It’s important to study the liquid motion and its effect on the tanks. The method of fundamental solution (MFS) is a novel meshless numerical method proposed to solve incompressible inviscid fluid flow problems with moving boundaries. In this paper, this method is developed for two-dimensional rectangular water reservoirs under harmonic and earthquake excitations. For modeling of fluid motion with a moving free surface, Lagrangian formulation is used to pressure equation, like a potential equation and so the geometry is updated in each time step through an implicit algorithm. In recent research, equations are used with linearized boundary conditions, while due to the Lagrangian approach of pressure-based equations; the boundary conditions of the problem are very simple and it’s easy to solve complex problems. The innovation of this study is considering earthquake loads to simulate sloshing water surfaces applied by the Method of fundamental solution (MFS). The nature of earthquake excitation due to frequency content and fast acceleration changes leads to singularity problems in tank corners. So, the solution is expressed as a linear Green basis function in the method of fundamental solutions to avoid the singularity problem and to obtain better results. The numerical results are compared with other numerical and experimental results to show the proposed procedure precisely taking into account the effects of earthquake excitation.

Sloshing phenomenon is one of the complex problems in free surface flow phenomena. Numerical meshless methods as a new method can be used to solve this problem. In these methods, the lack of a mesh and complex elements for the domain of problems due to the change in geometry of the solution over time provides a lot of flexibility in solving numerical problems. In the previous researches, the sloshing problem in reservoirs was solved, using the Laplace equation with respect to the velocity potential, but the solution to this problem with pressure equations has not much considered; therefore, using the pressure equations and a suitable lagrangian time algorithm, generalized exponential basis function method has been developed for dynamic stimulation reservoirs. The approximation is solved, using a meshless method of generalized exponential basis functions and the entire domain of problem will discrete to a number of nodes and then with appropriate boundary conditions, the unknowns are approximated. In this study, linear and nonlinear examples have been solved under harmonic stimulation, in two-dimensional form of rectangular cube tanks, and the results of them have been compared with the analysis solving methods, other numerical methods, and experimental data. The results show that the present method in two-dimensional mode is very noticeable compared with other available lagrangian methods because of accuracy in solving problem and spending time.

In this article we study harmonic analysis on the proper velocity (PV) gyrogroup using the gyrolanguage of analytic hyperbolic geometry. This PV addition is the relativistic addition of proper velocities in special relativity, and it is related with the hyperboloid model of hyperbolic geometry. The generalized harmonic analysis depends on a complex parameter zz and on the radius tt of the hyperboloid, and it comprises the study of the generalized translation operator, the associated convolution operator, the generalized Laplace–Beltrami operator and its eigenfunctions, the generalized Poisson transform and its inverse, the generalized Helgason–Fourier transform and its inverse, and Plancherel’s theorem. In the limit of large tt, t→+¥, the generalized harmonic analysis on the hyperboloid tends to the standard Euclidean harmonic analysis on RnRn, thus unifying hyperbolic and Euclidean harmonic analysis.

Many different methods for gravity field modelling have been investigated, among which, the harmonic expansion has been widely used due to harmonic nature of gravity potential field that satisfies Laplace equation in an empty space. This method, however, cannot reach to a high resolution in a gravity field, and suffers from omitting the high frequency gravity signals and therefore it is not appropriate for local gravity field modelling. To overcome this drawback and recover high frequency features of gravity field, appropriate basis functions with local support should be used. One of the methods for local gravity field modeling based on local harmonic function is spherical cap harmonic analysis. In this method, the Dirikhlet boundary value problem for Laplace equation is solved for boundary conditions on the surface of a spherical cap which results in Eigen expansion of the solution in terms of the associated Legendre function of noninteger degree and integer order. Another method that can be used for local gravity field modeling is rectangular harmonic analysis. In this method, Laplace equation is solved in a local Cartesian coordinate system and boundary conditions are applied on a plane area which. In this approach, trigonometric functions are used as basis functions. In this study, the problem of local gravity field modeling based on both spherical cap, and rectangular harmonic expansion is investigated. Also, a numerical study is conducted to show the performance of each method for local gravity field modeling. To do so the observations of vector airborne gravimetry in the northwest of Tanzania in Highland region are used to derive the coefficients of each model. The low-frequency part of observed gravity field is removed from the data using EGM2008 geo-potential model, and the resulting residual gravity field is considered for local modelling. Since the governing equations for determination of the coefficients suffer from an ill-conditioning problem, it is necessary to apply some regularization schemes to find the optimum solution. Here, the Tikhonov regularization method is utilized to obtain the regular solution. In this study, the edge effect for each model is also analyzed. To show this effect, the results of models are compared with the observations of gravity at some control points distributed both within the study area and its margin. It should be noted that the maximum degree of expansion in harmonic series, plays an important role in appropriate fitting of local gravity field models to the gravity data and it has significant effects on the computational task of determining the coefficients of each model. For this purpose, local gravity field modelling is calculated with different value of maximum degree of expansion and then regarding to the result (accuracy of local gravity model by comparing with control points), appropriate value of maximum degree of expansion for each model is determined. Finally the results of two models are compared to each other to show the performance of each models in local gravity field modeling. The results of this study reveal that ASHA has the ability to model local gravity with accuracy of about 1 mGal, and RHA method in the best situation can just achieve to a 3 mGal accuracy, although the convergence rate in RHA model is faster than ASHA model. Also by comparing the edge effect on each models, it is seen that the edge effect in two models and in all directions occurred but in a Z direction of RHA model that are more significant than the other directions in two models and one may conclude that the edge effect of RHA are much larger than that of ASHA. Finally, the result obtained shows that ASHA model can have better results for local gravity modelling.

