Narrow Results

This study investigates the error which occurs when numerically integrating the equation of motion of a single degree of freedom system excited by a harmonic force near resonance. The Constant Average Acceleration method was considered in particular as it features in many finite element software packages. It was found that a considerable error in the calculated responses occurs in systems with low damping due to the well known phenomenon of period elongation. However, the error is reduced for systems with higher damping and/or when smaller time step is used. With regard to this, recommendations are given as to the time steps required to obtain solutions with a pre-defined level of accuracy.

The interaction between a bridge and a train moving on the bridge is a coupled dynamic problem. The equations of motion of the bridge and the vehicle are coupled by the time dependent contact forces. At each time step, the motion of the bridge influences the forces transferred to the vehicle and this, in turn, changes the forces acting on the bridge. In this paper, a comparison of three different time domain solution algorithms for the coupled equation of motion of the train–bridge system is presented. Guidelines are given for a good choice of the time step.

This chapter provides a detailed analysis on the performance of a photovoltaic (PV) generator operating under varying irradiance levels. The PV generator is connected to a single-phase grid supply and the nonlinear behavior of the system is analyzed. The PV generator produces total harmonic distortion (THD) of current fed to the grid; improvements are evaluated to stabilize the quality of supply injected into the grid. Increasing the size of the inductor is proposed to stabilize and maintain the PV generator current fed to the grid. The response of the maximum power point tracking (MPPT) controller is analyzed by simulating the PV generator system with and without an MPPT controller. It is noted that the introduction of MPPT can maintain the maximum PV generator power output irrespective of changes in irradiation.

In time history linear dynamic analysis of structures, one approach is to employ Duhamel's integral but because its lower bound is zero, for each time step the integral needs to be evaluated in the domain from zero up to the specified time. In this paper, a modified form of the Duhamel's integral is proposed in which for each time step the last time interval is integrated, therefore, it is considerably faster than its original form. In this formulation, at each time, in addition to displacement, velocity is also calculated and they are used as initial values for the next step. Then, for the solution of the next step, the transient solution is added to the effect of loads in that interval. The method proposes two integrals for displacements and the same two integrals for the velocity in one time step. Indeed, for a problem with n time steps, total number of integration intervals for Duhamel's integral is n(n+1)/2, while, for the proposed method the is just 2n. The proposed method enunciates that the savings in the computational time becomes more obvious for MDOF systems due to the fact that the aforementioned saving is the multiple of the number of modes.