Arbitrary External Excitations Research Articles

Plasmon dispersion in a multilayer solid torus in terms of three-term vector recurrence relations and matrix continued fractions

Toroidal confinement, which has played a crucial role in magnetized plasmas and Tokamak physics, is emerging as an effective means to obtain useful electronic and optical response in solids. In particular, excitation of surface plasmons in metal nanorings by photons or electrons finds important applications due to the engendered field distribution and electromagnetic energy confinement. However, in contrast to the case of a plasma, often the solid nanorings are multilayered and/or embedded in a medium. The non-simply connected geometry of the torus results in surface modes that are not linearly independent. A three-term difference equation was recently shown to arise when seeking the nonretarded plasmon dispersion relations for a stratified solid torus (Garapati et al 2017 Phys. Rev. B 95 165422). The reported generalized plasmon dispersion relations are here investigated in terms of the involved matrix continued fractions and their convergence properties including the determinant forms of the dispersion relations obtained for computing the plasmon eigenmodes. We also present the intricacies of the derivation and properties of the Green’s function employed to solve the three term amplitude equation that determines the response of the toroidal structure to arbitrary external excitations.

Influence of model order reduction methods on dynamical–optical simulations

In this work, the influence of model order reduction (MOR) methods on optical aberrations is analyzed within a dynamical–optical simulation of a high precision optomechanical system. Therefore, an integrated modeling process and new methods have to be introduced for the computation and investigation of the overall dynamical–optical behavior. For instance, this optical system can be a telescope optic or a lithographic objective. In order to derive a simplified mechanical model for transient time simulations with low computational cost, the method of elastic multibody systems in combination with MOR methods can be used. For this, software tools and interfaces are defined and created. Furthermore, mechanical and optical simulation models are derived and implemented. With these, on the one hand, the mechanical sensitivity can be investigated for arbitrary external excitations and on the other hand, the related optical behavior can be predicted. In order to clarify these methods, academic examples are chosen and the influences of the MOR methods and simulation strategies are analyzed. Finally, the systems are investigated with respect to the mechanical–optical frequency responses, and in conclusion, some recommendations for the application of reduction methods are given.

Vibration of axially moving beam supported by viscoelastic foundation

In this paper, transverse vibration of an axially moving beam supported by a viscoelastic foundation is analyzed by a complex modal analysis method. The equation of motion is developed based on the generalized Hamilton’s principle. Eigenvalues and eigenfunctions are semi-analytically obtained. The governing equation is represented in a canonical state space form, which is defined by two matrix differential operators. The orthogonality of the eigenfunctions and the adjoint eigenfunctions is used to decouple the system in the state space. The responses of the system to arbitrary external excitation and initial conditions are expressed in the modal expansion. Numerical examples are presented to illustrate the proposed approach. The effects of the foundation parameters on free and forced vibration are examined.

Vibration of an Axially Moving String Supported by a Viscoelastic Foundation

The transverse vibration of an axially moving string supported by a viscoelastic foundation is analysed using the complex modal method. The equation of motion is developed using the generalized Hamilton principle. The exact closed-form solution of eigenvalues and eigenfunctions are obtained. The governing equation is represented in a canonical state space form defined by two matrix differential operators, and the eigenfunctions and adjoint eigenfunctions are proved to be orthogonal with respect to each operator. This orthogonality is applied so that the response to arbitrary external excitations and initial conditions can be expressed in modal expansion. Numerical examples are presented to validate the proposed approach.

Transverse vibration of viscoelastic Timoshenko beam-columns

Transverse vibration of viscoelastic Timoshenko beam-columns is investigated. The normal and the shear stress-strains are constituted by the Kelvin model with different viscosity parameters. The governing equations and the boundary conditions are derived from the generalized Hamilton principle. The exact frequency equations and the modal functions are proposed. The orthogonality conditions are established in the state space. The transverse response to arbitrary external excitation and initial conditions is determined via decoupling the governing equations based on the orthogonality. The natural frequencies and the decrement coefficients of various beam and beam-column models are numerically contrasted. The effects of the length-to-depth ratio, the axial tension, and the viscosity coefficients on the natural frequencies and the decrement coefficients are numerically demonstrated.

Vibration Analysis Based on Time-Frequency Analysis with Digital Filter

The primary aim of this study is to model and identify vibrations in mechanical systems subject to arbitrary external excitations. We propose a method based on infinite impulse response digital filter technology—termed time-frequency analysis—to analyze transient and steady-state vibrations. First, we introduce the time-frequency analysis procedure and the algorithm that implements it. Second, we analyze typical discrete signal inputs, such as impulse, sinusoidal and swept sine signals, and present time-frequency characteristics for transient and steady-state signals. Third, we apply our analysis method to the mechanical vibration behavior of a single-degree-of-freedom system subjected to various types of external excitations. The results of our analysis for steady-state vibration are verified as being equivalent to those from a Fast Fourier Transform (FFT) analysis. Moreover, the proposed analysis has the advantage over FFT analysis that we can also use it to analyze transient vibration phenomena.

