Periodic Steady State Response of Complex Vehicle Models Using Multi-Level Substructuring

2007 ◽  
Author(s):  
I. Stavrakis ◽  
C. Theodosiou ◽  
S. Natsiavas
Keyword(s):  
Nonlinear Models ◽  
Equations Of Motion ◽  
Response Spectra ◽  
Computationally Efficient ◽  
Sparsity Pattern ◽  
Strongly Nonlinear ◽  
Road Excitation ◽  
Multi Level ◽  
Set Up ◽  
Coordinate Reduction

A systematic methodology is presented for investigating long term ride dynamics of large order vehicle models in a computationally efficient way. First, the equations of motion for each of the main structural components of the vehicle are set up by applying the finite element method. As a consequence of the geometric complexity of these components, the number of the resulting equations is so high that the classical coordinate reduction methodologies become numerically ineffective to apply. In addition, the composite model possesses strongly nonlinear characteristics. However, the method applied overcomes some of these difficulties by imposing a multi-level substructuring procedure, based on the sparsity pattern of the stiffness matrix. In this way, the number of the equations of motion of the complete system is substantially reduced. Subsequently, this allows the application of appropriate numerical methodologies for predicting response spectra of the nonlinear models to periodic road excitation. Results obtained by direct integration of the equations of motion are also presented. Where possible, the accuracy and validity of the applied methodology is verified by comparison with results obtained for the original models.

Ride Dynamics of Nonlinear Vehicle Models Using Component Mode Synthesis

2002 ◽  
Vol 124 (3) ◽  
pp. 427-434 ◽  
Author(s):  
G. Verros ◽  
S. Natsiavas
Keyword(s):  
Nonlinear Models ◽  
Equations Of Motion ◽  
Original System ◽  
Response Spectra ◽  
Component Mode Synthesis ◽  
Computationally Efficient ◽  
Strongly Nonlinear ◽  
Shock Absorbers ◽  
Road Excitation ◽  
Set Up

A general methodology is presented for investigating ride dynamics of large order vehicle models in a systematic and computationally efficient way. First, the equations of motion of representative vehicle models are set up by applying classical finite element techniques. In the simplest version of these models, the important system parameters are assumed to be constant, leading to linear formulations. Then, more accurate and involved models are examined by including typical nonlinearities in the tires and the shock absorbers of the vehicle suspension. Also, emphasis is placed on taking into account the possibility of temporary separation of a wheel from the ground. These models are strongly nonlinear and as their order increases the existing numerical methodologies for a systematic determination of their dynamics become inefficient to apply. Therefore, the first step of the present methodology is to reduce the dimensions of the original system by applying a component mode synthesis approach. Subsequently, this allows the application of appropriate numerical methodologies for predicting response spectra of the nonlinear models to periodic road excitations. Finally, results obtained by direct integration of the equations of motion are also presented for transient road excitation. In all cases, the accuracy and validity of the applied methodology is verified by comparison with results obtained for the original models.

Long Term Ride Dynamics of Large Order Vehicle Models With Nonlinear Suspension

2005 ◽  
Author(s):  
P. Metallidis ◽  
I. Stavrakis ◽  
G. Verros ◽  
S. Natsiavas
Keyword(s):  
Nonlinear Models ◽  
Equations Of Motion ◽  
Original System ◽  
Response Spectra ◽  
Computationally Efficient ◽  
Large Order ◽  
Composite Models ◽  
Road Excitation ◽  
Set Up

This work presents a systematic methodology for investigating long term ride dynamics of large order vehicle models in a computationally efficient way. First, the equations of motion for each of the main structural components of the vehicle are set up by applying finite element techniques. The resulting composite models possess strongly nonlinear characteristics and as their order increases the existing numerical methodologies for a systematic determination of their dynamics become inefficient to apply. Therefore, the first step of the present methodology is to reduce the dimensions of the original system by applying a suitable component mode synthesis approach. Subsequently, this allows the application of appropriate numerical methodologies for predicting response spectra of the nonlinear models to periodic road excitation. Results obtained by direct integration of the equations of motion are also presented. The accuracy and validity of the applied methodology is verified by comparison with results obtained for the original models. The frequency ranges examined are useful for studies referring to both ride and acoustics response of the vehicle.

