Showing papers on "Inertia published in 2011"

A novel particle swarm optimization algorithm with adaptive inertia weight

Abstract: Particle swarm optimization (PSO) is a stochastic population-based algorithm motivated by intelligent collective behavior of some animals. The most important advantages of the PSO are that PSO is easy to implement and there are few parameters to adjust. The inertia weight (w) is one of PSO's parameters originally proposed by Shi and Eberhart to bring about a balance between the exploration and exploitation characteristics of PSO. Since the introduction of this parameter, there have been a number of proposals of different strategies for determining the value of inertia weight during a course of run. This paper presents the first comprehensive review of the various inertia weight strategies reported in the related literature. These approaches are classified and discussed in three main groups: constant, time-varying and adaptive inertia weights. A new adaptive inertia weight approach is also proposed which uses the success rate of the swarm as its feedback parameter to ascertain the particles' situation in the search space. The empirical studies on fifteen static test problems, a dynamic function and a real world engineering problem show that the proposed particle swarm optimization model is quite effective in adapting the value of w in the dynamic and static environments.

Inertia Weight strategies in Particle Swarm Optimization

Abstract: Particle Swarm Optimization is a popular heuristic search algorithm which is inspired by the social learning of birds or fishes. It is a swarm intelligence technique for optimization developed by Eberhart and Kennedy [1] in 1995. Inertia weight is an important parameter in PSO, which significantly affects the convergence and exploration-exploitation trade-off in PSO process. Since inception of Inertia Weight in PSO, a large number of variations of Inertia Weight strategy have been proposed. In order to propose one or more than one Inertia Weight strategies which are efficient than others, this paper studies 15 relatively recent and popular Inertia Weight strategies and compares their performance on 05 optimization test problems.

Adaptive Sliding Mode Control for Attitude Stabilization With Actuator Saturation

Abstract: The problem of attitude stabilization for a spacecraft system which is nonlinear in dynamics with inertia uncertainty and external disturbance is investigated in this paper. An adaptive law is applied to estimate the disturbances, where a sliding mode controller is designed to force the state variables of the closed-loop system to converge to the origin. Then, the spacecraft system subjected to control constraints is further considered, and another adaptive sliding mode control law is designed to achieve the attitude stabilization. No prior knowledge of inertia moment is required for both of the proposed adaptive control laws, which implies that the designed control schemes can be applied in spacecraft systems with a large parametric uncertainty existing in inertial matrix or even in unknown inertial matrix. Also, simulation results are presented to illustrate the effectiveness of the control strategies.

Resonances arising from hydrodynamic memory in Brownian motion

Abstract: In Brownian motion, a particle's movement is driven by rapid collisions with the surrounding solvent molecules; this thermal force is assumed to be random and characterized by a Gaussian white noise spectrum. Friction between the particle and the viscous solvent damps its motion. However, the displaced fluid acts back on the particle, giving rise to a hydrodynamic 'memory' and thermal forces with a coloured noise spectrum. Direct experimental observation of a coloured spectrum has proved difficult. Sylvia Jeney and colleagues now report clear evidence for it in measurements of the Brownian fluctuations of a microsphere in a strong optical trap. They anticipate that such details in thermal noise could be exploited for the development of new types of sensors and particle-based assays in lab-on-a-chip applications. Observation of the Brownian motion of a small probe interacting with its environment provides one of the main strategies for characterizing soft matter1,2,3,4. Essentially, two counteracting forces govern the motion of the Brownian particle. First, the particle is driven by rapid collisions with the surrounding solvent molecules, referred to as thermal noise. Second, the friction between the particle and the viscous solvent damps its motion. Conventionally, the thermal force is assumed to be random and characterized by a Gaussian white noise spectrum. The friction is assumed to be given by the Stokes drag, suggesting that motion is overdamped at long times in particle tracking experiments, when inertia becomes negligible. However, as the particle receives momentum from the fluctuating fluid molecules, it also displaces the fluid in its immediate vicinity. The entrained fluid acts back on the particle and gives rise to long-range correlations5,6. This hydrodynamic ‘memory’ translates to thermal forces, which have a coloured, that is, non-white, noise spectrum. One hundred years after Perrin’s pioneering experiments on Brownian motion7,8,9, direct experimental observation of this colour is still elusive10. Here we measure the spectrum of thermal noise by confining the Brownian fluctuations of a microsphere in a strong optical trap. We show that hydrodynamic correlations result in a resonant peak in the power spectral density of the sphere’s positional fluctuations, in strong contrast to overdamped systems. Furthermore, we demonstrate different strategies to achieve peak amplification. By analogy with microcantilever-based sensors11,12, our results reveal that the particle–fluid–trap system can be considered a nanomechanical resonator in which the intrinsic hydrodynamic backflow enhances resonance. Therefore, instead of being treated as a disturbance, details in thermal noise could be exploited for the development of new types of sensor and particle-based assay in lab-on-a-chip applications13,14.

