Approximate determination of the plasma potential spatial distribution in the isolated dust particle vicinity

In this paper, results of two numerical models are compared. The main purpose of these models is to determine the self-consistent spatial distributions of plasma (electric potential and space charge) near isolated spherical dust particles. In the first model, the spatial distribution of the self-consistent plasma potential is determined by expanding the plasma space charge spatial distribution in Legendre polynomials; in the second model, it is determined by direct numerical integration of the Poisson equation solution. The results show that the dependences of the system main parameters (wake magnitude and position, dipole moment of the ion cloud) coincide for small values of the external electrostatic field. With an increase in the external field strength, the dependences for two models cease to coincide, which is due to the inapplicability of Legendre polynomial decomposition in the case of strong anisotropy.

Two tractable models of dynamic light scattering and their application to Fano resonances

We introduce two tractable analytical models to describe dynamic effects at resonant light scattering by subwavelength particles. One of them is based on a generalization of the temporal coupled-mode theory, and the other employs the normal mode approach. We show that sharp variations in the envelope of the incident pulse may initiate unusual, counterintuitive dynamics of the scattering associated with interference of modes with fast and slow relaxation. To exhibit the power of the models, we apply them to explain the dynamic light scattering of a square-envelope pulse by an infinite circular cylinder made of GaP, when the pulse carrier frequency lies in the vicinity of the destructive interference at the Fano resonances. We observe and explain intensive sharp spikes in scattering cross-sections just behind the leading and trailing edges of the incident pulse. The latter occurs when the incident pulse is over and is explained by the electromagnetic energy released in the particle at the previous scattering stages. The accuracy of the models is checked against their comparison with results of the direct numerical integration of the complete set of Maxwell’s equations and occurs very high. The models’ advantages and disadvantages are revealed, and the ways to apply them to other types of dynamic resonant scattering are discussed.

A Novel Hybrid Algorithm for Transient Near-Field Scattering from Rough Surface in 2-D Case

A novel hybrid algorithm is proposed to reduce the computation cost of the finite-difference time-domain (FDTD) method in calculating the transient near-field scattering from rough surface. The scattering problem is split into the FDTD calculation of equivalent sources on the contour enclosing rough surface and the calculation of the near-field radiation with the two-dimensional (2-D) time-domain Huygens’ principle. The radiation fields are found from a surface integral of the temporal convolution for which the direct numerical integration of the convolution is computationally expensive. In this paper, the 2-D time-domain Green’s function as the convolution kernel is approximated with a sum of exponential terms by using the Prony’s method. Then, the semianalytical recursive convolution (SARC) approach is applied to complete the update of the near-field radiation. Compared with the traditional FDTD, this hybrid algorithm can significantly reduce the memory usage and run time, especially for the large distance between the rough surface and observation point.

A Family of Functionally-Fitted Third Derivative Block Falkner Methods for Solving Second-Order Initial-Value Problems with Oscillating Solutions

One of the well-known schemes for the direct numerical integration of second-order initial-value problems is due to Falkner (Falkner, 1936. Phil. Mag. S. 7, 621). This paper focuses on the construction of a family of adapted block Falkner methods which are frequency dependent for the direct numerical solution of second-order initial value problems with oscillatory solutions. The techniques of collocation and interpolation are adopted here to derive the new methods. The study of the properties of the proposed adapted block Falkner methods reveals that they are consistent and zero-stable, and thus, convergent. Furthermore, the stability analysis and the algebraic order conditions of the proposed methods are established. As may be seen from the numerical results, the resulting family is efficient and competitive compared to some recent methods in the literature.

Multibody Dynamic Analysis of a Wind Turbine Drivetrain in Consideration of the Shaft Bending Effect and a Variable Gear Mesh Including Eccentricity and Nacelle Movement

Due to the energy crisis and global warming issues, the wind energy is becoming one of the most attractive renewable energy resources in the world. The drivetrains in the wind turbine tend to fail more prematurely than those in any other applications. Gearbox is the subsystem that causes the most downtime for the wind turbines. In the previous research, only the torsional flexibility of the shaft was considered in the drivetrain model. However, because the shaft is longer than other parts, and components connected by the shaft affect each other via shaft bending, the flexibility of the shaft cannot be ignored. In this study, a spherical joint that consists of three rotational springs was used to define the shaft bending. This shaft bending will affect the drivetrain rotation, the translational motion and the gear mesh contact force. Additionally, the eccentricity and the nacelle movement are analyzed due to the coupled motion. In this paper, a mathematical model of the drivetrain is proposed, which is a three-dimensional dynamic model that includes flexible bearings, a gear mesh model, shaft flexibility, eccentricity, and nacelle movement. The equation of motion of the drivetrain is derived using Lagrange's equation. The governing equation is solved numerically via direct numerical integration. The dynamic responses of the system and contact forces between the gear tooth in the time and frequency domains are calculated numerically. The study shows that this dynamic model of the drivetrain will be highly useful for subsequent studies on the wind turbine condition monitoring.

