Effects Of Nonlinear Forces Research Articles

Design and experimental study of broadband hybrid energy harvester with frequency-up conversion and nonlinear magnetic force

In this paper, a novel broadband hybrid piezoelectric and electromagnetic energy harvester using in the low frequency vibration environment is proposed, which combines nonlinear magnet force and frequency-up conversion mechanism simultaneously. Performances are studied by theoretical analysis and experimental test. Electromechanical governed equations of harvester are established, and analytical solutions of vibration response, output voltage and power are derived. Then, effects of nonlinear force, spacing between low frequency vibration beam and piezoelectric beam, load resistance and input excitation on harvester performances are investigated by experimental test. It can be concluded that the harvester can be used to work at the low-frequency environment efficiently, and the resonant frequency and harvesting bandwidth can be tuned by the nonlinear force between the magnets and the spacing between beams. Moreover, the larger the nonlinear magnetic force and the smaller the distance between two beams, the lower working frequency and the larger bandwidth. Compared with the corresponding linear apartment, output power and bandwidth of proposed harvester are improved 90% and 125% respectively.

Numerical study of nonlinear stability boundaries for orifice-compensated hole-entry hybrid journal bearings

A high-performance and finite-length bearing system requires that the shaft can be stabilized even under a strong perturbation. The linear stability theory neglects the effects of nonlinear forces and the initial point of the shaft. Therefore, the stability of the bearing system is largely determined by the rotating speed of the shaft. In the present numerical investigation, the nonlinear forces and initial point of the shaft are accounted for to obtain the nonlinear stability boundary. The objective of this study is extended to orifice-compensated and hole-entry hybrid journal bearings with finite length. The critical rotating speed and the shaft center trajectory are acquired by solving Reynolds equation using the finite element method. By identifying the states of the orbits (stable or unstable), the nonlinear stability boundaries can be obtained. Results show that for the hybrid bearing system under the nonlinear conditions, the critical speed is a determinant factor while the initial location is another key factor. The shaft can be unstable if the initial point is outside of the stability boundary, although the speed is lower than the critical speed. There exists an obvious transitional region between the stable and unstable condition when the speed approaches the critical speed.

Nonlinear vibration analysis of a rotor supported by magnetic bearings using homotopy perturbation method

Abstract In this paper, the effects of nonlinear forces due to the electromagnetic field of bearing and the unbalancing force on nonlinear vibration behavior of a rotor is investigated. The rotor is modeled as a rigid body that is supported by two magnetic bearings with eight-polar structures. The governing dynamics equations of the system that are coupled nonlinear second order ordinary differential equations (ODEs) are derived, and for solving these equations, the homotopy perturbation method (HPM) is used. By applying HPM, the possibility of presenting a harmonic semi-analytical solution, is provided. In fact, with equality the coefficient of auxiliary parameter ( p ), the system of coupled nonlinear second order and non-homogenous differential equations are obtained so that consists of unbalancing effects. By considering some initial condition for displacement and velocity in the horizontal and vertical directions, free vibration analysis is done and next, the forced vibration analysis under the effect of harmonic forces also is investigated. Likewise, various parameters on the vibration behavior of rotor are studied. Changes in amplitude and response phase per excitation frequency are investigated. Results show that by increasing excitation frequency, the motion amplitude is also increases and by passing the critical speed, it decreases. Also it shows that the magnetic bearing system performance is in stable maintenance of rotor. The parameters affecting on vibration behavior, has been studied and by comparison the results with the other references, which have a good precision up to 2nd order of embedding parameter, it implies the accuracy of this method in current research.

Dynamics and stability of micro-cutting operations

Abstract In spite of considerable advances toward the understanding of the mechanics of micro-cutting operations their dynamics and stability that are dominated by the influence of nonlinear effects imposed by the minimum chip thickness and grain size effects and the dominance of ploughing over shearing still remain largely uncharted. Hence, the objective of this paper is to explore the fundamental mechanisms that lead to instabilities in micro-cutting. For dynamic stability analysis, linear stability theory was adopted to model regenerative chatter. The rationale for using linear stability theory is to perform a rigorous parametric study of the major factors that influence stability in light of the nonlinear phenomena that dominate micro-cutting processes. A linearized micro-cutting dynamic force model and a linear structural dynamics model are presented to formulate stability criteria for the different characteristic operating regimes encountered in micro-cutting. It has been shown that the three physical operating regimes, pure ploughing, simultaneous ploughing and shearing and the shearing dominant, govern the micro-cutting process. They are primarily a function of the relationship between the undeformed chip thickness and cutting edge radius and exert different influences on process stability. Based on the linearized cutting dynamics models characterizing these regimes, a generalized approach to dealing with nonlinear force effects was proposed for process stability analysis. The method is applicable for cutting process nonlinearities at all scales if they are present.

Nonlinear mathematical modeling of vibrating motion of nanomechanical cantilever active probe

Nonlinear vibration response of nanomechanical cantilever (NMC) active probes in atomic force microscope (AFM) application has been studied in the amplitude mode. Piezoelectric layer is placed piecewise and as an actuator on NMC. Continuous beam model has been chosen for analysis with regard to the geometric discontinuities of piezoelectric layer attachment and NMC's cross section. The force between the tip and the sample surface is modeled using Leonard-Jones potential. Assuming that cantilever is inclined to the sample surface, the effect of nonlinear force on NMC is considered as a shearing force and the concentrated bending moment is regarded at the end. Nonlinear frequency response of NMC is obtained close to the sample surface using the dynamic modeling. It is then become clear that the distance and angle of NMC, the probe length, and the geometric dimensions of piezoelectric layer can affect frequency response bending of the curve.

