Dynamic Rocking Response and Optimization of the Nonlinear Suspension of a Railroad Freight Car

1980 ◽  
Vol 102 (1) ◽  
pp. 86-93 ◽  
Author(s):  
M. Samaha ◽  
T. S. Sankar
Keyword(s):  
Equations Of Motion ◽  
Sine Wave ◽  
Optimization Techniques ◽  
Model Accuracy ◽  
Frequency Responses ◽  
Optimum Parameters ◽  
Freight Car ◽  
Six Degree Of Freedom ◽  
Railroad Freight ◽  
Rocking Response

A modified mathematical model of a large capacity railroad freight vehicle is presented. The model for this investigation is constructed in such a way to describe the bounce, sway and rocking modes of the system and also to account for most of the vehicle non-linearity effects. Equations of motion of the six degree of freedom nonlinear model are derived assuming that the excitations from the track in vertical and lateral directions are purely periodic in the form of a rectified sine wave. The solution for the time and frequency responses on digital computer are compared with available measured data to investigate the model accuracy. Multivariable optimization techniques are employed to find the optimum suspension parameters that minimizes the maximum car rocking response over the frequency range of interest. The optimum parameters are presented in different forms either for the existing or for stabilized vehicle configuration.

Calculation of Dynamic Tire Forces from Aircraft Instrumentation Data

2010 ◽  
Vol 38 (3) ◽  
pp. 182-193 ◽  
Author(s):  
Gary E. McKay
Keyword(s):  
System Performance ◽  
Equations Of Motion ◽  
Test Laboratory ◽  
Excellent Correlation ◽  
Friction Behavior ◽  
Aircraft Landing ◽  
Data Scatter ◽  
Tire Forces ◽  
Six Degree Of Freedom ◽  
Tire Friction

Abstract When evaluating aircraft brake control system performance, it is difficult to overstate the importance of understanding dynamic tire forces—especially those related to tire friction behavior. As important as they are, however, these dynamic tire forces cannot be easily or reliably measured. To fill this need, an analytical approach has been developed to determine instantaneous tire forces during aircraft landing, braking and taxi operations. The approach involves using aircraft instrumentation data to determine forces (other than tire forces), moments, and accelerations acting on the aircraft. Inserting these values into the aircraft’s six degree-of-freedom equations-of-motion allows solution for the tire forces. While there are significant challenges associated with this approach, results to date have exceeded expectations in terms of fidelity, consistency, and data scatter. The results show excellent correlation to tests conducted in a tire test laboratory. And, while the results generally follow accepted tire friction theories, there are noteworthy differences.

scholarly journals Seismic Assessment of 10-Story Building Using Tuned Mass Damper

2020 ◽  
Author(s):  
Mohammad Aghajani Delavar
Keyword(s):  
Frequency Tuning ◽  
Damping Ratio ◽  
Equations Of Motion ◽  
Tuned Mass Dampers ◽  
Earthquake Excitation ◽  
Optimum Parameters ◽  
Seismic Records ◽  
Structural Responses ◽  
Lateral Displacements ◽  
Shear Building

In this paper, optimum parameters of Tuned Mass Dampers (TMD) are considered to control the responses of 10-story shear building under harmonic loading and 22 set of seismic records of FEMA-P695. The criterion used to obtain the optimum parameters is to select mass ratio, the frequency (tuning) and damping ratio that would result in smallest lateral displacements. State-space equations of motion are presented to compute the structural responses by developing a MATLAB file. A 10-story shear building is presented as a case study to assess the effects of TMDs on the multi-story structures. The results indicate that using TMD can reduce structural responses up to the average 20% under earthquake excitation and up to 90% under harmonic loadings. TMDs are not always effective under any type of ground motion; therefore, being aware of the given location is significant to design TMDs properly.

Added Fluid Mass and the Equations of Motion of a Parachute

1983 ◽  
Vol 34 (3) ◽  
pp. 226-242 ◽  
Author(s):  
John A. Eaton
Keyword(s):  
Equations Of Motion ◽  
Added Mass ◽  
Unsteady Forces ◽  
Fluid Mass ◽  
Mass Tensor ◽  
Body Shapes ◽  
The Stability ◽  
External Forces ◽  
Six Degree Of Freedom ◽  
Nonlinear Solutions

SummaryWhile it has long been known that added fluid mass may be important in the dynamics of parachutes, due to inadequate or incorrect derivation and/or implementation of the added mass tensor its full significance in the stability of parachutes has yet to be appreciated. The concept of added mass is outlined and some general conditions for its significance are presented. Its implementation in the parachute equations of motion is reviewed, and the equations used in previous treatments are shown to be erroneous. A general method for finding the equivalent external forces and moments due to added mass is given, and the correct, anisotropic forms of the added mass tensor are derived for the six degree-of-freedom motion in an ideal fluid of rigid body shapes with planar-, twofold- and axisymmetry, These derivations may also be useful in dynamic stability studies of other low relative density bodies such as airships, balloons, submarines and torpedoes. Full nonlinear solutions of the equations of motion for the axisymmetric parachute have been obtained, and results indicate that added mass effects are more significant than previously predicted. In particular, the component of added mass along the axis of symmetry has a strong influence on stability. Better data on unsteady forces and moments on parachutes are needed.