Nonlinear inertia weight variation for dynamic adaptation in particle swarm optimization

Abstract: A nonlinear inertia weight variation for dynamic adaptation in particle swarm optimization (NDWPSO) was presented to solve the problem that it easily stuck at a local minimum point and its convergence speed is slow, when the linear decreasing inertia weight PSO (LDWPSO) adapt to the complex nonlinear optimization process. The rate of particle evolution changing was introduced in this new algorithm and the inertia weight was formulated as a function of this factor according to its impact on the search performance of the swarm. In each iteration process, the weight was changed dynamically based on the current rate of evolutionary changing value, which provides the algorithm with effective dynamic adaptability. The algorithm of LDWPSO and NDWPSO were tested with three benchmark functions. The experiments show that the convergence speed of NDWPSO is significantly superior to LDWPSO, and the convergence accuracy is improved.

Design of an active one-degree-of-freedom lower-limb exoskeleton with inertia compensation

Abstract: Limited research has been done on exoskeletons to enable faster movements of the lower extremities. An exoskeleton’s mechanism can actually hinder agility by adding weight, inertia and friction to the legs; compensating inertia through control is particularly difficult due to instability issues. The added inertia will reduce the natural frequency of the legs, probably leading to lower step frequency during walking. We present a control method that produces an approximate compensation of an exoskeleton’s inertia. The aim is making the natural frequency of the exoskeleton-assisted leg larger than that of the unaided leg. The method uses admittance control to compensate for the weight and friction of the exoskeleton. Inertia compensation is emulated by adding a feedback loop consisting of low-pass filtered acceleration multiplied by a negative gain. This gain simulates negative inertia in the low-frequency range. We tested the controller on a statically supported, single-degree-of-freedom exoskeleton that assists swing movements of the leg. Subjects performed movement sequences, first unassisted and then using the exoskeleton, in the context of a computer-based task resembling a race. With zero inertia compensation, the steady-state frequency of the leg swing was consistently reduced. Adding inertia compensation enabled subjects to recover their normal frequency of swing.

Efficient formulation for dynamics of corotational 2D beams

Abstract: The corotational method is an attractive approach to derive non-linear finite beam elements. In a number of papers, this method was employed to investigate the non-linear dynamic analysis of 2D beams. However, most of the approaches found in the literature adopted either a lumped mass matrix or linear local interpolations to derive the inertia terms (which gives the classical linear and constant Timoshenko mass matrix), although local cubic interpolations were used to derive the elastic force vector and the tangent stiffness matrix. In this paper, a new corotational formulation for dynamic nonlinear analysis is presented. Cubic interpolations are used to derive both the inertia and elastic terms. Numerical examples show that the proposed approach is more efficient than using lumped or Timoshenko mass matrices.

