrated on model problems. [ABSTRACT FROM AUTHOR]

Blades of powerful steam turbines are subjected to significant unsteady loads, which, in some cases, can lead to the appearance of self-excited oscillations or auto-oscillations. These fluctuations are extremely dangerous and negatively affect the life time of the blading. When developing new or upgrading existing turbine stages, it is necessary to carry out research on the aeroelastic behavior of the rotor blades. As a result of the modernization of a low-pressure cylinder of a 1000 MW steam turbine, the length of the rotor blades of the last stage increased to 1650 mm. In this regard, a numerical analysis of the aeroelastic characteristics of the last-stage rotor blades in the nominal operation mode was carried out. The analysis used the method of solving the coupled problem of unsteady aerodynamics and elastic blade vibrations, which allows the prediction of the amplitude-frequency spectrum of unsteady loads and blade vibrations in a viscous gas flow. The paper presents the results of numerical analysis of aeroelastic characteristics of the last stage rotor blades both for the mode of controlled harmonic oscillations with a given amplitude and inter-blade phase shift, and for the mode of coupled oscillations of the blades under influence of unsteady aerodynamic forces. The results of the simulation of coupled oscillations of blades for the first five natural forms are presented in the form of the time distribution of displacement of the blade peripheral cross-section, as well as the time distribution of forces and moments acting on the peripheral cross-section. The corresponding amplitude-frequency spectra of displacements and loads in the peripheral section are also given. The results of the calculations showed a positive damping of oscillations, the absence of flutter and auto-oscillations for the first five natural forms of oscillations of the blades in the nominal operation mode of the steam turbine

Shape sensing, i.e. the reconstruction of the displacement field of a structure from discrete strain measurements, is becoming crucial for the development of a modern Structural Health Monitoring framework. Nevertheless, an obstacle to the affirmation of shape sensing as an efficient monitoring system for existing structures is represented by its requirement for a significant amount of sensors. Two shape sensing methods have proven to exhibit complementary characteristics in terms of accuracy and required sensors that make them suitable for different applications, the inverse Finite Element Method (iFEM) and the Modal Method (MM). In this work, the formulations of these two methods are coupled to obtain an accurate shape sensing approach that only requires a few strain sensors. In the proposed procedure, the MM is used to virtually expand the strains coming from a reduced number of strain measurement locations. The expanded set of strains is then used to perform the shape sensing with the iFEM. The proposed approach is numerically and experimentally tested on the displacement reconstruction of composite stiffened structures. The results of these analyses show that the formulation is able to strongly reduce the number of required sensors for the iFEM and achieve an extremely accurate displacement reconstruction. • The method reduces the number of sensors required for an accurate shape sensing. • The novel method couples two shape sensing methods, the iFEM and the Modal Method. • The method overcomes the limitations of two methods when applied separately. • The method is based on the strain pre-extrapolation using the modal strain shapes. • The method allows the monitoring of a stiffened panel with sparse arrays of sensors. [ABSTRACT FROM AUTHOR]

Large-scale floating rafts have been widely applied to marine propulsion. Due to the presence of elastic supports, it belongs to the elastic constraints rather than the fixed constraints found in aerospace and bridge structures. This leads to displacement is no longer just elastic deformation, but also includes some rigid-body displacement. However, the existing displacement reconstruction methods are all based on fixed constraints. To address this issue, an improved modal method (IMM) is proposed. The boundary conditions are extended from fixed constraints to elastic constraints and the displacement field is uniformly described. Firstly, by analyzing the modal characteristics of three types of constraints, the reasons for the failure of the current modal method under elastic constraints are presented. Secondly, the IMM is established based on a dimensionless error function between the discrete strain, finite displacement measurements, and their theoretical values. Finally, the feasibility of the IMM is verified by numerical analysis and experiment tests on an elastic support plate structure with high precision and excellent suitability. This method can be applied to the full-filled displacement reconstruction in large-scale floating rafts of marine propulsion systems, which provides significant engineering value for improving the shafting alignment and the raft attitude balance. • It realizes the unity of constraint types and can be used for elastic constraints, such as large-scale floating rafts. • This method eliminates the singularity problem of the current modal method under elastic constraints. [ABSTRACT FROM AUTHOR]

