Abstract
In this paper, aeroelastic stability analysis of hingeless helicopter blades in frequency domain is studied. In this regard, the nonlinear structural beam model of Hodges–Dowell and an unsteady aerodynamic model based on Greenberg theory and using Loewy aerodynamic function are considered to construct the aeroelastic model. Then, the concept of optimum equivalent linear frequency response function (OELF) is implemented to derive the aeroelastic FRF by coupling the aerodynamic and structural FRFs. Finally, for stability analysis, the efficient and simple criterion of condition number (CN) of aeroelastic OELF is applied. The comparison of the obtained results against those in the literature shows the capability of the OELF and condition number criterion for capturing the instability boundaries of a complex, nonlinear, aeroelastic system such as helicopter blades.
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Abbreviations
- \(A_{i}-O_{ij}\) :
-
Modal integrals
- \(c\) :
-
Blade chord
- \({C}'(k)\) :
-
Loewy’s lift deficiency function
- \(C_{l_\alpha }, C_{d_0}\) :
-
Lift coefficient and profile drag coefficient, respectively
- \(H\) :
-
FRF/OELF
- \(k\) :
-
Reduced frequency
- \(k_A\) :
-
Radius of gyration of blade cross-section
- \(k_m \) :
-
Mass radius of gyration of blade cross-section
- K:
-
\({k_A^2}/{k_m^2}\)
- \(L_\nu , L_w\) :
-
Dimensionless generalized aerodynamic forces per unit length
- \(M_\phi \) :
-
Dimensionless aerodynamic pitching moment per unit length
- \(S_{ ff} \) :
-
Power spectral density of excitation
- \(S_{x_n f} \) :
-
Cross-spectral density of excitation and response
- \(\bar{{V}}_{i}\) :
-
Induced flow velocity
- \(u, v, w\) :
-
Displacements in the \(x\), \(y\), \(z\) directions, respectively
- \(V_j, W_j, \Phi _{j} \) :
-
Generalized coordinates
- \(x, y, z\) :
-
Undeformed coordinate system
- \(\gamma \) :
-
Lock number
- \(\delta _{ij} \) :
-
Kronecker delta
- \(\theta , \theta _f \) :
-
Collective pitch angle and collective angle of instability of linearized aeroelastic system, respectively
- \(\alpha _{j}, \beta _{j}, \gamma _{j} \) :
-
Constants related to mode shapes
- \(\beta _{pc} \) :
-
Precone angle
- \(\kappa \) :
-
Dimensionless torsional rigidity
- \(\Lambda _1, \Lambda _2 \) :
-
Dimensionless bending stiffnesses
- \(\mu , \mu _1, \mu _2 \) :
-
Dimensionless mass radius of gyration
- \(\sigma \) :
-
Solidity
- \(\varphi \) :
-
Elastic torsion deflection
- \(\omega \) :
-
Frequency
- \(\bar{(\,)}\) :
-
Non-dimensional parameter
- \(\left( \,\right) _0, \Delta \left( \, \right) \) :
-
Equilibrium and perturbation components of generalized coordinates
- \(\left( \, \right) ^{\prime }\) :
-
\(\frac{\partial }{\partial x}\)
-
: -
\(\frac{\partial }{\partial t}\)
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Roknizadeh, S.A.S., Nobari, A.S. & Shahverdi, H. Nonlinear aeroelastic stability analysis of hingeless helicopter rotor blades using FRF coupling and condition number. Nonlinear Dyn 82, 289–297 (2015). https://doi.org/10.1007/s11071-015-2157-3
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DOI: https://doi.org/10.1007/s11071-015-2157-3