On the stationary macroscopic inertial effects for one phase flow in ordered and disordered porous media

Abstract: We report on the controversial dependence of the inertial correction to Darcy’s law upon the filtration velocity (or Reynolds number) for one-phase Newtonian incompressible flow in model porous media. Our analysis is performed on the basis of an upscaled form of the Navier-Stokes equation requiring the solution of both the micro-scale flow and the associated closure problem. It is carried out with a special focus on the different regimes of inertia (weak and strong inertia) and the crossover between these regimes versus flow orientation and structural parameters, namely porosity and disorder. For ordered structures, it is shown that (i) the tensor involved in the expression of the correction is generally not symmetric, despite the isotropic feature of the permeability tensor. This is in accordance with the fact that the extra force due to inertia exerted on the structure is not pure drag in the general case; (ii) the Forchheimer type of correction (which strictly depends on the square of the filtration velocity) is an approximation that does not hold at all for particular orientations of the pressure gradient with respect to the axes of the structure; and (iii) the weak inertia regime always exists as predicted by theoretical developments. When structural disorder is introduced, this work shows that (i) the quadratic dependence of the correction upon the filtration velocity is very robust over a wide range of the Reynolds number in the strong inertia regime; (ii) the Reynolds number interval corresponding to weak inertia, that is always present, is strongly reduced in comparison to ordered structures. In conjunction with its relatively small magnitude, it explains why this weak inertia regime is most of the time overlooked during experiments on natural media. In all cases, the Forchheimer correction implies that the permeability is different from the intrinsic one.

A Review of Tilting Pad Bearing Theory

Abstract: A theoretical basis for static and dynamic operation of tilting pad journal bearings (TPJBs) has evolved over the last 50 years. Originally demonstrated by Lund using the pad assembly method and a classic Reynolds equation solution, the current state of the art includes full thermoelastohydrodynamic solutions of the generalized Reynolds equation that include fluid convective inertia effects, pad motions; and thermal and mechanical deformations of the pads and shaft. The development of TPJB theory is reviewed, emphasizing dynamic modeling. The paper begins with the early analyses of fixed geometry bearings and continues to modern analyses that include pad motion and stiffness and damping effects. The development of thermohydrodynamic, thermoelastohydrodynamic, and bulk-flow analyses is reviewed. The theories of TPJB dynamics, including synchronous and nonsynchronous models, are reviewed. A discussion of temporal inertia effects in tilting pad bearing is considered. Future trends are discussed, and a path for experimental verification is proposed.

Stretching liquid bridges with moving contact lines: The role of inertia

Abstract: Liquid bridges with moving contact lines are found in a variety of settings such as capillary feeders and high-speed printing. Although it is often assumed that the length scale for these flows is small enough that inertial effects can be neglected, this is not the case in certain applications. To address this issue, we solve the Navier-Stokes equations with the finite element method for the stretching of a liquid drop between two surfaces for non-zero Reynolds numbers. We consider an axisymmetric liquid bridge between a moving flat plate and either a stationary flat plate or a cavity. The contact lines are allowed to slip, and we evaluate the effect of the Reynolds number and contact angles on the transfer of liquid to the moving plate. In the case of two flat plates, we find that inertia forces the interface to map onto a similarity solution in a manner that shifts the breakup point toward the more wettable surface. Inertia and wettability are thus competing effects, with inertia driving fluid toward th...

Magnetization Dynamics, Gyromagnetic Relation, and Inertial Effects

Abstract: The gyromagnetic relation - i.e. the proportionality between the angular momentum $\vec L$ (defined by an inertial tensor) and the magnetization $\vec M$ - is evidence of the intimate connections between the magnetic properties and the inertial properties of ferromagnetic bodies. However, inertia is absent from the dynamics of a magnetic dipole (the Landau-Lifshitz equation, the Gilbert equation and the Bloch equation contain only the first derivative of the magnetization with respect to time). In order to investigate this paradoxical situation, the lagrangian approach (proposed originally by T. H. Gilbert) is revisited keeping an arbitrary nonzero inertial tensor. A dynamic equation generalized to the inertial regime is obtained. It is shown how both the usual gyromagnetic relation and the well-known Landau-Lifshitz-Gilbert equation are recovered at the kinetic limit, i.e. for time scales above the relaxation time $\tau$ of the angular momentum.