With recent developments in nanotechnologies, metal nanoparticles permeate a wide range of dimension scales, from light wavelength-scale domains down to a few nanometers approaching electronic scales. The electrodynamics at metal surfaces hosts a rich interplay between plasmon oscillations, retardation effects of light, and nonclassical (quantum) effects of electrons. Incorporating all these effects and modeling optical responses of nanoparticles generally rely on pure numerical methods, which are, however, disadvantageous in physical interpretations and computational speed. Herein, we establish a modal method that accurately predicts plasmon responses of metal nanoparticles, including both retardation and nonclassical corrections on an equal footing. The proposed method, based on electrostatic plasmon modes, is parameterized by a set of geometrically dependent factors, which, once computed, can be repeatedly used for same-shaped nanoparticles independent of size and material composition. The predictive accuracy of the method is examined for single nanoparticles, multi-scale plasmonic architectures—such as dimer structures with deep-nanometer gap—and geometrically deformed structures, with feature dimensions ranging from a few nanometers to hundreds of nanometers.

This work aims to achieve real-time monitoring of strains and structural displacements for the target Joined-Wing aircraft. To this end, a Fiber Optic Sensing System (FOSS) is designed and deployed in the aircraft. The classical modal method, which is used for Strain-to-Displacement Transformation (SDT), is improved to adapt to different boundary conditions by introducing extra constraint equations. The method is first verified by numerical studies on a cantilever beam model and the high-fidelity finite element model of the Joined-Wing aircraft. Ground static tests are then carried out to further demonstrate the capability of the developed FOSS and SDT algorithm in practical application. The results have shown that the improved modal method is able to predict structural deformation under different boundary conditions by using only free–free modes. In addition, the errors between the predicted displacement and the reference in the ground test are within 10%, which proves the FOSS has reasonable accuracy and the potential for future flight tests. [ABSTRACT FROM AUTHOR]

Shape sensing is the reconstruction of the displacement field of a structure from some discrete surface strain measurements and is a key technology for structural health monitoring. The aim of this paper is to compare two approaches to shape sensing that have been shown to be more efficient, especially for aircraft structures applications, in terms of required input strain measurements: the Ko's Displacement Theory and the Modal Method. An object of the shape-sensing analysis is the half-wing of a multirotor UAV. The approaches are summarized in order to set the framework for the numerical comparative investigation. Then, the multirotor UAV is presented and a finite element model of its half-wing is used to simulate the static response to straight-and-level flight conditions. For a given common set of surface strain measurement points, Ko's Displacement Theory and the Modal Method are compared in terms of accuracy of the reconstructed half-wing deflection and twist angle. The Modal Method is shown to be more accurate than Ko's Displacement Theory, especially for the evaluation of the deflection field. Further numerical analyses show that the Modal Method is influenced by the set of mode shapes included in the analysis and that excellent reconstructed deflections can be obtained with a reduced number of sensors, thus assessing the approach as an efficient shape-sensing tool for aircraft structures real applications. [ABSTRACT FROM AUTHOR]

The solution of the time-dependent neutron diffusion equation can be approximated using quasi-static methods that factorise the neutronic flux as the product of a time dependent function times a shape function that depends both on space and time. A generalization of this technique is the updated modal method. This strategy assumes that the neutron flux can be decomposed into a sum of amplitudes multiplied by some shape functions. These functions, known as modes, come from the solution of the eigenvalue problems associated with the static neutron diffusion equation that are being updated along the transient. In previous works, the time step used to update the modes is set to a fixed value and this implies the need of using small time-steps to obtain accurate results and, consequently, a high computational cost. In this work, we propose the use of an adaptive control time-step that reduces automatically the time-step when the algorithm detects large errors and increases this value when it is not necessary to use small steps. Several strategies to compute the modes updating time step are proposed and their performance is tested for different transients in benchmark reactors with rectangular and hexagonal geometry.

