Longitudinal Dynamic Response Research Articles

Flight dynamics model for preliminary design of PrandtlPlane wing configuration with sizing of the control surfaces

This paper deals with the evaluation of the flight dynamics response of aircraft with a PrandtlPlane configuration by means of simple models to be used during the preliminary design. The study is completed by a method for an initial sizing of the elevators and the ailerons (positioned on both the front and the rear wing) in order to achieve adequate handling qualities. The flight dynamics model considers the rigid aircraft, the steady aerodynamics, and separating the longitudinal and the lateral-directional motions. The force derivatives are extrapolated through a VLM solver whose the reliability of the results has been proven. The methods have been applied on the IDINTOS aircraft with the conclusion that we obtain a proper longitudinal dynamic response with a reduced Margin of Stability because of the very high values of the aerodynamic damping Mq and the pitch stiffness Malpha.

Experimental analysis of occupational whole-body vibration exposure of agricultural tractor with large square baler

This study investigates longitudinal whole-body vibration in agricultural tractors powering a large square baler. The aim is to test the hypothesis that four-wheel drive has an influence on the longitudinal dynamic response. A number of experimental measurements are carried out on a specific vehicle combination driving uphill and downhill. The whole-body vibration exposure is measured at the operator seat under different conditions.The statistic results show a significant difference on the whole-body vibration exposure depending on operating conditions. Driving uphill and downhill with four-wheel drive activated showed the highest difference with increased vibration level at downhill driving.The results indicate that four-wheel drive influences the longitudinal dynamics and hence the whole-body vibration exposure on tractors with large square balers. Relevance to industryThe findings of this work are highly relevant to the manufacturers of agricultural tractors and machinery as well advisers within occupational health. The paper demonstrates potential in reducing damaging vibrations by simple manual or automatic control of four-wheel drive.

Una metodología de cálculo para la determinación de la respuesta dinámica longitudinal de estructuras altas bajo la acción del viento

The optimization of computing methods along with the advance of construction technology of civil structures, allow nowadays to design and build lighter and low stiffness and damping structures, turning them into elements of high sensitivity against wind-induced dynamic effects. The purpose of this work is to describe and to apply a simple calculation methodology that enables the determination of the longitudinal dynamic response of tall buildings in time domain. The wind velocity field is reproduced by velocity series that incorporate the coherence function which then are transformed into fluctuating nodal forces using the quasi-static loading model. Furthermore, to include the effect of imperfect averaging associated with the discretized nodes, the aerodynamic admittance function is added.Through the proposed methodology two structures widely studied by other authors are analyzed: a steel tower and the CAARC Standard Tall Building. The results thus obtained show agreement with those reported in the literature.

Dynamic modeling for a morphing aircraft and dynamic characteristics analysis

The physical model of a variable-span variable-sweep morphing aircraft was simplified. Based on Kane's method,the morphing movements were assumed to be controllable known input,and the wings' movements were expressed by constraint equations. The six components of the translational velocity and the angular velocity of the morphing aircraft's body in the body coordinate frame were selected as the generalized speeds. Six degree-of-freedom dynamic model was built. Additional forces and additional moments were defined to describe the dynamic influence imposed on the morphing aircraft by the morphing movement. The simulation results show that,in the condition of steady-state flight,the additional forces and moments cased by the wings' morphing are small compared to the variations of aerodynamic forces. The aircraft's longitudinal dynamic responses during the morphing process are simulated and analyzed at different morphing speeds. Results show that the aircraft 's height,velocity and pitch angle will change considerably during morphing process.

Longitudinal dynamic response of pile foundation in a nonuniform initial strain field

This paper presents an investigation into the dynamic response of pile and soil due to pile installation in a radially inhomogeneous initial strain field. The radial variation rule for the shear modulus and physical parameters of the soil caused by the initial strain field is deduced. On the basis of the plane strain and complete P-S (pile-soil) contact assumptions, the analytical solution of longitudinal dynamic impedance of the soil is derived by means of subdividing the soil domain into a number of annular vertical zones. The longitudinal impedance of the pile top and velocity response in frequency and time domains, are also obtained. The parametric study of interfacial pressure on the dynamic response of P-S system is undertaken within a relatively lower frequency domain. Comparison results between previous solutions and the present study indicates that the analytical solution derived in this paper is more stable.

