A Fast Frequency Domain Method for Steady-State Solution of Forced Vibration of System with Complex Damping
Abstract
:1. Introduction
2. Fast Frequency Domain Method
2.1. Theoretical Background
2.2. Development of Fast Frequency Domain Method
2.3. The Algorithm Workflow
3. Numerical Analysis
3.1. Harmonic Force with a Zero Mean Value
3.2. Harmonic Force with a Non-Zero Mean Value
3.3. Seismic Excitation
4. Conclusions
Author Contributions
Funding
Conflicts of Interest
References
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CFDM | DTDM | Accurate FFDM | Approximate FFDM | Direct TDM | |
---|---|---|---|---|---|
uR | 0 | 0 | 0 | 0 | 100 |
uI | 100 | 0 | 0 | 0 | 0 |
CFDM | DTDM | Accurate FFDM | Approximate FFDM | |
---|---|---|---|---|
uR | 0.09 | 0 | 0 | 0 |
uI | 99.01 | 0 | 0 | 0 |
CFDM | Accurate FFDM | Approximate FFDM | |
---|---|---|---|
uR | 0 | 0 | 4.59 × 10−5 |
uI | 100 | 0 | 4.59 × 10−9 |
Cases | Calculation Time/(s) | |||
---|---|---|---|---|
CFDM | DTDM | Accurate FFDM | Approximate FFDM | |
Example 1: Zero mean sine excitation | 6.48 × 10−4 | 1.81 | 1.99 × 10−4 | 1.04 × 10−4 |
Example 2: Non-zero mean cosine excitation | 5.91 × 10−4 | 1.78 | 2.04 × 10−4 | 1.98 × 10−4 |
Example 3: Seismic excitation | 6.01 × 10−4 | 1.72 | 2.05 × 10−4 | 1.95 × 10−4 |
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Qi, W.; Pan, D.; Gao, Y.; Lu, W.; Huang, Y. A Fast Frequency Domain Method for Steady-State Solution of Forced Vibration of System with Complex Damping. Appl. Sci. 2020, 10, 3442. https://doi.org/10.3390/app10103442
Qi W, Pan D, Gao Y, Lu W, Huang Y. A Fast Frequency Domain Method for Steady-State Solution of Forced Vibration of System with Complex Damping. Applied Sciences. 2020; 10(10):3442. https://doi.org/10.3390/app10103442
Chicago/Turabian StyleQi, Wenrui, Danguang Pan, Yongtao Gao, Wenyan Lu, and Ying Huang. 2020. "A Fast Frequency Domain Method for Steady-State Solution of Forced Vibration of System with Complex Damping" Applied Sciences 10, no. 10: 3442. https://doi.org/10.3390/app10103442