Journal of Engineering Mathematics最新文献

In this study, the effects of the surge radiation force are investigated by a floating cylinder in two-layer fluid over a bottom-mounted cylinder. The proposed device consists of a floating cylinder in the upper layer and another a coaxial bottom cylinder in the lower layer of a two-layer fluid system of finite depth having the infinite horizontal extent. The radiation problem is taken into consideration under the framework of linear water wave and the entire fluid domain is divided into two regions, say, an exterior and interior regions. The analytical solutions for the surge radiation potential to the boundary-value problems in the respective regions are obtained by utilizing the method of separation of variables. By making use of the matched eigenfunction expansion method, the unknown coefficients that arise in the radiation potentials are evaluated. With the help of the expressions of the surge radiated potential, the corresponding radiation forces are obtained as a linear combination of added mass and damping coefficient. A bunch of numeric outcomes of added mass and damping coefficient are investigated for a distinct set of parameters of the device, i.e., the effect of the variation in frequencies with the radii of the cylinders, drafts of the floating cylinder, and the density ratio between the fluid layers on the surge radiated force are presented and their significant results are discussed. The 3D free surface and interface elevations due to the effect of surge radiated waves are presented in both surface- and internal-wave modes. The oscillations in added mass and damping coefficients are observed with variations of the parameters of the device.

The goal of this paper is to develop a nonstandard finite difference-based numerical technique for solving the one-dimensional linear and non-linear Fokker–Planck equations. Characteristics of the nonstandard finite difference method are presented to understand the development of the proposed method. Conditions for the dynamic consistency of positivity and stability of the schemes are obtained. Numerical experiments have been carried out to demonstrate the competitiveness of the proposed methods in comparison to some existing standard methods. In support of the proposed method and analysis, the (l_2) and (l_infty ) errors are also presented.

This paper deals with the thermoelasticity problem in an orthotropic hollow sphere. A unified governing equation is derived which includes the classical, Lord–Shulman and Green–Lindsay coupled theories of thermoelasticity. Time-dependent thermal and mechanical boundary conditions are applied to the inner and outer surfaces of the hollow sphere and the problem is solved analytically using the finite Hankel transform. The inner surface of the sphere is subjected to a thermal shock in the form of a prescribed heat flux. Subsequently, the thermal response, radial displacement, as well as radial, tangential, and circumferential stresses of the sphere are determined. The influence of different orthotropic material properties and relaxation time values is investigated and presented graphically. The obtained results demonstrate excellent agreement with the existing literature.

The application of Fourier analysis in combination with the Proper Orthogonal Decomposition (POD) is investigated. In this approach to turbulence decomposition, which has recently been termed Spectral POD (SPOD), Fourier modes are considered as solutions to the corresponding Fredholm integral equation of the second kind along homogeneous-periodic or homogeneous coordinates. In the present work, the notion that the POD modes formally converge to Fourier modes for increasing domain length is challenged. A family of analytical correlation functions parametrized by the Taylor macro/micro scale ratio (MMSR) is investigated numerically. The results of the analysis indicate that the discrepancy between POD and Fourier modes along locally translationally invariant coordinates is coupled to the MMSR of the flow. Increasing discrepancies are observed for smaller MMSRs, which are characteristic of low Reynolds number flows. The asymptotic convergence rate of the eigenspectrum matches the corresponding convergence rate of the exact analytical Fourier spectrum of the kernel in question, even for extremely small domains and small MMSRs where the corresponding DFT spectra suffer heavily from windowing effects. The Taylor micro scales are consistently underestimated when reconstructed using Fourier modes—failing to converge to the correct value even if all Fourier modes are used—while these are accurately reconstructed using POD modes.

In this paper, the class of uncertain multi-dimensional fractional control problems with the first-order PDE constraints is investigated. The robust approach and the parametric method are applied for solving such control problems. Then, robust optimality is analyzed for the considered PDE-constrained multi-dimensional fractional control problem with uncertainty. Further, the exact absolute penalty function method is used for solving control problems created in both the aforementioned approaches. Then, under appropriate convexity hypotheses, exactness of the penalization of this exact penalty function method is investigated in the case when it is used for solving the considered control problem with uncertainty. Further, an algorithm based on the used method is presented, the main goal of which is to illustrate the precise steps to solve the unconstrained multi-dimensional non-fractional control problem with uncertainty associated with the constrained fractional control problem.