Due to the limitation of working environment and structure conditions, it is difficult to directly measure the propeller excitation of ship propulsion shafting system. A method based on waveguide function and modal method combining with shafting vibration response measurement was proposed to estimate the propeller longitudinal excitation indirectly. Firstly, a waveguide transfer model for the general structure of the propulsion shafting is proposed that is suitable for estimating propeller excitation from shafting vibration response. Secondly, the longitudinal excitation of the propeller is calculated by measuring the waveguide coefficients of any shaft sections via the proposed hybrid method. Finally, the scheme is verified by a concrete example. The simulation results prove its feasibility and effectiveness for estimating propeller excitation by measuring the shafting vibration response, which provides a novel scheme for accurately grasping the propeller excitation and effectively controlling the vibration and noise of hull structure. [ABSTRACT FROM AUTHOR]

This work aims to achieve real-time monitoring of strains and structural displacements for the target Joined-Wing aircraft. To this end, a Fiber Optic Sensing System (FOSS) is designed and deployed in the aircraft. The classical modal method, which is used for Strain-to-Displacement Transformation (SDT), is improved to adapt to different boundary conditions by introducing extra constraint equations. The method is first verified by numerical studies on a cantilever beam model and the high-fidelity finite element model of the Joined-Wing aircraft. Ground static tests are then carried out to further demonstrate the capability of the developed FOSS and SDT algorithm in practical application. The results have shown that the improved modal method is able to predict structural deformation under different boundary conditions by using only free–free modes. In addition, the errors between the predicted displacement and the reference in the ground test are within 10%, which proves the FOSS has reasonable accuracy and the potential for future flight tests.

This paper presents an improved substrate integrated non‐radiative dielectric (SINRD) bandpass filter design. The LSE01 (Longitudinal Section Electric) mode is used as fundamental mode, which allows substrate height reduction compared to classical lowest LSM (Longitudinal Section Magnetic mode). A new modelization is proposed to characterize such a bandpass filter using the circuits equivalent method. Simulation results are successfully compared to finite element software results. In the design, permittivity choices are justified through a sensitivity analysis to meet the bandpass filter requirements. Finally, the SINRD bandpass filter is synthesized by drilling an air hole pattern in the dielectric substrate. This new filter is characterized by simulations and measurements. [ABSTRACT FROM AUTHOR]

Shape sensing is the reconstruction of the displacement field of a structure from some discrete surface strain measurements and is a key technology for structural health monitoring. The aim of this paper is to compare two approaches to shape sensing that have been shown to be more efficient, especially for aircraft structures applications, in terms of required input strain measurements: the Ko’s Displacement Theory and the Modal Method. An object of the shape-sensing analysis is the half-wing of a multirotor UAV. The approaches are summarized in order to set the framework for the numerical comparative investigation. Then, the multirotor UAV is presented and a finite element model of its half-wing is used to simulate the static response to straight-and-level flight conditions. For a given common set of surface strain measurement points, Ko’s Displacement Theory and the Modal Method are compared in terms of accuracy of the reconstructed half-wing deflection and twist angle. The Modal Method is shown to be more accurate than Ko’s Displacement Theory, especially for the evaluation of the deflection field. Further numerical analyses show that the Modal Method is influenced by the set of mode shapes included in the analysis and that excellent reconstructed deflections can be obtained with a reduced number of sensors, thus assessing the approach as an efficient shape-sensing tool for aircraft structures real applications.

