Mode Competition Phenomena and Impact of the Initial Conditions in Nonlinear Vibrations Leading to Railway Curve Squeal
Abstract
1. Introduction
2. Materials and Methods
2.1. Description of the Model
2.1.1. Contact Forces
2.1.2. Equations of Motion
2.2. Stability Analysis of the Self-Excited System
2.3. Derivation of the Initial Conditions
2.3.1. Initial Condition on Velocity
2.3.2. Initial Condition on Displacement
2.3.3. Modal-Derived Initial Conditions
3. Results and Discussion
3.1. System’s Parameters
3.2. Stability Results
3.3. Initial Conditions
3.3.1. Initial Condition on Velocity
3.3.2. Initial Condition on Displacement
3.3.3. Modal-Derived Initial Conditions and Summary of the Test Cases
- All unstable modes
- Mode 0Ln, with
3.4. Time Integration Results
4. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Parameter [Units] | Description | Value |
---|---|---|
[km/h] | Rolling speed | 30 |
[mrad] | Angle of attack | 11 |
N [kN] | Normal load per wheel | 51 |
[m] | Wheel diameter | 0.86 |
[mm] | Lateral offset of the contact point | 15 |
[rad] | Contact plane angle | −0.0145 |
[m] | Rail transverse radius | 0.3 |
E [Gpa] | Young modulus | 210 |
[-] | Poisson’s ratio | 0.3 |
[-] | Static friction coefficient | 0.3 |
[-] | Parameter for friction law | 0.05 |
[-] | Falling ratio on saturated regime | 0.2 |
Free Modes | Stability Analysis | ||||
---|---|---|---|---|---|
Mode | Denomination | Frequency [Hz] | Damping Ratio [-] | Frequency [Hz] | Equivalent Damping Ratio [-] |
5 | 0L0 | 304.43 | 304.43 | ||
6 | 0L2 | 386.38 | 386.35 | ||
9 | 0L3 | 1028.8 | 1028.79 | ||
12 | 0L4 | 1853.9 | 1853.91 | ||
16 | - | 2369.8 | 2369.8 | ||
17 | 0L5 | 2776.3 | 2776.3 | ||
22 | 0L6 | 3752.6 | 3752.59 | ||
26 | - | 4561.5 | 4561.5 | ||
28 | 0L7 | 4762.2 | 4762.19 | ||
33 | 0L8 | 5794.7 | 5794.69 |
Case Name | ||
---|---|---|
Modal-derived initial conditions | ||
All_unstable_V0.1 | With Unstable modes and | |
All_unstable_V1.0 | ⋯ Unstable modes and | |
All_unstable_V2.0 | ⋯ Unstable modes and | |
0L0 | ⋯ “mode 0L0” | |
0L1 | ⋯ “mode 0L1” | |
0L2 | ⋯ “mode 0L2” | |
0L3 | ⋯ “mode 0L3” | |
0L4 | ⋯ “mode 0L4” | |
0L5 | ⋯ “mode 0L5” | |
0L6 | ⋯ “mode 0L6” | |
0L7 | ⋯ “mode 0L7” | |
0L8 | ⋯ “mode 0L8” | |
Physically-derived initial conditions | ||
V_-1.0 | With | |
V_-0.5 | ||
V_0.01 | ||
V_0.1 | ||
V_0.2 | ||
V_0.3 | ||
V_0.5 | ||
V_1.0 | ||
U_0.5 | With | |
U_-0.5 |
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Arango Montoya, J.; Chiello, O.; Sinou, J.-J.; Tufano, R. Mode Competition Phenomena and Impact of the Initial Conditions in Nonlinear Vibrations Leading to Railway Curve Squeal. Appl. Sci. 2025, 15, 509. https://doi.org/10.3390/app15020509
Arango Montoya J, Chiello O, Sinou J-J, Tufano R. Mode Competition Phenomena and Impact of the Initial Conditions in Nonlinear Vibrations Leading to Railway Curve Squeal. Applied Sciences. 2025; 15(2):509. https://doi.org/10.3390/app15020509
Chicago/Turabian StyleArango Montoya, Jacobo, Olivier Chiello, Jean-Jacques Sinou, and Rita Tufano. 2025. "Mode Competition Phenomena and Impact of the Initial Conditions in Nonlinear Vibrations Leading to Railway Curve Squeal" Applied Sciences 15, no. 2: 509. https://doi.org/10.3390/app15020509
APA StyleArango Montoya, J., Chiello, O., Sinou, J.-J., & Tufano, R. (2025). Mode Competition Phenomena and Impact of the Initial Conditions in Nonlinear Vibrations Leading to Railway Curve Squeal. Applied Sciences, 15(2), 509. https://doi.org/10.3390/app15020509