Robust transport by multiple motors with nonlinear force–velocity relations and stochastic load sharing

Transport by processive molecular motors plays an important role in many cell biological phenomena. In many cases, motors work together to transport cargos in the cell, so it is important to understand the mechanics of the multiple motors. Based on earlier modeling efforts, here we study effects of nonlinear force–velocity relations and stochastic load sharing on multiple motor transport. We find that when two or three motors transport the cargo, then the nonlinear and stochastic effects compensate so that the mechanical properties of the transport are robust. Similarly, the transport is insensitive to compliance of the cargo-motor links. Furthermore, the rate of movement against moderate loads is not improved by increasing the small number of motors. When the motor number is greater than 4, correlations between the motors become negligible, and the earlier analytical mean-field theory of the multiple motor transport holds. We predict that the effective diffusion of the cargo driven by the multiple motors under load increases by an order of magnitude compared to that for the single motor. Finally, our simulations predict that the stochastic effects are responsible for a significant dispersion of velocities generated by the ‘tug-of-war’ of the multiple opposing motors.

Effects of Nonlinear Forces on Dynamic Mode Atomic Force Microscopy and Spectroscopy

In this paper, we describe the effects of nonlinear tip-sample forces on dynamic mode atomic force microscopy and spectroscopy. The jumps and hysteresis observed in the vibration amplitude (A) versus tip-sample distance (h) curves have been traced to bistability in the resonance curve. A numerical analysis of the basic dynamic equation was used to explain the hysteresis in the experimental curve. It has been found that the location of the hysteresis in the A-h curve depends on the frequency of the forced oscillation relative to the natural frequency of the cantilever.

A core-particle model for periodically focused ion beams with intense space-charge

A core-particle (CP) model is derived to analyze transverse orbits of test-particles evolving in the presence of a core ion beam that has uniform density within an elliptical cross-section. The model can be applied to both quadrupole and solenoidal focused beams in periodic or aperiodic lattices. Efficient analytical descriptions of electrostatic space-charge fields external to the beam core are derived to simplify model equations. Image-charge effects are analyzed for an elliptical beam centered in a round, conducting pipe to estimate model corrections resulting from image-charge nonlinearities. Transformations are employed in diagnostics to remove coherent flutter motion associated with oscillations of the ion beam core due to rapidly varying, linear applied-focusing forces. Diagnostics for particle trajectories, Poincare phase-space projections, and single-particle emittances based on these transformations better illustrate the effects of nonlinear forces acting on particles evolving outside the core. A numerical code has been written based on this model. Example applications illustrate model characteristics. The CP model described has recently been applied to identify physical processes leading to space-charge transport limits for an rms-envelope matched beam in a periodic quadrupole focusing-channel [S.M. Lund, S.R. Chawla, Nucl. Instr. and Meth. A 561 (2006) 203]. Further characteristics of these processes are presented here.

A method to measure the nonlinear force caused emittance growth in a RF photoinjector

Based on the multi-slit method, a new method is introduced to measure the non linear force caused emittance growth in a RF photoinjector. It is possible to reconstruct the phase space of a beam under some conditions by the multi-slit method. Based on the reconstructed phase space, besides the emittance, the emittance growth from the distortion of the phase space can also be measured. The emittance growth results from the effects of nonlinear force acting on electron, which is very important for the high quality beam in a RF photoinjector.

Effects of ps and ns laser pulses for giant ion source

Abstract Laser driven ion sources produce giant ion emission current densities at the emission area which exceed the few mA/cm 2 of classical ion sources (MEVVA or ECR) by many orders of magnitude. Very energetic highly charged fast ions, separated by their charge number Z , from ns laser pulses were explained by relativistic self-focusing and nonlinear force effects. Recently a strong difference with ps pulses was found in contrast to the ns pulses depending on the prepulses. We present an explanation based on a skin layer process. This has consequences to sub-picosecond laser-plasma interaction for the studies of the fast ignitor physics for laser fusion and to the new field of nuclear physics opened by these laser pulses which produce up to 100 MeV particles and gammas of high density as well as for ion source applications.

Computer-aided design of robotic manipulators

Abstract A technique which enables the observation of the time constants for joint velocity changes and effects of nonlinear forces in a robot has been developed. This method will now be utilized to create a software package for the design of robotic manipulators. An interactive procedure is derived to help a designer to choose proper actuators, their locations and optimal dimensions on each component in a robot so that the robot has the same time constant for any direction of motion and less nonlinear effects. An integrated solution of the following problems will be sought from which to derive the procedure. A data structure to represent a robot including the drive mechanisms in a database will be created. A proper objective function, which represents the dynamic characteristics of robots (ie time constants and nonlinear effects) must be defined. A method of computing the objective function from a set of optimization variables should be derived. A case study using the Rhino robot exemplifies the integration of the aforementioned developments.

Spectral analysis of nonlinear wave load effects on offshore platforms

Abstract This paper deals with stochastic theory of nonlinear wave forces emphasizing their effects on the structural response of offshore towers. The analysis of forces and response is limited to second-order statistics expressed in terms of power spectral densities. Numerical examples are included to demonstrate the potential of the theory and to quantify the effects of nonlinear forces on the structural response.