Terahertz wave propagation in uniform nanorods: A nonlocal continuum mechanics formulation including the effect of lateral inertia

Abstract: The dynamic testing of materials and components often involves predicting the propagation of stress waves in slender rods. The present work deals with the analysis of the wave propagation characteristics of nanorods. The nonlocal elasticity theory and also the lateral inertia are incorporated into classical/local rod model to capture unique features of the nanorods under the umbrella of continuum mechanics theory. The strong effect of the nonlocal scale has been obtained which leads to substantially different wave behaviors of nanorods from those of macroscopic rods. Nonlocal rod/bar model is developed for nanorods including the lateral inertia effects. The analysis shows that the wave characteristics are highly over estimated by the classical rod model, which ignores the effect of small-length scale. The wave propagation properties of the nanorod obtained from the present formulations are compared with the continuum rod model, nonlocal second and fourth order strain gradient models, Born-K a ´ rm a ´ n model and the nonlocal stress gradient model. It has also been shown that, the unstable second order strain gradient model can be replaced by considering the inertia gradient terms in the formulations. The effects of both the nonlocal scale and the diameter of the nanorod on spectrum curves are highlighted in the present manuscript. The results provided in this article are useful guidance for the study and design of the next generation of nanodevices that make use of the wave propagation properties of single-walled carbon nanotubes.

Accounting for Inertia in Modal Choices: Some New Evidence Using RP/SP Data Set

Abstract: Inertia measures the effect that experiences in previous periods have on the current choice. As such it measures the tendency of sticking with the past choice or the disposition to change, when some alternative becomes particularly appealing. At the same time new situations force individuals to rethink about their choice and new preferences are formed. A learning process begins that release the effect of inertia in the current choice. In this paper the authors use a mixed dataset of revealed preference (RP)-stated preference (SP) to study the effect of inertia between RP and SP observations and to study if inertia is stable along the SP experiments. Inertia has extensively been studied with panel dataset but only few works used RP/SP dataset. In this paper the authors extend these previous works in several ways. The authors test and compare several ways of measuring inertia, including measures that have been proposed to test inertia in both short and long RP panel dataset. The authors explore some new measures of inertia to test for the effect of learning along the SP experiment and we disentangle this later effect from the pure inertia effect. A mixed logit model is used that allows us to account for both systematic and random variation in the inertia effect and for correlations among RP and SP observations. Finally the authors explore the relation between the utility specification (especially in the SP dataset) and the role of the inertia in explaining current choices.

Series Viscoelastic Actuators Can Match Human Force Perception

Abstract: Series elastic actuators (SEAs) are frequently used for force control in haptic interaction, because they decouple actuator inertia from the end effector by a compliant element. This element is usually a metal spring or beam, where the static force-deformation relationship offers a cheap force sensor. For high-precision force control, however, the remaining small inertia of this elastic element and of the end effector still limit the sensing performance and rendering transparency. Here, we extend the concept to deformable end effectors manufactured of viscoelastic materials. These materials offer the advantage of extremely low mass at high maximum deformation and applicable load. However, force and deformation are no longer statically related, and history of force and deformation has to be accounted for. We describe an observer-based solution, which allows drift-free force measurement with high accuracy and precision. Although the description of the viscoelastic behavior involves higher-order derivatives, the proposed observer does not require any numerical differentiation. This new integrated concept of sensing and actuation, called series viscoelastic actuator (SVA), is applied to our high-precision haptic device OSVALD, which is targeted at perception experiments that require sensing and rendering of forces in the range of the human tactile threshold. User-device interaction force is controlled using state-of-the-art control strategies of SEAs. Force estimation and force control performance are evaluated experimentally and prove to be compatible with the intended applications, showing that SVAs open up new possibilities for the use of series compliance and damping in high-precision haptic interfaces.