In practical applications of inverters, unbalanced conditions may be occurred. For instance, semiconductor switches of a converter may not be exactly the same or switching circuit may be unbalanced. This unbalance leads to additional harmonics in the output of converter. The additional harmonics usually are not considered in the design of circuit, so cause many problems. For precise investigation of these harmonics, a new model of inverter based on switching functions is presented. With this model, analytical equations of harmonics in unbalanced switching are calculated. These analytical equations can be used for designing process such as investigation of optimal cases or elimination of undesired harmonics. The accuracy of the analytical calculations is verified by simulation results. As well, an experimental prototype is constructed to verify analytical results.

One of the most variability of atmospheric parameter is precipitation, which changes seasonally. It is important to understand exact characteristic of rainfall seasonal variable. Therefore, it is avoidable to study rainfall season in Hamedan province, because Hameden is one of the important centers of agriculture in Iran. In this research, the seasonal variability of rainfall is considered in Hamedan province. For this object, precipitation data spanning 30 years (1979-2009) were analysed to determine the onset and cessation, trend and seasonal variability of rainfall, based on the daily rainfall for there separated decades. The result of this study show the duration of rainfall is from early falls until end of spring in the first decade. This result indicated the duration of rainfall is long. In the second decade, there is no significant change in rainfall season, but only in some part of the province, the rainfall duration is shortfall and in the other part is long falls. Nevertheless, in the third decade there is considerable movement, i.e. the onset of rainfall duration has been in winter and cessation of rainfall duration has been in summer. It express that rainfall season has moved to summer slowly. The trend of rainfall duration has increasing trend. On the other hand, the duration length of rainfall is longer than before. In order to classify, rainfall seasonal variability is interpolated and the cluster analysis is done base on the “Oghlidos distance” and “Ward” integrated method. According to this method, Hamedan province is classified to 3 groups. The first group indicates the shortfall in the most parts, the second group indicates rainfall season onset is moved to winter, and in the third part the rainfall season hasn’t had change.

harmonic analysis has become an important issue in modern power systems. The widespread penetration of non-linear loads into the emergence of power systems has turned power quality analysis into an important operation issue under both steady state and transient conditions. This paper employs a Dynamic harmonic Domain (DHD) based framework for the dynamic harmonic analysis of VSC-HVDC systems. These systems are widely used in modern power systems in both distribution and transmission levels in order to provide voltage profile improvement, power flow control, and power loss reduction. In this paper, appropriate modeling of VSC-HVDC systems for harmonic propagation is performed by means of switching function which provides a connection between DC and AC sides. Also in this paper, dynamics related to DC side capacitor are taken into account which can greatly affect the transient response. In order to validate the results, the proposed method has been successfully tested on a test system and the obtained results are compared to those of a time-domain software, followed by a discussion on results.

In this research, in order to investigate the effect of the piezoelectric patch which is used as a sensor or actuator in rotating flexible structures such as a helicopter blade, the free vibrations of the rotating rectangular sheet with and without the piezoelectric patch have been presented. First-order shear deformation theory is considered for plate displacement and piezoelectric field. Considering the effect of Coriolis acceleration, centrifugal acceleration and centrifugal in-plane forces, the equations of motion are derived from Hamilton's principle and the electromechanical couple equation is obtained from Maxwell's equation. For piezoelectric, two electrical conditions, open circuit and closed circuit, which are used in sensors and actuators, respectively, have been considered. The equations are discretized with the help of the numerical method of generalized differential squares and the matrices of inertia mass, eccentricity, Coriolis and stiffness matrix are obtained. Natural frequency values for beam and rotating plate have been compared in Abaqus software. Also, the values obtained from the numerical solution in MATLAB have been verified with articles and ABAQUS, which have high accuracy. The effect of parameters such as hub radius, rotation speed, sheet thickness, aspect ratio, piezoelectric patch thickness and applied voltage on the natural frequency of the system has also been investigated.