A new modal method for controlling the deformation of a linear elastic structure under conditions of quasi-static loading is proposed. The advantage of the new method is independent control of orthogonal modes, which increases the accuracy and speed of control. To illustrate the proposed method, compensation of the deformation error in a rotary table with a high tilt accuracy is considered. [ABSTRACT FROM AUTHOR]

Multi-parameter sensitivity algorithms can be used to construct a Hessian matrix and second-degree Taylor expansion. In terms of an asymmetric dynamic system, two multi-parameter sensitivity algorithms are proposed in this paper. The modal method with its consistence proof is firstly derived to compute the first- and second-order sensitivities of the eigenpair, and the algebraic method with its stability proof is also proposed. One significant difference between the algebraic method and the modal method is that the algebraic method uses the derivative of the normalization condition as the bordered equation to remove the singularity of the coefficient matrix in the sensitivity dominant equation, whereas the modal method uses the derivative of the normalization condition as the supplementary equation to determine the special coefficient in the modal superposition for a normalized undamped mode shape. As both the proposed methods adopt the same normalization condition, the resulting sensitivities are consistent with each other. Three numerical example are used to determine the correctness, accuracy and validity of the proposed methods in three cases: a single-parameter system, a two-parameter system, and a special system which has complex eigenpairs caused by the asymmetric property of the dynamic system. [ABSTRACT FROM AUTHOR]

The behaviour of the neutrons inside a nuclear reactor core can be modelled by using the time dependent neutron diffusion equation. Different time schemes have been used to integrate this equation. One possibility is to use a modal method, which is based on the expansion of the neutron flux in terms of spatial modes that are the eigenfunctions associated with a given configuration of the reactor core. Several spatial modes can be defined for the neutron diffusion equation such as the λ , α and γ -modes. In this work, the λ , the α and the γ -modes have been used to develop different modal kinetics equations, using a high order finite element method for the spatial discretization of the neutron diffusion equation. The performance of the different modal kinetic equations has been tested and compared using two 3D transient benchmark problems. [ABSTRACT FROM AUTHOR]

The main purpose of a fast internal circulating fluidized bed gasifier is the steam reforming of solid organic matter, like biomass, to a nearly nitrogen-free syngas. The calorific value of this syngas is approximately three times higher than the gas from common air-driven gasifiers. This article deals with a study of the particle dynamics in a 1 MWt fast internal circulating fluidized bed plant and focuses on the design of the gasification reactor's geometry. Superheated steam is used for the fluidization and gasification in the reactor. The gasification of solid fuels causes an increase in the volume flow of the fluidizing gas and at the same time also a change in the fluidization regime. Approaching a turbulent fluidization regime or even fast fluidization is not desirable. However, with the proper design of reactor, i. e., an appropriately conical bed angle, suitable gasification conditions in the form of a fluidizing regime can be achieved across the entire height of the bed. For the purposes of the experimental research, a semi-industrial unit was set-up. The process was designed and experimentally tested on a lab-scale, cold-flow model and scaled-up to a semi-industrial process. The guidelines for designing the geometry of the gasification reactor were set. [ABSTRACT FROM AUTHOR]

In the work, we describe a simplified method for numerical analysis of a FRP composite footbridge in the field of wind induced vibrations. We consider a simply supported structure with a span length of 16 m and U-shape cross-section. Firstly, a two dimensional flow analysis is performed of the fixed bridge cross-section which is subjected to a lateral wind action with 10 m/s velocity. Calculations are performed using ANSYSSYSSYS FLUENT 14 software. Results of the flow analysis (Strouhal’s number) are compared with the results presented in a monograph by A. Flaga, entitled Inżynieria Wiatrowa. Podstawy i zastosowania (Wind Engineering. The bases and applications) (in Polish), Arkady, Warszawa, 2008, in order to validate calculations. After that, a three dimensional spatial model of the footbridge is built in ABAQUS 6.12-3 finite element method software. A modal dynamics problem is solved, where the loading conditions are adopted on the basis of the flow analysis and applied as an evenly distributed pressure on the bridge deck surface. Finally, the users’ vibration comfort criterion is checked for the considered structure.[b]Keywords[/b]: composite shell footbridge, wind flow, modal method, footbridges vibrations