210 デジタルフィルタによる時間-周波数分析を用いた振動解析に関する基礎的検討 : 非線形振動への適用

The main purpose of the current study is to model and identify vibrations in mechanical systems subject to arbitrary external excitations. In this paper, we apply our method based on infinite impulse response digital filter technology - termed time-frequency analysis - to analyze nonlinear vibrations. Firstly, we consider transient and nonstationary forced vibrations of weekly nonlinear systems having a single degree of freedom. With the use of time-frequency analysis method, secondly, we analyze transient forced vibrations for primary and secondary resonances, which is unable to be analyzed by a fast Fourier transform (FFT) analysis. Thirdly, we discuss the passage of the system through resonance when the frequency of the excitation is varied. Moreover, the proposed analysis has the advantage over FFT analysis that we can also analyze transient and nonstationary vibration phenomena.

Dynamics of a prestressed Timoshenko beam subject to arbitrary external load

The free vibration and transient wave in a prestressed Rayleigh-Timoshenko beam subject to arbitrary transverse forces are analyzed by the newly developed method of reverberation-ray matrix (MRRM). The effects of shear deformation and rotational inertia are taken into consideration. With a Fourier transform technique, the general wave solutions with two sets of unknown amplitude coefficients are obtained in the transformed domain for an unbonded prestressed beam under the action of arbitrary external excitations. From the coupling at joints and the compatibility of displacements in each member, the free and forced vibration responses of a beam with various boundary conditions are finally evaluated through certain numerical algorithms. Results are presented for a simply-supported beam subject to either a point fixed load or moving load. Good agreement with the finite element method (FEM) is obtained. The present work is instructive for high-speed railway bridge design and structural health monitoring.

Electrical modelling of homogeneous dielectric barrier discharges under an arbitrary excitation voltage

In order to quantitatively describe the electrical working principles of dielectric barrier discharges (DBDs), a dynamic electrical model for homogeneous DBDs has been put forward that is composed of a new equivalent circuit for homogeneous DBDs and the equations derived from it. This model is a global and self-consistent model, valid for an arbitrary external excitation voltage. This model reveals instantaneous relations of internal electrical quantities in the gap (gap voltage, internal discharge current and internal power consumption process) to external electrical quantities (external voltage and external total current) and provides the theoretical fundamentals to calculate the temporal development processes of all internal electrical quantities in the discharge gap from the measured external voltage and external total current. The knowledge obtained of dynamic processes of DBDs in the discharge gap explains quantitatively the mechanisms that result in ignition, development and extinction of DBDs and provide physical interpretation of the measured external total current and other phenomena such as memory effect and multiple current pulses in one half period. In this model, several current terms (external total current, external displacement current, external discharge current, internal discharge current and internal displacement current) are introduced to distinguish the different currents involved in DBDs. Moreover, the equations for charge and energy deposition by one discharge and in one half period are derived. Applications of this model to studying a bipolar sine wave excited DBD and a unipolar pulse excited DBD are also included. This model has been proved to be a useful tool to understand DBDs better.

Refined Solutions of Externally Induced Sloshing in Half-Full Spherical Containers

A mathematical model is developed for calculating liquid sloshing effects such as hydrodynamic pressures and forces in half-full spherical containers under arbitrary external excitation. The velocity potential is expressed in a series form, where each term is the product of a time function and the associated spatial function. Because of the spherical configuration, the problem is not separable and the associated spatial functions are nonorthogonal. Application of the boundary conditions results in a system of coupled nonhomogeneous ordinary linear differential equations. The system is solved numerically, implementing a typical fourth-order Runge-Kutta integration scheme. The proposed simple methodology is capable of predicting sloshing effects in half-full spherical containers under arbitrary external excitation in an accurate manner. Hydrodynamic pressures and horizontal forces on the wall of a spherical container are calculated for real earthquake ground motion data. Dissipation effects are included in ...

Analysis of Ring-Stiffened Cylindrical Shells

A new analytical and numerical method is presented for modeling and analysis of cylindrical shells stiffened by circumferential rings. This method treats the shell and ring stiffeners as individual structural components, and considers the ring eccentricity with respect to the shell middle surface. Through use of the distributed transfer functions of the structural components, various static and dynamic problems of stiffened shells are systematically formulated. With this transfer function formulation, the static and dynamic response, natural frequencies and mode shapes, and buckling loads of general stiffened cylindrical shells under arbitrary external excitations and boundary conditions can be determined in exact and closed form. The proposed method is illustrated on a Donnell-Mushtari shell, and compared with finite element method and two other modeling techniques.

Computer-aided analysis of solid-state analog delay lines using conventional circuit analysis programs

A method is described for analyzing the two-dimensional behavior of minority carriers in a solid-state analog delay line by applying, without modification, existing computer-aided circuit analysis programs to a lumped model. Development of the model in two dimensions is based on an approximate solution of the minority carrier partial differential equation using an analogous electrical network. The model includes injecting and collecting junction nonlinearities and thereby permits the study of responses to arbitrary external excitations. Several examples of the use of the model are given.