The vertical and the longitudinal dynamic responses of the vehicle–track system to squat-type short wavelength irregularity

The squat, a kind of rolling contact fatigue occurring on the rail top, can excite the high-frequency vehicle–track interaction effectively due to its geometric deviations with a typical wavelength of 20–40 mm, leading to the accelerated deterioration of a track. In this work, a validated 3D transient finite element model is employed to calculate in the time domain the vertical and the longitudinal dynamic contact forces between the wheel and the rail caused by squats. The vehicle–track structure and the wheel–rail continua are both considered in order to include all the important eigencharacteristics of the system related to squats. By introducing the rotational and translational movements of the wheel, the transient wheel–rail rolling contact is solved in detail by a 3D frictional contact model integrated. The contact filter effect is considered automatically in the simulations by the finite size of the contact patch. The present work focuses on the influences of the length, width and depth of a light squat on the resulted dynamic contact forces, for which idealised defect models are used. The growth of a squat is also modelled to a certain extent by a series of defects with different dimensions. The results show that the system is mainly excited at two frequencies separately in the vertical and the longitudinal dynamics. Their superposition explains the typical appearance of mature squats. As a squat grows up, the magnitude of the excited vibration at the lower frequency increases faster than the one at the higher frequency.

Longitudinal Linear Parameter Varying Modeling and Simulation of Morphing Aircraft

The purpose of this paper is to present linear parameter varying modeling and simulation of a folding-wing morphing aircraft in the wing-folding process. Morphing aircraft can alter the shape to adapt to mission environment changing. When the wing shape is varying, the dynamic responses of the morphing aircraft will be dependent on the time-varying aerodynamic forces and moments, which will be a function of the wing shape change by the morphing command. The folding-wing morphing aircraft is regarded as a variable geometry rigid body, and the six-degree-of-freedom nonlinear dynamic model in the wing-folding process is founded. The decoupled longitudinal dynamic equation of the morphing process is deduced by simplification, and the longitudinal dynamic responses of the wing morphing process are numerically simulated by the quasi-steady aerodynamic assumption. Furthermore, using the Jacobian linearization approach, the longitudinal nonlinear dynamics equations of morphing aircraft are linearized, and the longitudinal linear parameter varying model of the morphing aircraft in the wing-folding process is obtained. Finally, the linear parameter varying model is validated by the open-loop time responses compared to the nonlinear aircraft responses. The research results can be as great reference for the linear parameter varying controller design for the morphing aircraft in the wing shape varying.

Simulation of longitudinal dynamics of long freight trains in positioning operations

Positioning operations are performed in a railway goods yard, in which the freight train is pulled precisely at a specific point by a positioner. The positioner moves strictly according to the predesigned speed and provides all the traction and braking forces which are highly dependent on the longitudinal dynamic response. In order to improve the efficiency and protect the wagons from damage during positioning operations, the design speed of the positioner has to be optimised based on the simulation of longitudinal train dynamics. However, traditional models of longitudinal train dynamics are not accurate enough in some aspects. In this study, we make some changes in the traditional theory to make it suitable for the study of long freight trains in positioning operations. In the proposed method, instead of the traction force on the train, the motion of the positioner is assumed to be known; more importantly, the traditional draft gear model with nonlinear spring and linear damping is replaced by a more detailed model based on the achievement of contact and impact mechanics; the switching effects of the resistance and the coupler slack are also taken into consideration. Numerical examples that deal with positioning operations on the straight lines, slope lines and curving lines are given.

Longitudinal dynamic response of pile in layered soil based on virtual soil pile model

Taking the effect of finite soil layers below pile end into account, the longitudinal dynamic response of pile undergoing dynamic loading in layered soil was theoretically investigated. Firstly, finite soil layers below pile end are modeled as virtual soil pile whose cross-section area is the same as that of the pile and the soil layers surrounding the pile are described by the plane strain model. Then, by virtue of Laplace transform and impedance function transfer method, the analytical solution of longitudinal dynamic response at the pile head in frequency domain is yielded. Also, the semi-analytical solution in time domain undergoing half-cycle sine pulse at the pile head is obtained by means of inverse Laplace transform. Based on these solutions, a parametric study is conducted to analyze emphatically the effects of parameters of soil below pile end on velocity admittance and reflected wave signals at the pile head. Additionally, a comparison with other models with different supporting conditions from soil below pile end is performed to verify the model presented.