Dynamics of Semi-Actively Controlled Vehicles Involving Wheel Hop

2001 ◽  
Author(s):  
G. Verros ◽  
S. Natsiavas
Keyword(s):  
Control Strategy ◽  
Nonlinear Models ◽  
Control Strategies ◽  
Damping Ratio ◽  
Equations Of Motion ◽  
Response Spectra ◽  
Shock Absorbers ◽  
Road Excitation ◽  
Active Control Strategy ◽  
Synthesis Approach

Abstract The present study investigates dynamic response of vehicle models, subjected to road excitation. In these models, a semi-active control strategy is applied on the suspension dampers, which is based on a switch of their damping coefficient between different values, so that the resulting system approximates the performance of a vehicle involving sky-hook damping. An alternative control strategy is also applied, which is passive and is based on selecting a different damping ratio when the wheel velocity relative to the car body is positive or negative. Both of these control strategies lead to oscillator models with parameter discontinuities. Similar terms are also introduced into the equations of motion by considering wheel hop phenomena, where a vehicle wheel leaves the ground temporarily. First, simple quarter-car models are examined but the analysis is also applied to more complicated models. For these models, their dimensions are reduced substantially by applying a component mode synthesis approach. Subsequently, this allows the efficient application of appropriate methodologies for predicting response spectra of the nonlinear models to periodic road excitation. Finally, results obtained by direct integration of the equations of motion are also presented for transient road excitation. In all cases, the results are compared to those obtained for vehicles with suspensions including passive shock absorbers. Moreover, special consideration is given to cases where wheel hop is possible to occur.

Design Optimization of Quarter-car Models with Passive and Semi-active Suspensions under Random Road Excitation

2005 ◽  
Vol 11 (5) ◽  
pp. 581-606 ◽  
Author(s):  
G. Verros ◽  
S. Natsiavas ◽  
C. Papadimitriou
Keyword(s):  
Equations Of Motion ◽  
Damping Coefficient ◽  
Active Suspensions ◽  
Vehicle Performance ◽  
Strongly Nonlinear ◽  
Suspension Parameters ◽  
Shock Absorbers ◽  
Road Excitation ◽  
Quarter Car ◽  
Definition Of

A methodology is presented for optimizing the suspension damping and stiffness parameters of nonlinear quarter-car models subjected to random road excitation. The investigation starts with car models involving passive damping with constant or dual-rate characteristics. Then, we also examine car models where the damping coefficient of the suspension is selected so that the resulting system approximates the performance of an active suspension system with sky-hook damping. For the models with semi-active or passive dual-rate dampers, the value of the equivalent suspension damping coefficient is a function of the relative velocity of the sprung mass with respect to the wheel subsystem. As a consequence, the resulting equations of motion are strongly nonlinear. For these models, appropriate methodologies are first employed for obtaining the second moment characteristics of motions resulting from roads with a random profile. This information is next utilized in the definition of a vehicle performance index, which is optimized to yield representative numerical results for the most important suspension parameters. Special attention is paid to investigating the effect of road quality as well as on examining effects related to wheel hop. Finally, a critical comparison is performed between the results obtained for vehicles with passive linear or bilinear suspension dampers and those obtained for cars with semi-active shock absorbers.

Dynamics of Large Scale Mechanical Models Using Multilevel Substructuring

2006 ◽  
Vol 2 (1) ◽  
pp. 40-51 ◽  
Author(s):  
C. Papalukopoulos ◽  
S. Natsiavas
Keyword(s):  
Dynamical Systems ◽  
Degrees Of Freedom ◽  
Large Scale ◽  
Equations Of Motion ◽  
Numerical Results ◽  
Ground Vehicles ◽  
Response Characteristics ◽  
Sparsity Pattern ◽  
Mechanical Models ◽  
Set Up

