# Time domain aeroelastic analysis of clamped wings and determination of V-g-f plots using modal parameter identification

## Palavras-chave:

Aeroelasticity, Unsteady Vortex Lattice Method, Finite Element Method, System Identification, Flutter## Resumo

Aeroelastic analyses are performed either in time or frequency domains. Frequency domain

analyses have the advantage of providing a fast computation of the flutter speed and are more widespread.

Their results are presented in the so-called velocity-damping-frequency (V-g-f) plots, which shows the

evolution of the natural frequency and damping ratio of each vibration mode as a function of airspeed.

This way, the flutter speed (where zero damping occurs) can be determined with precision. On the other

hand, time domain analyses allow the inclusion of different types of nonlinearities in the simulations,

with the price of being more time consuming. Their results consist of time histories whose vibration

amplitudes should be visually inspected to find a constant amplitude situation (zero damping condition).

This paper presents time domain aeroelastic analysis of a set of rectangular cantilever plates with different

aspect ratios that represent aircraft wings in a simplified way. Time domain results are then used to

generate V-g-f plots through modal parameter identification. For the structural dynamics modeling,

both the classical beam theory (Euler-Bernoulli) and the classical plate theory have been applied, and

the natural frequencies and mode shapes were obtained via the Finite Element Method (FEM). For the

aerodynamic modeling of the plates, the Unsteady Vortex Lattice Method (UVLM) was used, which

is a three-dimensional aerodynamic model based on a potential flow formulation. The structural and

aerodynamic models are coupled using a surface splines interpolation method, and the movement equation

is solved iteratively on a time-domain basis, applying a predictor-corrector method. The frequency

spectrum of each time response serves as input to the modal parameter identification method, which uses

the Least Squares Complex Frequency estimator (LSCF). A stabilization chart is obtained based on the

frequency and damping convergence criteria, thereby allowing the identification of the modal parameters.

The structural and aeroelastic results of the plate, considering both beam theory and plate theory, are

evaluated. It was possible to obtain very clear V-g-f plots, with a precise identification of flutter speeds,

for all tested cases. The influence of the structural model on the flutter speed results was assessed.