To deal with the difficulty of directly measure the distributed wind load on structures, an indirect distributed wind load identification method based on modal space conversion and Karhunen-Loeve (K-L) expansion using displacement response was proposed. The Davenport spectrum was adopted to simulate the stochastic characteristics of the wind load and the displacement responses at limited locations were calculated as the "measured" input for wind load identification. The distribution function of the wind load was expanded by the structural mode shape functions, which transforms a distributed dynamic force identification problem with infinite time histories to a dynamic load identification problem with multiple parameters. Via the K-L expansion of the "measured" response sample sets, the distribution and statistics can be identified. Numerical simulations were conducted on a guyed mast structure which proofs the effectiveness of the proposed identification method. [ABSTRACT FROM AUTHOR]

Modeling of dynamic processes in nuclear reactors is carried out, mainly, on the basis of the multigroup diffusion approximation for the neutron flux. The basic model includes a multidimensional set of coupled parabolic equations and ordinary differential equations. Dynamic processes are modelled by a successive change of the reactor states, which are characterized by given coefficients of the equations. In the modal method, the approximate solution is represented as an expansion on the first eigenfunctions of some spectral problem. The numerical-analytical method is based on the use of the dominant time-eigenvalues of a multigroup diffusion model taking into account delayed neutrons. In this work, the application of the modal methodology based on calculation of the dominant eigenvalues and eigenfunctions of α -eigenvalue problem has been tested for the VVER-1000 reactor test model. The last is characterized by the fact that some eigenvalues are complex. Reactor dynamics behavior is simulated for symmetrical and non-symmetrical control rods insertion/withdrawal. The power calculation results obtained with the modal method were compared with the numerical solution of the dynamics problem. A rather good agreement was shown for the problem with single delayed neutron precursor group. [ABSTRACT FROM AUTHOR]

This paper deals with the use of Reduced Order Methods for neutronics modelling. This approach is used whether both accuracy and computational efficiency are required. A very popular category of these methods is based on projection approaches which use spatial basis and test functions for the development of the reduced order model. The selection of the spatial basis and test functions used in the projection phase is a crucial issue since it has an impact on the accuracy and the computational cost. In this work, different methods for the creation of the spatial basis and the test functions are analysed. In particular, an Adjoint Proper Orthogonal Decomposition (APOD) method is proposed combining the properties of the Proper Orthogonal Decomposition and the use of the adjoint flux as test function in the neutronics framework. The different methods are applied to create a spatial neutronics model for the ALFRED reactor. The simulation results show that the APOD method gives better results compared to the other methods (Modal Method and standard Proper Orthogonal Decomposition) increasing the accuracy of the reduced order model or minimizing the computational cost. [ABSTRACT FROM AUTHOR]

A novel method for reverse design of the rectangular-groove dielectric surface-relief grating by modal method is presented. The principle of the reverse design method is the excitation and coupling between the propagating modes in grating. When the modes 0 and 1 are transmission through the grating, the phase difference is accumulated. By adjusting the cumulative phase difference between the modes 0 and 1, the energy can be reallocated between the − 1st and 0th order diffraction light. Thereby the diffraction efficiency of the grating − 1st and 0th order are adjusted. By using these reverse design method, we analyze the design of the beam splitter and blazed grating. As an example, a − 1st transmitted order blazed grating has been designed by reverse design method. The comparative results have shown that the geometrical parameters of the grating calculated by modal method agree well with the results simulated by the rigorous couple-wave analysis (RCWA). [ABSTRACT FROM AUTHOR]

