<p>Ground resonance in helicopters is a dynamic instability caused by the coupling between rotor blade lead-lag motion and lateral fuselage motion on the landing gear. This study formulates tuned mass damper (TMD) design for ground-resonance suppression as a linear time-periodic (LTP) stability problem and minimizes the Floquet spectral radius <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$\rho =\max _i|\lambda _i|$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>ρ</mi> <mo>=</mo> <msub> <mo movablelimits="true">max</mo> <mi>i</mi> </msub> <mrow> <mo stretchy="false">|</mo> <msub> <mi>λ</mi> <mi>i</mi> </msub> <mo stretchy="false">|</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> on a 5-DOF rotor-fuselage model extended to 6-DOF by the attached TMD. The model preserves the natural rotor-fuselage periodicity without invoking the Coleman transformation. The TMD parameters <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$(\mu ,f,\zeta _d)$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mi>μ</mi> <mo>,</mo> <mi>f</mi> <mo>,</mo> <msub> <mi>ζ</mi> <mi>d</mi> </msub> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> are optimized by particle swarm optimization (PSO), with a gradient-based step retained as a local optimality check. The PSO-tuned TMD reduces the Floquet spectral radius from <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$\rho =1.0956$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>ρ</mi> <mo>=</mo> <mn>1.0956</mn> </mrow> </math></EquationSource> </InlineEquation> to <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$\rho =0.9416$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>ρ</mi> <mo>=</mo> <mn>0.9416</mn> </mrow> </math></EquationSource> </InlineEquation> at the nominal rotor speed, with an added mass of <InlineEquation ID="IEq5"> <EquationSource Format="TEX">$1.35\%$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>1.35</mn> <mo>%</mo> </mrow> </math></EquationSource> </InlineEquation> of the effective fuselage mass. A two-stage hyperparameter grid search and a 50-run multi-start analysis confirm reproducibility of the identified objective value within numerical precision. The classical Den Hartog, Warburton, and Asami <InlineEquation ID="IEq6"> <EquationSource Format="TEX">$H_{\infty }$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>H</mi> <mi>∞</mi> </msub> </math></EquationSource> </InlineEquation> formulas are evaluated only as diagnostic baselines under the same Floquet metric and do not satisfy <InlineEquation ID="IEq7"> <EquationSource Format="TEX">$\rho <1$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>ρ</mi> <mo><</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation> in the present LTP configuration. Robustness analyses, including objective-function surfaces, Monte Carlo simulations, and a worst-case multi-point reformulation, show that the nominal single-point design has a narrow local stability pocket (<InlineEquation ID="IEq8"> <EquationSource Format="TEX">$\Delta \Omega _{\text {local}}\approx 0.038$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="normal">Δ</mi> <msub> <mi mathvariant="normal">Ω</mi> <mtext>local</mtext> </msub> <mo>≈</mo> <mn>0.038</mn> </mrow> </math></EquationSource> </InlineEquation> rad/s) around the nominal speed. Within the tested design bounds (<InlineEquation ID="IEq9"> <EquationSource Format="TEX">$\mu \le 0.03$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>μ</mi> <mo>≤</mo> <mn>0.03</mn> </mrow> </math></EquationSource> </InlineEquation>, <InlineEquation ID="IEq10"> <EquationSource Format="TEX">$\zeta _d\le 0.35$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>ζ</mi> <mi>d</mi> </msub> <mo>≤</mo> <mn>0.35</mn> </mrow> </math></EquationSource> </InlineEquation>) and the prescribed <InlineEquation ID="IEq11"> <EquationSource Format="TEX">$\pm 5\%$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo>±</mo> <mn>5</mn> <mo>%</mo> </mrow> </math></EquationSource> </InlineEquation> rotor-speed uncertainty band, the multi-point worst-case optimization did not find a feasible single-TMD design satisfying <InlineEquation ID="IEq12"> <EquationSource Format="TEX">$\rho <1$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>ρ</mi> <mo><</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation> across the full band. This result indicates a bandwidth limitation of the single-TMD architecture under the tested conditions.</p>

Floquet-based tuned mass damper design for helicopter ground resonance using particle swarm optimization

期刊论文
发表日期：

2026年7月17日

查看全文

Huseyin Aggumus

摘要

Ground resonance in helicopters is a dynamic instability caused by the coupling between rotor blade lead-lag motion and lateral fuselage motion on the landing gear. This study formulates tuned mass damper (TMD) design for ground-resonance suppression as a linear time-periodic (LTP) stability problem and minimizes the Floquet spectral radius $\rho =\max _i|\lambda _i|$ $ρ = {max}_{i} | λ_{i} |$ on a 5-DOF rotor-fuselage model extended to 6-DOF by the attached TMD. The model preserves the natural rotor-fuselage periodicity without invoking the Coleman transformation. The TMD parameters $(\mu ,f,\zeta _d)$ $(μ, f, ζ_{d})$ are optimized by particle swarm optimization (PSO), with a gradient-based step retained as a local optimality check. The PSO-tuned TMD reduces the Floquet spectral radius from $\rho =1.0956$ $ρ = 1.0956$ to $\rho =0.9416$ $ρ = 0.9416$ at the nominal rotor speed, with an added mass of $1.35\%$ $1.35 %$ of the effective fuselage mass. A two-stage hyperparameter grid search and a 50-run multi-start analysis confirm reproducibility of the identified objective value within numerical precision. The classical Den Hartog, Warburton, and Asami $H_{\infty }$ $H_{\infty}$ formulas are evaluated only as diagnostic baselines under the same Floquet metric and do not satisfy $\rho <1$ $ρ < 1$ in the present LTP configuration. Robustness analyses, including objective-function surfaces, Monte Carlo simulations, and a worst-case multi-point reformulation, show that the nominal single-point design has a narrow local stability pocket ( $\Delta \Omega _{\text {local}}\approx 0.038$ $Δ Ω_{local} \approx 0.038$ rad/s) around the nominal speed. Within the tested design bounds ( $\mu \le 0.03$ $μ \leq 0.03$ , $\zeta _d\le 0.35$ $ζ_{d} \leq 0.35$ ) and the prescribed $\pm 5\%$ $\pm 5 %$ rotor-speed uncertainty band, the multi-point worst-case optimization did not find a feasible single-TMD design satisfying $\rho <1$ $ρ < 1$ across the full band. This result indicates a bandwidth limitation of the single-TMD architecture under the tested conditions.