A falling cloud of particles at a small but finite Reynolds number

Abstract: Through a comparison between experiments and numerical simulations, we have examined the dynamics of a cloud of spheres at a small but finite Reynolds number. The cloud is seen to flatten and to transition into a torus, which further widens and eventually breaks up into droplets. While this behaviour bears some similarity to that observed at zero inertia, the underlying physical mechanisms differ. Moreover, the evolution of the cloud deformation is accelerated as inertia is increased. Two inertial regimes in which macro-scale inertia and micro-scale inertia become successively dominant are clearly identified.

Virtual inertia control of DFIG-based wind turbines for dynamic grid frequency support

Abstract: This paper investigates virtual inertia control of doubly fed induction generator (DFIG)-based wind turbines to provide dynamic frequency support in the event of abrupt power change. The model and control scheme of the DFIG is analysed. The relationships among the virtual inertia, the rotor speed and the network frequency variation are then investigated. The "hidden" kinetic energy that can be released to contribute to the grid inertia by means of shifting the operating point from the maximum power tracking curve to a virtual inertia control curve is investigated. The virtual inertia control strategy based on shifting power tracking curves of the DFIG is proposed and the calculation method for determining these virtual inertia control curves is presented. A three-machine system with 20 percent of wind penetration is used to validate the proposed control strategy. Simulation results show that by the proposed control strategy, DFIG based wind farms have the capability of providing dynamic frequency support to frequency deviation, and thus improving the dynamic frequency performance of the grid with high wind power penetration. (6 pages)

Analysis of the swimming of microscopic organisms

Abstract: Large objects which propel themselves in air or water make use of inertia in the surrounding fluid. The propulsive organ pushes the fluid backwards, while the resistance of the body gives the fluid a forward momentum. The forward and backward momenta exactly balance, but the propulsive organ and the resistance can be thought about as acting separately. This conception cannot be transferred to problems of propulsion in microscopic bodies for which the stresses due to viscosity may be many thousands of times as great as those due to inertia. No case of self-propulsion in a viscous fluid due to purely viscous forces seems to have been discussed. The motion of a fluid near a sheet down which waves of lateral displacement are propagated is described. It is found that the sheet moves forwards at a rate 2π 2 b 2 /λ 2 times the velocity of propagation of the waves. Here b is the amplitude and λ the wave-length. This analysis seems to explain how a propulsive tail can move a body through a viscous fluid without relying on reaction due to inertia. The energy dissipation and stress in the tail are also calculated. The work is extended to explore the reaction between the tails of two neighbouring small organisms with propulsive tails. It is found that if the waves down neighbouring tails are in phase very much less energy is dissipated in the fluid between them than when the waves are in opposite phase. It is also found that when the phase of the wave in one tail lags behind that in the other there is a strong reaction, due to the viscous stress in the fluid between them, which tends to force the two wave trains into phase. It is in fact observed that the tails of spermatozoa wave in unison when they are close to one another and pointing the same way.

Accounting for inertia in modal choices: some new evidence using a RP/SP dataset

Abstract: Inertia is related with effect that experiences in previous periods may have on the current choice. In particular, it has to do with the tendency to stick with the past choice even when another alternative becomes more appealing. As new situations force individuals to rethink about their choices new preferences may be formed. Thus a learning process begins that relaxes the effect of inertia in the current choice. In this paper we use a mixed dataset of revealed preference (RP)-stated preference (SP) to study the effect of inertia between RP and SP observations and to study if the inertia effect is stable along the SP experiments. Inertia has been studied more extensively with panel datasets, but few investigations have used RP/SP datasets. In this paper we extend previous work in several ways. We test and compare several ways of measuring inertia, including measures that have been proposed for both short and long RP panel datasets. We also explore new measures of inertia to test for the effect of “learning” (in the sense of acquiring experience or getting more familiar with) along the SP experiment and we disentangle this effect from the pure inertia effect. A mixed logit model is used that allows us to account for both systematic and random taste variations in the inertia effect and for correlations among RP and SP observations. Finally we explore the relation between the utility specification (especially in the SP dataset) and the role of inertia in explaining current choices.