The novel reflective grating was studied under Littrow incidence as one sort of high-efficiency optical element. A covering layer and a dielectric layer are employed in this structure to achieve higher efficiency and wider bandwidth. For the given wavelength of 1550 nm, by using two-beam-interference theory of modal method, duty cycle and period of grating can be calculated, where the physical essence of high efficiency in the first-order is well explained by the modal method. The other grating parameters are optimized by using rigorous coupled-wave analysis. The optimized grating has an appropriate aspect ratio and shows that diffraction efficiencies of TE and TM polarizations in the first-order are greater than 97%. Compared with the reported surface-relief high-efficiency grating, the diffraction efficiencies of the proposed grating for TE and TM polarizations can be greatly improved. [ABSTRACT FROM AUTHOR]

A fully framed system consisting of four beams and a rectangular plate has been investigated in terms of the energy transfer between the beams and the plate when a force is applied to one of the beams. This configuration, which is a mixture of stiff and flexible elements, is a particularly important example in the industrial area, as it is widely used. A modal model based on interface basis functions is used. A wave model, which is an approximate method, has also been developed in which the plate, acting as a wave impedance, is separately attached to each beam. Experimental studies have been carried out for validation. The investigation with respect to power flow and energy shows the validity of both models in the mid-frequency region. The results show that most energy is dissipated by the flexible plate. The physical phenomena and limitations of the wave method for this particular structural configuration are discussed. Even though it is an approximate method, the wave approach can describe the dynamic characteristics of the excited beam and the plate in terms of the ratios of power and energy of each component. The comparison of the two methods shows that the plate rather than the beams plays a crucial role in transferring the energy from the excited beam to the parallel opposite beam in the beam-framed structure when these two beams have identical properties, whereas the energy transfer is reduced when the beams have dissimilar properties. [ABSTRACT FROM AUTHOR]

It is not possible to measure cross sectional load effects (i.e. bending moments and shear forces) of ships directly. In complex structures, the sectional load effects must be derived from strain measurements. Knowing these load effects is important because they do determine the necessary overall structural strength of the ship, both in ultimate load but also in fatigue loads. Traditionally, load effects in specific prismatic shaped sections are derived using strain gauges placed in the section itself. An alternative approach is to derive the load effects in a cross section using measurements of the global strains across the length of the vessel. When this derivation of load effects is based on the first few global flexural vibration modes of the ship, this method is referred to as the modal method. This paper explains both traditional and modal methods and applies them to a simple barge and a more complex ship structure. Experimental data from full scale trials and model tests are used along with numerical simulations to compare the methods. Although the paper focuses on the sectional load effects, it also shows that the local strains can be calculated through the modal approach. The modal method gives better results and has more advantages compared to the more traditional sectional method in ships with complex configurations and effective house structures. [ABSTRACT FROM AUTHOR]

Deep-etched rectangular fused-silica transmission gratings used as orthogonal polarizing beam combiners at the wavelength of 532 nm are designed based on the modal method. The fabrication tolerances and the properties of the orthogonal polarizing beam combiners are analyzed by rigorous coupled-wave analysis. It is shown that these gratings have large fabrication tolerances and good properties when the diffraction efficiencies are greater than 90%. The optimal grating is highly efficient (>95%) over broad incidence condition and also has large fabrication tolerances. [ABSTRACT FROM AUTHOR]

A modal method for designing the one-dimensional (1-D) dielectric multilevel antireflection gratings (ARGs) used for TE polarized waves is proposed based on the effective refractive indices concept of the modal method (MM). In this method, the effective refractive index (ERI) for each level is determined by the effective mode index of the modal method. The refractive indices under and above the grating region are equivalent to their effective refractive indices that is determined by the 0th order propagating wave vector of the Fourier expansion of the electric fields under and above the grating region, which are different from the conventional effective medium theory (EMT), and the relationship between the ERI in MM and that in EMT are also revealed. As an example, we designed and analyzed the fused-silica multilevel ARGs by using the MM and the commonly used second-order effective medium theory (SEMT). The designed results are numerically verified by using the rigorous coupled-wave analysis method (RCWA) and the thin-film theory. [ABSTRACT FROM AUTHOR]