Transient Dynamic Response of Generally Shaped Arches under Interval Uncertainties
Abstract
:1. Introduction
2. Generally Shaped Arch Model and Equations of Motion
3. Chebyshev Polynomial Approximation Method for Dynamic Responses
4. Numerical Results and Discussion
4.1. Comparison of the Chebyshev Interval Method with the Scanning Method in Transient Responses Calculation
4.2. Transient Dynamic Behavior Investigation of the Generally Shaped Arches Considering Different Uncertain Parameters
4.3. Transient Dynamic Responses Comparison of General Shaped Arches with the Same Total Length and Different Mid-Span Height
5. Conclusions
- Different uncertain parameters exert varying influences on the responses. The cross-sectional geometric parameters (the inner radius of the circular tube cross-section) have a more significant influence on the uncertain responses than Young’s modulus. Moreover, the greater the absolute value of the deterministic response, the more pronounced this influence becomes. When considering these two uncertain parameters concurrently, the influence of the cross-sectional geometric parameter is predominant.
- Arches of different shapes with the same rise span ratio exhibit distinct deterministic responses and corresponding uncertain responses under the same external excitation. Through comparison, it is observed that the response of the elliptical arch is the greatest and that of the parabolic arch is the smallest. When the rise span ratio is increased while maintaining the span constant, the responses of each arch decrease, and the above conclusion still holds, indicating that the shape and rise span ratio of the arch are the primary factors influencing the dynamic response.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
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Type of Arch | Geometry Description | Parametric Representation | Curvature Radius Concerning θ |
---|---|---|---|
Circumference | R(θ) = R | ||
Cycloid | R(θ) = 4acosθ | ||
Ellipse | |||
Parabola |
Description | Value |
---|---|
Young’s modulus E | 210 Gpa |
Density of mass ρ | 7860 kg/m3 |
Poisson ratio υ | 0.3 |
Outer radius r1 | 0.09 m |
Inner radius r2 | 0.078 m |
Shear factor κ | 1.2 |
Type | Description | Value | |
---|---|---|---|
Case 1 | Linear increasing concentrated load | F1 = 20t (kN) | |
Case 2 | Harmonic concentrated load | F2 = 20 × sin(2πt) (kN) | |
Case 3 | Harmonic distributed load with a linear increasing variation | F3 = 20t × sin(2πt) (kN/m) | |
Case 4 | Harmonic distributed load with negative exponential variation | F4 = 20 × e−t/2 × sin(2πt) (kN/m) |
Size | Response Type | Circumference | Cycloid | Ellipse | Parabola | ||
---|---|---|---|---|---|---|---|
H = 3 m L = 10 m | Deterministic | 1.156 | 1.396 | 5.073 | 0.271 | ||
IRCS * | Lower | 0.893 | 1.069 | 3.959 | 0.197 | ||
Upper | 1.673 | 2.027 | 7.267 | 0.416 | |||
YM * | Lower | 1.101 | 1.330 | 4.831 | 0.258 | ||
Upper | 1.217 | 1.470 | 5.340 | 0.286 | |||
Both * | Lower | 0.851 | 1.018 | 3.770 | 0.187 | ||
Upper | 1.761 | 2.133 | 7.650 | 0.438 | |||
H = 4 m L = 10 m | Deterministic | 0.953 | 1.240 | 1.681 | 0.098 | ||
Both * | Lower | 0.701 | 0.895 | 1.240 | 0.064 | ||
Upper | 1.452 | 1.926 | 2.557 | 0.168 |
Size | Response Type | Circumference | Cycloid | Ellipse | Parabola | ||
---|---|---|---|---|---|---|---|
H = 3 m L = 10 m | Deterministic | −1.611 | −1.948 | −7.068 | −0.379 | ||
IRCS * | Lower | −2.333 | −2.825 | −10.125 | −0.581 | ||
Upper | −1.245 | −1.491 | −5.516 | −0.275 | |||
YM * | Lower | −1.696 | −2.050 | −7.440 | −0.399 | ||
Upper | −1.535 | −1.855 | −6.731 | −0.361 | |||
Both * | Lower | −2.455 | −2.974 | −10.658 | −0.612 | ||
Upper | −1.186 | −1.421 | −5.253 | −0.261 | |||
H = 4 m L = 10 m | Deterministic | −1.328 | −1.730 | −2.343 | −0.137 | ||
Both * | Lower | −2.023 | −2.686 | −3.562 | −0.234 | ||
Upper | −0.977 | −1.248 | −1.728 | −0.089 |
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Nie, Z.; Fu, C.; Yang, Y.; Zhao, J. Transient Dynamic Response of Generally Shaped Arches under Interval Uncertainties. Appl. Sci. 2024, 14, 5918. https://doi.org/10.3390/app14135918
Nie Z, Fu C, Yang Y, Zhao J. Transient Dynamic Response of Generally Shaped Arches under Interval Uncertainties. Applied Sciences. 2024; 14(13):5918. https://doi.org/10.3390/app14135918
Chicago/Turabian StyleNie, Zhihua, Chao Fu, Yongfeng Yang, and Jiepeng Zhao. 2024. "Transient Dynamic Response of Generally Shaped Arches under Interval Uncertainties" Applied Sciences 14, no. 13: 5918. https://doi.org/10.3390/app14135918
APA StyleNie, Z., Fu, C., Yang, Y., & Zhao, J. (2024). Transient Dynamic Response of Generally Shaped Arches under Interval Uncertainties. Applied Sciences, 14(13), 5918. https://doi.org/10.3390/app14135918