International Journal of Modeling, Simulation, and Scientific Computing

The numerical solutions of two-dimensional (2D) and three-dimensional (3D) nonlinear viscous and nonviscous wave equations via the unified alternating direction implicit (ADI) finite difference methods (FDMs) are obtained in this paper. By making use of the discrete energy method, it is proven that their numerical solutions converge to exact solutions with an order of two in both time and space with respect to $H^1$-norm. Numerical results confirm that they are relatively accurate and high-resolution, and more successfully simulate the conservation of the energy for nonviscous equations, and the dissipation of the energy for viscous equation.

Piezoelectric energy harvesting refers to conversion of mechanical energy into usable electrical energy. In the modern connected world, wireless sensor nodes are scattered around the environment. These nodes are powered by batteries. Batteries require regular replacement, hence energy harvesters providing continuous autonomous power are used to power these sensor nodes. This work provides two different fixation modes for the resonant frequency for the two modes. Variation in geometric parameter and their effect on resonant frequency and output power have been analyzed. These harvesters capture a wide-band of ambient vibrations and convert them into usable electrical energy. To capture random ambient vibrations, the harvester used is a wide-band energy harvester based on conventional seesaw mechanism. The proposed structure operates on first two resonant frequencies in comparison to the conventional cantilever system working on first resonant frequency. Resonance frequency, as well as response to a varying input vibration frequency, is carried out, showing better performance of seesaw cantilever design. In this work, modeling of wide-band energy harvester with proof mass is being performed. Position of proof mass plays a key role in determining the resonant frequency of the harvester. Placing the proof mass near or away from fixed end results in increase and decrease in stress on the piezoelectric layer. Hence, to avoid the breaking of cantilever, the position of proof mass has been analyzed.

This paper presents a modeling and simulation of micro-milling process with finite element modeling (FEM) analysis to predict cutting forces. The micro-milling of Inconel 718 is conducted using high-speed steel (HSS) micro-end mill cutter of 1mm diameter. The machining parameters considered for simulation are feed rate, cutting speed and depth of cut which are varied at three levels. The FEM analysis of machining process is divided into three parts, i.e., pre-processer, simulation and post-processor. In pre-processor, the input data are provided for simulation. The machining process is further simulated with the pre-processor data. For data extraction and viewing the simulated results, post-processor is used. A set of experiments are conducted for validation of simulated process. The simulated and experimental results are compared and the results are found to be having a good agreement.

In order to find out the sensitivity of the thermophysical and structural parameters to the thermodynamic characteristics of twin-tube hydraulic shock absorbers, based on the bench test, a method for calculating the time-varying rate of the external work on the shock absorber oil is proposed. And then, a thermodynamic model of the twin-tube hydraulic shock absorber is established by using the basic thermodynamic principles. By analyzing the influence of each parameter on the thermodynamic characteristics of the shock absorber, it can be seen that, the radius of the working cylinder outer wall has the greatest influence on the temperature rise of the shock absorber, followed by the thermal conductivity of the oil, the height of the oil, the heat transfer length of the cylinder barrel, the radius of the oil storage cylinder outer wall, the emissivity of the oil storage cylinder outer wall, the height of the nitrogen, the thermal conductivity of the nitrogen, the specific heat capacity of the oil, the density of the oil, the thermal conductivity of the cylinder, and the mass of the working oil. The kinematic viscosity of the oil has the least influence on the temperature rise of the shock absorber. The research can provide an effective theoretical guidance and reference for the design of the twin-tube hydraulic shock absorber.

In this paper, the assumptions implicited in Leveque’s approximation are re-examined, and the variation of the temperature and the thickness of the boundary layer were illustrated using the developed solution. By defining a similarity variable, the governing equations are reduced to a dimensionless equation with an analytic solution in the entrance region. This report gives justification for the similarity variable via scaling analysis, details the process of converting to a similarity form, and presents a similarity solution. The analytical solutions are then checked against numerical solution programming by FORTRAN code obtained via using Runge–Kutta fourth order (RK4) method. Finally, other important thermal results obtained from this analysis, such as; approximate Nusselt number in the thermal entrance region was discussed in detail. A comparison with the previous study available in literature has been done and found an excellent agreement with the published data.

This study aims to investigate the scope of methods for the reconstruction of time-delay systems. We consider an approach to the reconstruction of time-delay systems based on the synchronous response of the driven system with the structure similar to the structure of the studied object. This approach is used for the recovery of the parameters of time-delay systems from short and noisy time series. To show the operational performance and capabilities of this approach, the parameters were reconstructed for a radiophysical chaotic generator with quadratic nonlinearity and for the model of a system for the baroreflectory regulation of the mean arterial pressure.

In this paper, we present a superlinear numerical method for multi-term fractional nonlinear ordinary differential equations (MTFNODEs). First, the presented problem is equivalently transformed into its integral form with multi-term Riemann–Liouville integrals. Second, the compound product trapezoidal rule is used to approximate the fractional integrals. Then, the unconditional stability and convergence with the order $1+{\alpha }_{N-1}-{\alpha }_{N-2}$ of the proposed scheme are strictly established, where ${\alpha }_{N-1}$ and ${\alpha }_{N-2}$ are the maximum and the second maximum fractional indexes in the considered MTFNODEs, respectively. Finally, two numerical examples are provided to support the theoretical results.

In this work, we develop a finite difference/finite element method for the two-dimensional distributed-order time-space fractional reaction–diffusion equation (2D-DOTSFRDE) with low regularity solution at the initial time. A fast evaluation of the distributed-order time fractional derivative based on graded time mesh is obtained by substituting the weak singular kernel for the sum-of-exponentials. The stability and convergence of the developed semi-discrete scheme to 2D-DOTSFRDE are discussed. For the spatial approximation, the finite element method is employed. The convergence of the corresponding fully discrete scheme is investigated. Finally, some numerical tests are given to verify the obtained theoretical results and to demonstrate the effectiveness of the method.

The strong vibration responses of the cab system can be restrained by the damper force and the friction of the suspensions for trucks. After the failures of dampers, especially in the case of the complete failure, the anti vibration effect of the friction is prominent. However, the nonlinear vibration response characteristics of the cab subject to the damper complete failure have not been revealed. In order to reveal the nonlinear vibration response characteristics, a dynamic model of the cab system was established and its vibration equations were given. The friction forces existing in the suspensions were determined by the bench test. The influences of the friction forces on the cab vibration under different amplitude harmonic inputs were investigated when the dampers completely fail. The cab vertical displacement changes with the excitation amplitude and the vibration represents various motion states, including the periodic motion, the quasi-periodic motion, and the chaotic motion. The simulation results show that when the dampers fail, the proper friction forces help to suppress the quasi-periodic motion and the chaotic motion of the cab and to reduce the amplitude of the periodic motion. The proper friction forces can make the cab movement far away from the chaos area. They also help to avoid the fatigue damage of the cab floor and suspension parts to improve the service life of the suspension parts and to reduce the maintenance cost of the cab suspensions.