In-Orbit Estimation of Inertia and Momentum-Actuator Alignment Parameters

Abstract: Knowledge of the mass distribution and momentum actuator-alignment parameters of a spacecraft is vital to the control of its attitude motion. The difficulty of measuring the complete set of these quantities before launch, along with the potential for changes in the spacecraft mass distribution during operations, suggests the utility of estimating these parameters in orbit from available telemetry data. This paper develops a series of possible onboard parameter estimation schemes based onmeasurement equations describing the angularmomentum and kinetic energy states of the rigid-body system. The performance of the algorithms is compared over both a simulated maneuver and a series of data sets from the MESSENGER spacecraft.

Energy and momentum of a spherically symmetric dilaton frame as regularized by teleparallel gravity

Abstract: We calculate energy and momentum of a spherically symmetric dilaton frame using the gravitational energy-momentum 3-form within the tetrad formulation of general relativity (GR). The frame we use is characterized by an arbitrary function ϒ with the help of which all the previously found solutions can be reproduced. We show how the effect of inertia (which is mainly reproduced from ϒ) makes the total energy and momentum always different from the well known result when we use the Riemannian connection . On the other hand, when use is made of the covariant formulation of teleparallel gravity, which implies to take into account the pure gauge connection, teleparallel gravity always yields the physically relevant result for the energy and momentum.

Increasing the critical time step: micro-inertia, inertia penalties and mass scaling

Abstract: Explicit time integration is a popular method to simulate the dynamical behaviour of a system. Unfortunately, explicit time integration is only conditionally stable: the time step must be chosen not larger than the so-called "critical time step", otherwise the numerical solution may become unstable. To reduce the CPU time needed to carry out simulations, it is desirable to explore methods that increase the critical time step, which is the main objective of our paper. To do this, first we discuss and compare three approaches to increase the critical time step: micro-inertia formulations from continuum mechanics, inertia penalties which are used in computational mechanics, and mass scaling techniques that are mainly used in structural dynamics. As it turns out, the similarities between these methods are significant, and in fact they are identical in 1D if linear finite elements are used. This facilitates interpretation of the additional parameters in the various methods. Next, we derive, for a few simple finite element types, closed-form expressions for the critical time step with micro-structural magnification factors. Finally, we discuss computational overheads and some implementational details.

The structural safety assessment of a tie-down system on a tension leg platform during hurricane events

Abstract: 【The performance of a rig tie-down system on a TLP (Tension Leg Platform) is investigated for 10-year, 100-year, and 1000-year hurricane environments. The inertia loading on the derrick is obtained from the three-hour time histories of the platform motions and accelerations, and the dynamic wind forces as well as the time-dependent heel-induced gravitational forces are also applied. Then, the connection loads between the derrick and its substructure as well as the substructure and deck are obtained to assess the safety of the tie-down system. Both linear and nonlinear inertia loads on the derrick are included. The resultant external forces are subsequently used to calculate the loads on the tie-down clamps at every time step with the assumption of rigid derrick. The exact dynamic equations including nonlinear terms are used with all the linear and second-order wave forces considering that some dynamic contributions, such as rotational inertia, centripetal forces, and the nonlinear excitations, have not been accounted for in the conventional engineering practices. From the numerical simulations, it is seen that the contributions of the second-order sum-frequency (or springing) accelerations can be appreciable in certain hurricane conditions. Finally, the maximum reaction loads on the clamps are obtained and used to check the possibility of slip, shear, and tensile failure of the tie-down system for any given environment.】

