Convolution-based time-domain simulation for fluidelastic instability in tube arrays

A convolution-based numerical algorithm is presented for the time-domain analysis of fluidelastic instability in tube arrays, emphasizing in detail some key numerical issues involved in the time-domain simulation. The unit-step and unit-impulse response functions, as two elementary building blocks for the time-domain analysis, are interpreted systematically. An amplitude-dependent unit-step or unit-impulse response function is introduced to capture the main features of the nonlinear fluidelastic (FE) forces. Connections of these elementary functions with conventional frequency-domain unsteady FE force coefficients are discussed to facilitate the identification of model parameters. Due to the lack of a reliable method to directly identify the unit-step or unit-impulse response function, the response function is indirectly identified based on the unsteady FE force coefficients. However, the transient feature captured by the indirectly identified response function may not be consistent with the physical fluid-memory effects. A recursive function is derived for FE force simulation to reduce the computational cost of the convolution operation. Numerical examples of two tube arrays, containing both a single flexible tube and multiple flexible tubes, are provided to validate the fidelity of the time-domain simulation. It is proven that the present time-domain simulation can achieve the same level of accuracy as the frequency-domain simulation based on the unsteady FE force coefficients. The convolution-based time-domain simulation can be used to more accurately evaluate the integrity of tube arrays by considering various nonlinear effects and non-uniform flow conditions. However, the indirectly identified unit-step or unit-impulse response function may fail to capture the underlying discontinuity in the stability curve due to the prespecified expression for fluid-memory effects.

Unit Impulse Response Estimation for Structural Damage Detection Under Planar Multiple Excitations

An unit impulse response (UIR) function is an inherent system function that depends only on the structure and the locations of excitation. When the structure is under general excitation, the effect can be obtained via Duhamel integral between the UIR function and the excitation. The possibility of the UIR function as a damage detection index under general excitation is studied here. However, the UIRs from multiple excitations will contribute to the identification equation together. Therefore, the estimation of UIRs will most probably become underdetermined with a limited number of measurements leading to an incorrect or nonfeasible solution of the inverse problem. This report addresses this problem by developing a transformation between the UIRs to facilitate the conversion of a multiple excitations problem into an equivalent single excitation problem. However, the method is limited to planar problems and the reference response is confined to those with larger vibration amplitude. The extraction of the UIR via Tikhonov regularization from the measured acceleration is then described. Numerical studies with a 31-bar plane truss structure are used to illustrate the performances of the proposed approach with different damage scenarios with or without noise effect and model errors. The stability of the UIR estimation with different periods of measured data is also studied. Moreover, this paper studies the effect of using a reduced number of sensors and an increased sampling rate. Results show that the regularization-based approach with the new transformation matrix is accurate and effective for the inverse solution and it is robust to measurement noise in the damage detection process.