An appropriate substructuring methodology is applied in order to study the dynamic response of very large scale mechanical systems. The emphasis is put on enabling a systematic study of dynamical systems with nonlinear characteristics, but the method is equally applicable to systems possessing linear properties. The accuracy and effectiveness of the methodology are illustrated by numerical results obtained for example vehicle models, having a total number of degrees of freedom lying in the order of a million or even bigger. First, the equations of motion of each component are set up by applying the finite element method. The order of the resulting models is so high that the classical substructuring methodologies become numerically ineffective or practically impossible to apply. However, the method developed overcomes these difficulties by imposing a further, multilevel substructuring of each component, based on the sparsity pattern of the stiffness matrix. In this way, the number of the equations of motion of the complete system is substantially reduced. Consequently, the numerical results presented demonstrate that besides the direct computational savings, this reduction in the dimensions enables the application of numerical codes, which capture response characteristics of dynamical systems sufficiently accurate up to a prespecified level of forcing frequencies. The study concludes by investigating biodynamic response of passenger-seat subsystem models coupled with complex mechanical models of ground vehicles resulting from deterministic or random road excitation.

Near Wall Turbulence Effects on Particle Transport and Deposition in Human Tracheobronchial Multi-Level Bifurcation Model

2015 ◽  
Author(s):  
Amir A. Mofakham ◽  
Lin Tian ◽  
Goodarz Ahmadi
Keyword(s):  
Boundary Conditions ◽  
Particle Deposition ◽  
Flow Simulation ◽  
Tracheobronchial Tree ◽  
Lung Model ◽  
Wall Turbulence ◽  
Nano Particles ◽  
Turbulent Regime ◽  
Computationally Efficient ◽  
Multi Level

Transport and deposition of micro and nano-particles in the upper tracheobronchial tree were analyzed using a multi-level asymmetric lung bifurcation model. The multi-level lung model is flexible and computationally efficient by fusing sequence of individual bifurcations with proper boundary conditions. Trachea and the first two generations of the tracheobronchial airway were included in the analysis. In these regions, the airflow is in turbulent regime due to the disturbances induced by the laryngeal jet. Anisotropic Reynolds stress transport turbulence model (RSTM) was used for mean the flow simulation, together with the enhanced two-layer model boundary conditions. Particular attention is given to evaluate the importance of the “quadratic variation of the turbulent fluctuations perpendicular to the wall” on particle deposition in the upper tracheobroncial airways.

scholarly journals A Multi-Objective Ground Motion Selection Approach Matching the Acceleration and Displacement Response Spectra

2018 ◽  
Vol 10 (12) ◽  
pp. 4659 ◽  
Author(s):  
Yabin Chen ◽  
Longjun Xu ◽  
Xingji Zhu ◽  
Hao Liu
Keyword(s):  
Ground Motion ◽  
Response Spectrum ◽  
Structural Response ◽  
Response Spectra ◽  
Computationally Efficient ◽  
Ground Motion Selection ◽  
Displacement Response ◽  
Rc Frames ◽  
Selection Approach ◽  
Displacement Response Spectra

For seismic resilience-based design (RBD), a selection of recorded time histories for dynamic structural analysis is usually required. In order to make individual structures and communities regain their target functions as promptly as possible, uncertainty of the structural response estimates is in great need of reduction. The ground motion (GM) selection based on a single target response spectrum, such as acceleration or displacement response spectrum, would bias structural response estimates leading significant uncertainty, even though response spectrum variance is taken into account. In addition, resilience of an individual structure is not governed by its own performance, but depends severely on the performance of other systems in the same community. Thus, evaluation of resilience of a community using records matching target spectrum at whole periods would be reasonable because the fundamental periods of systems in the community may be varied. This paper presents a GM selection approach based on a probabilistic framework to find an optimal set of records to match multiple target spectra, including acceleration and displacement response spectra. Two major steps are included in that framework. Generation of multiple sub-spectra from target displacement response spectrum for selecting sets of GMs was proposed as the first step. Likewise, the process as genetic algorithm (GA), evolvement of individuals previously generated, is the second step, rather than using crossover and mutation techniques. A novel technique improving the match between acceleration response spectra of samples and targets is proposed as the second evolvement step. It is proved computationally efficient for the proposed algorithm by comparing with two developed GM selection algorithms. Finally, the proposed algorithm is applied to select GM records according to seismic codes for analysis of four archetype reinforced concrete (RC) frames aiming to evaluate the influence of GM selection considering two design response spectra on structural responses. The implications of design response spectra especially the displacement response spectrum and GM selection algorithm are summarized.