Longitudinal Dynamics Response of M-Wing Morphing Aircraft

A simulation methodology suitable for morphing wing aircraft is presented, accounting for the changes in both inertial and aerodynamic properties. The aerodynamics was generated with vortex lattice method and solved concurrently with 6DOF nonlinear extended equations of motion. Due to the wing morphing, there are 4 additional forces and moments exhibiting in the extended equations of motion. The simulation mythology was applied to M-wing morphing aircraft, and the longitudinal dynamic response was analyzed with the wing morphing symmetrically. The results show that the additional forces and moments influence the flight dynamic considerably

Free longitudinal vibration of tapered nanowires in the context of nonlocal continuum theory via a perturbation technique

The free longitudinal vibration of tapered nanowires is investigated in the context of nonlocal continuum theory. The problem is studied for the nanowires with linearly varied radii under fixed–fixed and fixed–free boundary conditions. In order to assess the problem in a more general form, a perturbation technique is proposed based on the Fredholm alternative theorem. The natural frequencies, corresponding mode shapes, and phase velocities of the tapered nanowires are derived analytically up to the second-order perturbation for different boundary conditions. The predicted results by the perturbation technique are successfully verified with those of the exact solution. The obtained results reveal that the proposed methodology is a capable one in capturing the free longitudinal dynamic response of tapered nanowires with different boundary conditions. However, the differences of the results of the perturbation technique and those of the exact solution increase with the rate of radii change. In a special case, the obtained results are also compared with those of other researchers and a reasonably good agreement is achieved. It is also observed that for higher values of the small scale effect parameter, the variation of the rate of radii change has a more effect on the variation of the natural frequencies and phase velocities, irrespective of the boundary conditions of the tapered nanowire. Additionally, a scrutiny of the presented dispersion curves indicates that for a constant wavenumber, the value of the phase velocity decreases with the small scale effect parameter, particularly for higher wavenumbers.

Propagation and Relaxation of Tension in Stiff Polymers

We present a unified theory for the longitudinal dynamic response of a stiff polymer in solution to various external perturbations (mechanical excitations, hydrodynamic flows, electrical fields, temperature quenches, etc.) that can be represented as sudden changes of ambient/boundary conditions. The theory relies on a comprehensive analysis of the nonequilibrium propagation and relaxation of backbone stresses in a wormlike chain. We recover and substantially extend previous results based on heuristic arguments. New experimental implications are pointed out.

Transient vibration phenomena in deep mine hoisting cables. Part 1: Mathematical model

The classical moving co-ordinate frame approach and Hamilton's principle are employed to derive a distributed-parameter mathematical model to investigate the dynamic behaviour of deep mine hoisting cables. This model describes the coupled lateral–longitudinal dynamic response of the cables in terms of non–linear partial differential equations that accommodate the non-stationary nature of the system. Subsequently, the Rayleigh–Ritz procedure is applied to formulate a discrete mathematical model. Consequently, a system of non-linear non-stationary coupled second order ordinary differential equations arises to govern the temporal behaviour of the cable system. This discrete model with quadratic and cubic non-linear terms describes the modal interactions between lateral oscillations of the catenary cable and longitudinal oscillations of the vertical rope. It is shown that the response of the catenary–vertical rope system may feature a number of resonance phenomena, including external, parametric and autoparametric resonances. The parameters of a typical deep mine winder are used to identify the depth locations of the resonance regions during the ascending cycles with various winding velocities.

Langevin-dynamics study of the dynamical properties of small magnetic particles

The stochastic Landau-Lifshitz-Gilbert equation of motion for a classical magnetic moment is numerically solved (properly observing the customary interpretation of it as a Stratonovich stochastic differential equation), in order to study the dynamics of magnetic nanoparticles. The corresponding Langevin-dynamics approach allows for the study of the fluctuating trajectories of individual magnetic moments, where we have encountered remarkable phenomena in the overbarrier rotation process, such as crossing-back or multiple crossing of the potential barrier, rooted in the gyromagnetic nature of the system. Concerning averaged quantities, we study the linear dynamic response of the archetypal ensemble of noninteracting classical magnetic moments with axially symmetric magnetic anisotropy. The results are compared with different analytical expressions used to model the relaxation of nanoparticle ensembles, assessing their accuracy. It has been found that, among a number of heuristic expressions for the linear dynamic susceptibility, only the simple formula proposed by Shliomis and Stepanov matches the coarse features of the susceptibility reasonably. By comparing the numerical results with the asymptotic formula of Storonkin {Sov. Phys. Crystallogr. 30, 489 (1985) [Kristallografiya 30, 841 (1985)]}, the effects of the intra-potential-well relaxation modes on the low-temperature longitudinal dynamic response have been assessed, showing their relatively small reflection in the susceptibility curves but their dramatic influence on the phase shifts. Comparison of the numerical results with the exact zero-damping expression for the transverse susceptibility by Garanin, Ishchenko, and Panina {Theor. Math. Phys. (USSR) 82, 169 (1990) [Teor. Mat. Fiz. 82, 242 (1990)]}, reveals a sizable contribution of the spread of the precession frequencies of the magnetic moment in the anisotropy field to the dynamic response at intermediate-to-high temperatures.