A Study of Inertia Relief Analysis

Abstract: [] Inertia relief analysis is regarded as an effective technique for the modeling of unconstrained structural systems. In this paper the principle of inertia relief analysis is first described. Inertia relief capability of commercial finite element packages is discussed. The paper studies the implementation of inertia relief techniques into finite element analysis of a variety of structures. Two types of inertia relief methods of MSC/NASTRAN (conventional inertia relief and automatic inertia relief) are also addressed. The application of inertia relief method in the analysis of unbalanced and balanced structural systems is discussed. I. Introduction The technique of inertia relief has been a well-known approach for the analysis of unsupported systems such as air vehicles in flight, automotives in motion, or satellites in space. The sum of forces and moments are calculated and applied to achieve an equilibrium state in inertia relief analysis. Inertia relief was applied to calculate load redistribution in a helicopter rotor support structure due to flight load imbalances [1]. Inertia relief allowed for the analysis of free structures in space instead of conventional approach of grounding fuselage to landing gears. The finite element model was built with MSC/NASTRAN and the aircraft center of gravity was chosen to be the reference point for inertia relief analysis. Inertia relief method was employed to determine the distribution of nonlinear internal forces in aircrafts by counterbalancing rotor hub loads [2]. Inertia relief was also used to estimate impact loads of a space frame structure composed of welded tubular elements [3]. In order to obtain accurate inertia relief calculation, the periods of applied loads should be much greater than the periods of rigid body modes restrained. Inertia relief was used to balance externally applied forces on a free-flying solar sail [4]. The inertia loads were developed under steady-state rigid body acceleration and the center of mass of the solar sail was selected as the reference point for inertia relief calculation. The finite element model was constructed using ABAQUS and geometric nonlinearity was considered. Moreover, inertia relief method was employed to analyze aeroelasticity of non-rigid airships [5]. Airship nonlinearity was introduced due to large deformations and nonlinear material behavior of envelope membranes. Pagaldipti’s work showed that inertia relief effect had influence on optimal structural designs [6]. The selected constraints for inertia relief calculation eliminated rigid body motions and didn’t generate associated constraint forces while actual structural supports had constraint forces. Thus, the topology optimization was different for the case with inertia relief effects in comparison with the case without inertia relief. The presence of concentrated masses in structural systems with rigid body modes significantly altered load distribution. The implementation of sensitivity correction corresponding to inertia relief load vectors correction is an essential step in optimization procedure. Although inertia relief approach has been widely employed in the simulation of unconstrained aircrafts and space vehicles, the published work has rarely been found. There is still lack of research on inertia relief analysis of diverse types of basic structures and critical structural considerations associated with inertia relief calculation. In this paper, inertia relief method is applied to analyze a variety of structures including spring-mass structures, truss structures, plate structures, and etc. The work is aimed to study various key issues associated with inertia relief analysis, such as conventional inertia relief and automatic inertia relief, the effect of constraints and mass distribution on inertia relief calculation, the accuracy of inertia relief, and critical considerations. Commercial finite element program MSC/NASTRAN is applied to generate numerical results.

Modelling of condensed flexible bodies considering non-linear inertia effects resulting from gross motions

Abstract: Besides various other application fields, flexible multi-body dynamics simulation is used in particular during the development process of internal combustion engines and power units. Problems such as crankshaft and engine dynamics, radial slider bearing dynamics or noise, vibration, and harshness can be investigated using this methodology. Any specific engine component, called body, can be represented by different methods. Besides beam-mass representations and structured modelling, finite element models are commonly used. As these imply a large number of degrees of freedom, they cannot be applied directly to multi-body dynamics ensuring computational performance. Therefore, condensation methods need to be applied which result in a reduced model with equivalent dynamical properties. This is particularly important if detailed, highly non-linear contact dynamic models, for instance the well-known Reynolds equation, are considered.Typically, condensation methods are applied to structural matrices of bodies wh...