Nonlinear Transverse Vibration of a Hyperelastic Beam Under Harmonically Varying Axial Loading

2021 ◽  
Vol 16 (3) ◽  
Author(s):  
Yuanbin Wang ◽  
Weidong Zhu
Keyword(s):  
Governing Equation ◽  
Transverse Vibration ◽  
Harmonic Balance ◽  
Fourier Transforms ◽  
Multiple Scales ◽  
Equations Of Motion ◽  
Multiple Scales Method ◽  
Frequency Responses ◽  
Runge Kutta ◽  
Nonlinear Transverse Vibration

Abstract Nonlinear transverse vibration of a hyperelastic beam under a harmonically varying axial load is analyzed in this work. Equations of motion of the beam are derived via the extended Hamilton's principle, where transverse vibration is coupled with longitudinal vibration. The governing equation of nonlinear transverse vibration of the beam is obtained by decoupling the equations of motion. By applying the Galerkin method, the governing equation transforms to a series of nonlinear ordinary differential equations (ODEs). Response of the beam is obtained via three different methods: the Runge–Kutta method, multiple scales method, and harmonic balance method. Time histories, phase-plane portraits, fast Fourier transforms (FFTs), and amplitude–frequency responses of nonlinear transverse vibration of the beam are obtained. Comparison of results from the three methods is made. Results from the multiple scales method are in good agreement with those from the harmonic balance and Runge–Kutta methods when the amplitude of vibration is small. Effects of the material parameter and geometrical parameter of the beam on its amplitude–frequency responses are analyzed.

A Simulation Research for Railroad Freight Car-to-Car End Impact Based on Numerical Analysis

2015 ◽  
Vol 764-765 ◽  
pp. 1020-1025 ◽  
Author(s):  
Meng Qi Ma ◽  
Fang Ping Lei ◽  
Yu Qiao Ren ◽  
Bai Song Mu
Keyword(s):  
Numerical Analysis ◽  
Kinematic Model ◽  
Kutta Method ◽  
Simulation Research ◽  
Runge Kutta Method ◽  
Freight Car ◽  
Runge Kutta ◽  
Relationship Of ◽  
The Relationship ◽  
Railroad Freight

A method of establishing a kinematic model for simulated railroad freight car impact based on the Runge-Kutta method is introduced in this paper. The model is solved based on numerical analysis to obtain the relationship of variables, furthermore providing a basis for determining the loading support and loading securement method.

On the Elastic Bending of Columns Due to Dynamic Axial Forces Including Effects of Axial Inertia

1960 ◽  
Vol 27 (1) ◽  
pp. 125-131 ◽  
Author(s):  
Eugene Sevin
Keyword(s):  
Numerical Solutions ◽  
Equations Of Motion ◽  
Sine Wave ◽  
Elastic Response ◽  
Secondary Importance ◽  
Inertia Effects ◽  
Elastic Bending ◽  
Axial Forces ◽  
Compression Members ◽  
Constant Rate

This study is concerned with the influence of axial inertia upon the elastic bending motion of initially slightly curved columns acted on by time-dependent axial forces. The equations of motion include both axial inertia and nonlinear strain terms. Numerical solutions were obtained for a similar problem previously studied by Hoff [1] but in which axial-inertia effects were neglected; i.e., the problem of a simply supported column initially bent in the shape of a half sine wave and loaded by displacing one end axially at a constant rate. The range of solutions pertains to conventional structural compression members (slenderness ratios less than 150), and to minimum rates of loading compatible with elastic response of common engineering materials. This study suggests that axial-inertia effects are of secondary importance in so far as the gross elastic response of conventional structural columns is concerned.

scholarly journals Power Conversion Techniques Using Multi-Phase Transformer: Configurations, Applications, Issues and Recommendations

Machines ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 13
Author(s):  
Md Tabrez ◽  
Pradip Kumar Sadhu ◽  
Molla Shahadat Hossain Lipu ◽  
Atif Iqbal ◽  
Mohammed Aslam Husain ◽  
...  
Keyword(s):  
Power Generation ◽  
Transformation Method ◽  
Sine Wave ◽  
Fault Analysis ◽  
Optimization Techniques ◽  
Phase System ◽  
Voltage Unbalance ◽  
Three Phase ◽  
Phase Systems ◽  
Multi Phase

Recently, the superiority of multi-phase systems in comparison to three-phase energy systems has been demonstrated with regards to power generation, transmission, distribution, and utilization in particular. Generally, two techniques, specifically semiconductor converter and special transformers (static and passive transformation) have been commonly employed for power generation by utilizing multi-phase systems from the available three-phase power system. The generation of multi-phase power at a fixed frequency by utilizing the static transformation method presents certain advantages compared to semiconductor converters such as reliability, cost-effectiveness, efficiency, and lower total harmonics distortion (THD). Multi-phase transformers are essential to evaluate the parameters of a multi-phase motor, as they require a multi-phase signal that is pure sine wave in nature. However, multi-phase transformers are not suitable for variable frequency applications. Moreover, they have shortcomings with regard to impedance mismatching, the unequal number of turns which lead to inaccurate results in per phase equivalent circuits, which results in an imbalance output in phase voltages and currents. Therefore, this paper aims to investigate multi-phase power transformation from a three-phase system and examine the different static multi-phase transformation techniques. In line with this matter, this study outlines various theories and configurations of transformers, including three-phase to five-, seven-, eleven-, and thirteen-phase transformers. Moreover, the review discusses impedance mismatching, voltage unbalance, and per phase equivalent circuit modeling and fault analysis in multi-phase systems. Moreover, various artificial intelligence-based optimization techniques such as particle swarm optimization (PSO) and the genetic algorithm (GA) are explored to address various existing issues. Finally, the review delivers effective future suggestions that would serve as valuable opportunities, guidelines, and directions for power engineers, industries, and decision-makers to further research on multi-phase transformer improvements towards sustainable operation and management.

Sign in / Sign up

Export Citation Format

Share Document