Differential-Geometric Methods in Multibody Dynamics and Control

2005 ◽  
Author(s):  
P. Maißer
Keyword(s):  
Configuration Space ◽  
High Performance ◽  
Multibody System ◽  
Equations Of Motion ◽  
Geometric Approach ◽  
Motion Equations ◽  
Constrained Mechanical Systems ◽  
Dynamics And Control ◽  
Set Up ◽  
Lagrangian Motion

This paper presents a differential-geometric approach to the multibody system dynamics regarded as a point dynamics in a n-dimensional configuration space Rn. This configuration space becomes a Riemannian space Vn the metric of which is defined by the kinetic energy of the multibody system (MBS). Hence, all concepts and statements of the Riemannian geometry can be used to study the dynamics of MBS. One of the key points is to set up the non-linear Lagrangian motion equations of tree-like MBS as well as of constrained mechanical systems, the perturbed equations of motion, and the motion equations of hybrid MBS in a derivative-free manner. Based on this approach transformation properties can be investigated for application in real-time simulation, control theory, Hamilton mechanics, the construction of first integrals, stability etc. Finally, a general Lyapunov-stable force control law for underactuated systems is given that demonstrates the power of the approach in high-performance sports applications.

scholarly journals A Study of the Stability of a Plate-Like Load Towed beneath a Helicopter

1971 ◽  
Vol 13 (5) ◽  
pp. 330-343 ◽  
Author(s):  
D. F. Sheldon
Keyword(s):  
Equations Of Motion ◽  
Physical Parameters ◽  
Recent Experience ◽  
Wind Tunnel Testing ◽  
Stability Derivatives ◽  
Direct Indication ◽  
Metric Dimensions ◽  
Set Up ◽  
The Stability ◽  
Derivative Information

Recent experience has shown that a plate-like load suspended beneath a helicopter moving in horizontal forward flight has unstable characteristics at both low and high forward speeds. These findings have prompted a theoretical analysis to determine the longitudinal and lateral dynamic stability of a suspended pallet. Only the longitudinal stability is considered here. Although it is strictly a non-linear problem, the usual assumptions have been made to obtain linearized equations of motion. The aerodynamic derivative data required for these equations have been obtained, where possible, for the appropriate ranges of Reynolds and Strouhal number by means of static and dynamic wind tunnel testing. The resulting stability equations (with full aerodynamic derivative information) have been set up and solved, on a digital computer, to give direct indication of a stable or unstable system for a combination of physical parameters. These results have indicated a longitudinal unstable mode for all practical forward speeds. Simultaneously the important stability derivatives were found for this instability and modifications were made subsequently in the suspension system to eliminate the instabilities in the longitudinal sense. Throughout this paper, all metric dimensions are given approximately.

Periodic Steady State Response and Fatigue Analysis of a Nonlinear City Bus Model

2009 ◽  
Author(s):  
George Valsamos ◽  
Christos Theodosiou ◽  
Sotirios Natsiavas
Keyword(s):  
Steady State ◽  
Degrees Of Freedom ◽  
Nonlinear Models ◽  
Equations Of Motion ◽  
High Stress ◽  
Direct Determination ◽  
Accurate Information ◽  
Steady State Response ◽  
State Response ◽  
Periodic Steady State

Dynamic response related to fatigue prediction of an urban bus is investigated. First, a quite complete model subjected to road excitation is employed in order to extract sufficiently reliable and accurate information in a fast way. The bus model is set up by applying the finite element method, resulting to an excessive number of degrees of freedom. In addition, the bus suspension units involve nonlinear characterstics. A step towards alleviating this difficulty is the application of an appropriate coordinate transformation, causing a drastic reduction in the dimension of the final set of the equations of motion. This allows the application of a systematic numerical methodology leading to direct determination of periodic steady state response of nonlinear models subjected to periodic excitation. Next, typical results were obtained for excitation resulting from selected urban road profiles. These profiles have either a known form or known statistical properties, expressed by an appropriate spatial power spectral density function. In all cases examined, the emphasis was put on investigating ride response. The main attention was focused on identifying areas of the bus suspension and frame subsystems where high stress levels are developed. This information is based on the idea of a nonlinear transfer function and provides the basis for applying suitable criteria in order to perform analyses leading to prediction of fatigue failure.

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