As a manipulation terminal for a teleoperated system, a joystick requires force sensors to accurately reproduce the haptic information, resulting in large and expensive haptic joysticks. Moreover, the actuator of the haptic joystick usually contains uncertain parameters related to its DC servo motor, making accurate haptic reproduction control a challenge. This study proposes an adaptive haptic control scheme based on the backstepping method for a haptic joystick system with unknown parameters and unmeasurable disturbances without using force sensors. In the scheme, the joystick end force is considered an unknown disturbance of the DC motor. A universal model of the joystick system actuator, i.e., a DC servo motor, and the dynamic model of the joystick are established. The control law is then derived on the basis of the established model. The stability of the closed-loop system is demonstrated analytically on the basis of the Lyapunov function. Furthermore, numerical simulation results verify the effectiveness of the proposed control scheme.

To improve the accuracy of displacement discontinuity method and enhance its adaptivity, a general-purpose 3D displacement discontinuity method with both linear and quadratic isoparametric elements has been developed to model engineering problems where discontinuous surfaces such as cracks are involved. Linear and quadratic isoparametric elements have linear and quadratic distributions of displacement discontinuity values, respectively. Both of them belong to discontinuous elements, in which the geometry shape functions are different from the interpolation shape functions. The new general formulation, based on the boundary integral functions, is given for displacement discontinuity problems with arbitrary boundary shapes. This formulation contains hypersingular integrals which can be evaluated in the sense of Hadamard principal value. The radial integration technique is applied to perform these singular integrals with sufficiently high accuracy. Various numerical examples including stress intensity factor calculation are given to validate the accuracy of the proposed approach. Compared with the constant displacement discontinuity element, the present isoparametric displacement discontinuity elements show better accuracy.

Since a floating solar panel is set above a water surface, the ground effect due to the small gap between the panel and the free surface may be induced by the wind load, in turn causing a high lift force on the panel. In this paper, the wind load on a three-dimensional thin flat plate floating on surface waves is studied analytically under linear assumptions. The clearance between the panel and the free surface is set to be smaller than the panel length and the effects of the base of the floating system are ignored. The pitch motion of the plate due to linear surface waves is considered and the effects of the aspect ratio of the plate, wave number, and wave speed of the free surface are discussed. The analytical solution shows that, if the plate is stationary and the free surface is flat (no waves), then the lift coefficient increases with aspect ratio. For a pitching plate above surface waves, lift coefficient increases with aspect ratio for longer wavelengths, but decreases when the aspect ratio increases for shorter wavelengths. Minimum lift and the associated wave number and aspect ratio for different wave speeds are also discussed. The findings of this study are anticipated to enhance the design of floating solar panels, improving their capacity to withstand substantial wind and waves.

The discontinuity of the medium and the irregularity of the ground significantly affect the propagation of seismic waves. However, the comprehensive effects of these two factors on seismic motion have not yet been fully investigated. To reveal the mechanism of dynamic interaction between the discontinuity and the irregular topography, this study provides a series of solution for the scattering of plane SH waves caused by a concentric semi-cylindrical discontinuity and canyon in an elastic half-space, using the displacement discontinuity model and the wave function expansion method. Based on the proposed series solution, a systematic analysis is conducted to investigate the influences of the stiffness of the discontinuity, the radius ratio between the discontinuity and the canyon, and the properties (e.g., frequency and angle) of the incident wave on the ground motion and underground motion. The results indicate that the stiffness of the discontinuity is a key factor determining the distribution of seismic motion. A high stiffness leads to a distribution similar to that of the canyon alone, while a low stiffness results in a much more complex distribution.

We consider the model of Mindlin–Timoshenko for a multi-structure composed of an elastic plate surrounded by a thin layer of uniform thickness. From the viewpoint of numerical simulation, the treatment of the behavior of this structure is difficult because of the presence of the thin coating. In order to overcome this difficulty, we use the asymptotic expansion method to identify an approximate model that does not involve the thin layer geometrically but which accounts for its effect through new approximate boundary conditions. These conditions are set on the junction interface between the two sub-structures and depend on the thickness and the physical characteristics of the thin layer. Moreover, we give optimal error estimates between the exact and the approximate solutions of the considered transmission problem, which validate this approximation.