Dynamical behavior of particles in a Paul trap has been investigated by solving the set of differential equations considering the effect of Damping force. Positions of the trapped ions as a function of time, ion trajectories and the phase space curves in the first stability region have been obtained in the presence of the Damping force. The region of stability for r and z components as well as the first stability region with and without the Damping force have been computed using the fourth-order Runge-Kutta method. Furthermore, for a Paul trap with specified dimensions and a typical RF frequency, the first stability region for 3H+ and 1H+ ions has been determined in the Vdc – Vac plane. It is worthwhile to note that computation of the stability region in the presence of Damping force through the use of this method has been reported for the first time.

With the change of an ion trap geometrical shape, ring and end-cap electrodes, and also Damping force effects, the first and second stability regions are studied in a stretched Paul ion trap. In this article, according to a new idea, we changed the trap geometry based on the change in distances between the ring electrode (2r˳ ) and end-cap electrodes (2z˳ ). For this purpose, the geometrical parameter n=(r˳ /z˳ )2 was introduced in our calculations. Also, for the Damping effects, we entered a viscous Damping factor (k) in the Mathieu equation. The set of differential equation governing the motion of the confined ion is considered, taking into account the effect of Damping force and the ion trap geometry. The Mathieu type differential equations were solved using Runge-Kutta Verner fifth-order and sixth-order method (RKV56). Comparisons were made with the corresponding stability diagrams without considering the effects of Damping force in an ideal ion trap 2 2 (r  2z ). The numerical results showed that, for a given ion trap mode i. e., rf only mode, the Damping force and the trap geometry played important roles in the relocation of the stability diagrams. The first and second stability regions in the presence of the Damping force, according to trap’ s geometry, are reported for the first time.

This paper studies the dynamics of a non-smooth vibrating system of the Filippov type. The main focus is on investigating the stability and bifurcation of a simple harmonic oscillator subjected to a non-smooth velocity-dependent Damping force. In this way, we can analyze the effects of Damping on the system's vibrations. For this purpose, we will find a parametric region for the existence of generalized Hopf bifurcation, in order to compute a branch of periodic orbits for the system. The tool for our purpose is the theoretical results about generalized Hopf bifurcation for planar Filippov systems. Some numerical simulations as examples are given to illustrate our theoretical results. Our theoretical and numerical findings indicate that the harmonic oscillator can experience different kinds of vibrations, in the presence of a non-smooth Damping.

In this paper, green function and transfer function are used for analytical solution of mass equation, nonlinear spring and Damping with effective wind force. This equation has been used to model space structure, wing and all of the structure used at high altitude. Furthermore this equation is applied frequently in modeling foundation similar to nonlinear spring and Damping and the equation is better solved analytically where answer of the analytical solution is similar to the mechanical action.

In this paper, the effects of particles size of Magnetorheological Carbonyl iron powder on Damping force and energy dissipation capacity for a Magnetorheological double ended type damper is investigated experimentally. Despite of the considerable researches on the effects of particles size on the viscosity of Magnetorheological fluids, sedimentation of fluids and electromagnetic field intensity in damper, there is no a published work about the effects of iron particles size on the Damping force amplitude and energy dissipation capacity of double-ended Magnetorheological damper. Therefore, in the present research, two different Magnetorheological fluids were prepared with the same volumetric percentage of % 35 from two different sizes of Iron particles i. e. 40 μ m and 63μ m and filled into a double ended type damper. The double-ended damper had three electric coils and was tested in different frequencies, different electric currents and 15 mm displacement stroke. The effects of Magnetorheological fluid particles on produced Damping force and energy dissipation capacity were analyzed by extracting force-displacement and force-time curves from experiments. The results showed that the maximum amplitude of Damping force is increased with increasing the applied electric current on the damper and the amount of this force for fluid with 63μ m particles size is slightly higher than that for the fluid with 40μ m particles size. However, the energy dissipation capacity of the investigated damper in all excitation frequencies with the all applied electrical currents for fluid with 63μ m particles size was considerably higher than that for fluid with 40μ m particles size.

Background and Aim: Superelasticity refers to the same amount of force exerted by an ideal archwire independent of the degree of activation. Clinical findings show that in most of situations these materials do not fulfill the expected properties. The aim of this study was to evaluate the bending properties of some of these archwires.Materials and Methods: In this experimental research eight specimens of each of the round wires with 0.14, 0.16 and 0.018 inch sizes of force I, rematitan lite and superelastic G & H types were tested. These wires were subjected to a three point bending test by DARTEC machine. Data were tested by ANOVA and Duncan tests at 0.05 level of significance. Results: All of these materials showed superelastic properties or at least superelastic tendencies. More pronounced superelastic properties were observed in thicker wires. However, their force level of plateau for 0.014 inch rematitan lite wires the end of the plateau was observed when the wire was displaced at least 0.6 mm.Conclusion: In all of these wires, the force level of plateau was higher than the optimal force required for tipping movements.

The stability of synchronous generator and its improvement is one of the important problems in power systems. Stability can be divided into steady state, dynamic and transient stability. The dynamic stability is studied in this paper. DFIG capabilities will be one the effective ways to improve the stability of synchronous generator in the power network including wind generations based on doubly fed induction generator (DFIG). In this paper, a dynamic Damping controller (DDC) is suggested in the reactive power band of DFIG tuned by genetic algorithm. For this purpose, two feedbacks, i. e., synchronous generator speed differences and DFIG electromagnetic torque are used. Eigenvalues and Damping torque analysis are used for demonstrating the effectiveness of the suggested controller, requiring system small signal study. The simulation results verify that the controller has the ability to improve dynamic stability of synchronous generator.