A Decoupled Unified Observation Method of Stochastic Multidimensional Vibration for Wind Tunnel Models

Active vibration control is the most effective method for stochastic multidimensional vibration in wind tunnel tests, in which vibration monitoring is the core foundation. Vibrations are induced by the disturbances of several complex air flow instabilities under extreme test conditions with high attack angles. Here, a decoupled unified observation method is proposed in order to fully monitor stochastic multidimensional vibration. First, stochastic multidimensional vibration is explained using the Cartesian coordinate system. Then, the multidimensional vibration decoupling of the pitch plane and the yaw plane is realized according to the proposed decoupling design principle of the long cantilever sting. A unified observation method is presented, based on inertial force theory, to observe multidimensional vibration due to acceleration in each decoupling plane. Verification experiments were conducted in lab and a transonic wind tunnel, using an established real-time monitoring system. The results of lab experiments indicate that, in the frequency region of 0–120 Hz, three vibration modes of a selected stochastic vibration can be decoupled and observed through the vibration components in pitch plane and yaw plane. In addition, wind tunnel tests were carried out according to the working conditions (α = −4~10° with γ = 45°) at Ma = 0.6 and Ma = 0.7, respectively. The results show that six vibration modes of two selected stochastic vibrations can be decoupled and observed through the vibration components in pitch plane and yaw plane. The experimental results prove that stochastic vibration can be fully monitored in multiple dimensions through the vibration components in pitch plane and yaw plane using the proposed decoupled unified observation method. Therefore, these results lay the foundation for active vibration control.

Nonlinear Stochastic Analysis of Footbridge Lateral Vibration Based on Probability Density Evolution Method

Footbridge lateral vibration remains an unsolved problem and is characterized by the following: (1) pedestrians are sensitive to bridge vibration, which causes the pedestrian’s excitation being dependent on the bridge vibration; (2) pedestrian lateral excitation is a stochastic process rather than a perfect periodic load. Therefore, footbridge lateral vibration is essentially a complex nonlinear stochastic vibration system. Thus far, an effective method of dealing with such nonlinear stochastic vibration of footbridges remains lacking. A framework based on the probability density evolution (PDE) method is presented. For the mathematical model, the parameter resonance model is used to describe the pedestrian-bridge interaction while treating the pedestrian lateral excitation as a narrow-band process. For the analysis method, PDE is used to solve the nonlinear stochastic equations in combination with the number theoretical and finite difference methods. The proposed method establishes a new approach in studying footbridge lateral vibration. First, PDE based on the small sample strategy avoids the large amount of computation. Second, the randomness of both structural parameters and pedestrian lateral excitation could be taken into consideration by the proposed method. Third, based on the probability results with rich information, the serviceability, dynamic reliability, and random stability analyses are realized in a convenient manner.

Analytical Solutions for Stochastic Vibration of Orthotropic Membrane under Random Impact Load

Orthotropic membrane materials have been applied in the numerous fields, such as civil engineering, space and aeronautics, and mechanical engineering, among others. During their serving lifespan, these membranes are always facing strong stochastic vibrations induced by the random impact load such as hail, heavy rain, and noise, among others. In this paper, the stochastic vibration problem of orthotropic membrane subjected to random impact load is investigated. The statistical characteristics of random impact load are initially obtained based on the stochastic pulse theory. Then, the Von Karman theory is applied to model the nonlinear vibration of membrane with geometric nonlinearity, which is then used to derive and solve the corresponding fokker–plank–kolmogorov (FPK). The theoretical model developed is validated by means of experiment study and monte carlo simulation (MCS) analysis. The effects of variables like pretension force, velocity of impact load, and material features on stochastic dynamic behavior of membranes are discussed in detail. This exposition provides theoretical framework for stochastic vibration control and design of membranes subjected to random dynamic load.