On the Nonlinear Vibration Analysis of a Hand-Held Impact Machine

Prolonged exposure of the human arm to vibrations from hand-held impact (HIM) tools can be hazardous as such, it is important that the level of vibration suppression in HIMs is improved. This paper sought to address this issue by studying a model of the hand-arm system (HAS) coupled to a HIM which is also coupled to a nonlinear tuned vibration absorber inerter (NVAI). The HAS is modelled as a 2-DOF system coupled to the HIM at a single point. The HIM is modelled as an oscillator with linear damping, and both linear and nonlinear stiffnesses. The nonlinear stiffness of the HIM is introduced to represent the nonlinearities introduced by the vibro-impact dynamics of the HIM. After obtaining the equations of motion for the system, an analytical solution is obtained using the harmonic balance method. The analytical solution is validated using direct numerical integration and the results show very good agreement. The performance of the NVAI is compared to those of the classical nonlinear and linear vibration absorbers. Parametric study is carried out to examine the role of key design parameters, such as the damping of the absorber, nonlinear stiffness of the HIM and inertance of the NVAI, on the performance of the NVAI.

Study of an electromechanical nonlinear vibration absorber: Design via analytical approach

This article deals with the behavior and design of a homogeneous beam linked to an electrical absorber, via a piezoelectric material patched on the beam. The beam presents a cubic nonlinearity, which is consistent with geometrical nonlinearities for clamped-free beams. A cubic nonlinearity is added to the electrical circuit for similarity purposes. The coupled electromechanical equations are reduced to a two degrees of freedom system. The equation representing the mechanical response of the system is seen as the main system, whereas the equation coming from the electrical circuit would represent a nonlinear absorber. An analytical treatment at different time scales is endowed to identify electrical coefficients allowing the design of the electromechanical vibration absorber behavior. The equilibrium and singular points are identified, allowing the definition of ranges of forcing amplitudes leading to periodic and modulated regimes. The analytical results are compared with those obtained from direct numerical integration of the two degree of freedom system.

Optimum inelastic tuned mass dampers without using viscous elements for minimizing steady-state vibration of base-excited systems

A special type of a tuned mass damper, which consists of a mass and an elasto-plastic spring without using any viscous damper, is used to reduce the steady-state response of structures to base excitation. Previous work of the authors showed that the elasto-plastic tuned mass damper (P-TMD) could help reduce the seismic responses, and a method based on energy equalization was proposed to design it. In this study, the effectiveness of the P-TMD is investigated under harmonic support motion, and a direct approach is developed to find its optimum parameters. To estimate the nonlinear steady-state response of P-TMD-controlled systems, an analytical framework is established using the Fourier series approximation, which is validated by direct numerical integration of the equations of motion. The obtained results for the optimum P-TMD are discussed and compared with those of the optimum elastic tuned mass damper.

Efficient Nonlinear Response Determination of an Array of OWC Energy Harvesters

Oscillating Water Columns (OWC) are utilized for producing electrical energy from sea waves by exploiting the oscillation of a water column located under an air chamber for producing an air flow driving an air turbine connected to an electrical generator. The array configuration is considered in several engineering applications, where the OWCs are embedded in coastal infrastructures, such as vertical breakwaters. In this context, the water columns are likely to be placed nearby. Thus, interactions among chambers occur because of wave radiation phenomena. This article describes a nonlinear model governing the dynamics of an OWC array embedded in a vertical breakwater. The differential equations include effects associated with hydrodynamic memory and isentropic thermodynamics, which prohibit the derivation of an exact solution giving the OWC array response. Thus, the article develops approximate solutions determined by relying on the concept of equivalent linearization, which is applied under the assumption of both deterministic, and stochastic excitations. Juxtaposition of the approximate approach results with relevant direct numerical integration data confirm its reliability and efficiency.