Existence of Fixed Point in the Frequency Response of Deepsea Riser and its Influence on the Design

The 4000 m class deepsea drilling vessel will be realized in Japan in near future. The drilling vessel is equipped with deepsea riser, and this paper discusses longitudinal dynamic response of the deepsea riser in hung-off condition. This paper shows that there exist fixed points in the frequency response of strain of hung-off deepsea risers. A fixed point is a point in a frequency response which does not change irrespective of the change of some governing parameters of the dynamic system. The fixed point is originally found in the discreet mass-spring system, and this paper shows that the fixed point exist also for a continuum system, riser & BOP system. The fixed points are shown to exist in the frequency response of axial strain with respect to the damping of riser and also the damping of BOP. Considering the position of fixed points in the frequency response, it can be concluded that the increase of damping does not always improve the dynamic response of hung-off riser. When the external exciting frequency, namely heave motion of vessel, is lower than the fixed point, strain at riser top is increased with increase of damping. On the other hand, if the riser is excited at the frequency larger than the fixed point, response is significantly improved.

Singular perturbation theory of longitudinal dynamic stability and response of aircraft

SummaryThe estimation of the relative orders of the coefficients in the linear differential equations of longitudinal small perturbation of aircraft is used to analyse the classical simplified theory for the short- and long-period modes by the singular perturbation methods. The leading terms of the asymptotic expansions give the eigenvalues for short- and long-period modes with fairly good accuracy, except that the damping part of the eigenvalue for the long-period mode has relative error of the order of 10%. These approximate eigenvalues are improved by the method of strained co-ordinates which accounts for most of the differences. The dynamic response due to initial disturbances of velocity, angle of attack, and angle of pitch are also derived.

Reliability in InGaAsP/InP buried heterostructure 1.3 µm lasers

A study was conducted of aging-induced Sn whisker growth at the surface of Au-Sn bonding solder layers around a laser chip, as well as metallurgical reactions, especially in p-side down lasers, at the interface of the solder and laser crystal just below the active layer. These phenomena cause electrical shorts in InGaAsP/InP laser diodes, which occur suddenly in devices operated for long periods without any previous symptoms having appeared in their aging characteristics. To completely eliminate such failures, a novel assembling method in which chips were mounted p-side up on semiinsulating SiC submounts using Pb-Sn solder, was applied to InGaAsP/InP buried heterostructure (BH) lasers emitting at 1.3 μm. BH lasers assembled by this method do not suffer any shorting failure even after 8000 h operation under 60°C and 5 mW/facet output conditions. The small degradation rates obtained, for example, 3 percent/kh (median) at 60°C, certify the reliability of these improved lasers. As long as the stripe width of the active layer was optimized to be in the range of 1.5-2.5 \mu m necessary for obtaining kink-free light output versus current properties, no detrimental changes in laser characteristics, including transverse and longitudinal modes and dynamic output response, were observed in aged lasers. In this paper, the long-term degradation modes observed are presented, and possible causes are discussed.

Effects of Jerk Limiting on the Stability of Automated Transit Vehicles

In this paper a method is presented for estimating the effects of jerk limiting on the stability of the longitudinal dynamic response of automated transit vehicles.

Effects of parameter variations and sensor noise on the longitudinal dynamic response of automated guideway transit vehicles

Experience with existing automated guideway transit (AGT) vehicles has shown that variations in vehicle parameters can significantly affect dynamic response. A study is presented of the magnitude of headway errors resulting from variations in parameters such as mass, tire radius, and propulsion and control system gains. In addition, the effects of sensor bias and noise on dynamic response is determined. A typical rubber-tired, electrically-powered AGT vehicle operating at moderate speeds (15 m/s) and headways (15 s) is modeled for the purpose of establishing numerical estimates of headway errors. This vehicle model is based on the Morgantown, West Virginia AGT system.