Proxy-Based Sliding Mode Vibration Control with an Adaptive Approximation Compensator for Euler-Bernoulli Smart Beams

Proxy-based sliding mode control PSMC is an improved version of PID control that combines the features of PID and sliding mode control SMC with continuously dynamic behaviour. However, the stability of the control architecture maybe not well addressed. Consequently, this work is focused on modification of the original version of the proxy-based sliding mode control PSMC by adding an adaptive approximation compensator AAC term for vibration control of an Euler-Bernoulli beam. The role of the AAC term is to compensate for unmodelled dynamics and make the stability proof more easily. The stability of the proposed control algorithm is systematically proved using Lyapunov theory. Multi-modal equation of motion is derived using the Galerkin method. The state variables of the multi-modal equation are expressed in terms of modal amplitudes that should be regulated via the proposed control system. The proposed control structure is implemented on a simply supported beam with two piezo-patches. The simulation experiments are performed using MATLAB/SIMULINK package. The locations of piezo-transducers are optimally placed on the beam. A detailed comparison study is implemented including three scenarios. Scenario 1 includes disturbing the smart beam while no feedback loop is established (open-loop system). In scenario 2, a PD controller is applied on the vibrating beam. Whereas, scenario 3 includes implementation of the PSMC+AAC. For all previously mentioned scenarios, two types of disturbances are applied separately: 1) an impulse force of 1 N peak and 1 s pulse width, and 2) a sinusoidal disturbance with 0.5 N amplitude and 20 Hz frequency. For impulse disturbance signals, the results show the superiority of the PSMC+AAC in comparison with the conventional PD control. Whereas, both the PSMC+ACC and the PD control work well in the case of a sinusoidal disturbance signal and the superiority of the PSMC is not clear.

Hydrodynamic aspects of moving vehicle with sloshing tanks

Freight vehicles with partially filled liquid tanks will be affected by liquid sloshing during transient motion. The sloshing induced by vehicle motion will lead to extra force on the vehicle and sometimes is a potential threat to safety. Previous studies on this problem usually use a mass-spring analogy to represent the sloshing effect of the liquid tank. Its main disadvantage is that CFD analysis or experimental study has to be performed beforehand, so that an equivalent mass-spring model can be constructed by curve fitting. In this paper, frequency domain boundary element method (BEM) and analytical solution to the sloshing problems are used to derive the modal equation and hydrodynamic parameters of the sloshing fluid. The accuracy of the results will be examined by comparison with available CFD results in the literature. The paper then evaluates the accuracy of equivalent mass-spring model and explores the possibility to approximate the sloshing effects inside cylindrical tanks by using analytical solution to the sloshing inside equivalent rectangular tanks.

Mechanical Models of Low-Gravity Sloshing Taking Into Account Viscous Damping

Mechanical models of damped low-gravity sloshing are developed using a proposed analytical method for arbitrary axisymmetric tanks. It is shown that (a) the complex amplitudes of the force and moment caused by the conventional mechanical model do not coincide with the complex amplitudes of the force and moment calculated from the modal equation of sloshing and (b) these differences arise not only from the damping ratio but also from the surface tension although the surface tension does not cause energy dissipation. A mechanical model for correcting these differences is developed. The mass of this correction model is found to be equal to the mass of the liquid that fills the domain bounded by the meniscus and the plane that includes the contact line of the meniscus with the tank wall. With decreasing Bond number, the correction model mass as well as the damping ratio increase and, therefore, the correction becomes important. The force and moment caused by the conventional uncorrected mechanical model have phase lag with respect to the force and moment calculated from the modal equation of sloshing near the resonant frequency. Therefore, the correction is important for the dynamics and control analysis of a space vehicle.

Pseudo Excitation Method Based on Multiple Degree of Freedom Modal Equation

In recent years, on the one hand destructive earthquakes frequently occur, and vibration control devices such as dampers and isolation become increasingly application in actual large-scale structures, on the other hand modern structures with complex styles and diversified materials possess significant non-proportional damping characteristics, and traditional methods based on Rayleigh damping assumption no longer meet seismic calculation requirement. According to this situation, firstly multiple degree of freedom modal equation and pseudo excitation method are both utilized to establish a new efficient calculation method system which is suitable for stochastic analysis of non-proportionally damped structure, and the new method can achieve adjustive calculation efficiency and accuracy. Furthermore, advantages and features of established method are analyzed, and guidance suggestions for appropriate method use are also proposed. Finally, numerical study is carried out to verify conclusions proposed by theoretical derivation, and efficiency and accuracy of established method system used in stochastic response calculation of non-proportionally damped structure is confirmed.

Mistuning Identification and Model Updating of an Industrial Blisk

The results of a complete study of mistuning identification on an industrial blisk are presented. The identification method used here is based on a model-updating technique of a reduced order. This reduced-order model is built using component mode synthesis, and mistuning is introduced as perturbations of the cantilevered-blade modes. The measured modal data are extracted from global measurements of the blisk's forced response. As we use a single point excitation, this measurement procedure allows the acquisition of all the modes of a given family with a quite simple experimental set-up. A selection of the best identified modal data is finally performed. During the mistuning identification procedure, these measured data are regularized using an eigenvector assignment technique which reduces the influence of eventual measurement errors. An inverse problem, based on the perturbed (mistuned) modal equation, is defined with measured modes as input and mistuning parameters as unknown. Then, the reduced-order model is updated with the identified mistuning, we first perform a correlation on modal responses (using eigenfrequency deviation criteria and MACs). Finally, correlation results on forced responses are presented and discussed.

Mistuning Identification and Model Updating of an Industrial Blisk

The results of a complete study of mistuning identification on an industrial blisk are presented. The identification method used here is based on a model-updating technique of a reduced-order model where measured modal data are taken as input. This reduced-order model is build using component mode synthesis and mistuning is introduced as perturbations of the cantilevered-blade modes. The measured modal data are extracted from global measurements of the blisk’s forced response. As we use a one point excitation, this measurement procedure allows the acquisition of the all modes of a given family with a quite simple experimental setup. A selection of the best identified modal data is finally performed. During the mistuning identification procedure, these measured data are regularized using an eigenvector assignment technique which reduces the influence of eventual measurement errors. An inverse problem is defined based on the perturbed (mistuned) modal equation, with measured modes as input and mistuning parameters as unknown. Then, the reduced-order model is updated with the identified mistuning, we first perform a correlation on modal responses (using eigenfrequency deviation criteria and MACs). Finally, correlation results on forced responses are presented and discussed.

Low-Gravity Sloshing in an Axisymmetrical Container Excited in the Axial Direction

The response of low-gravity propellant sloshing is analyzed for the case where an axisymmetrical container is exposed to axial excitation. Spherical coordinates are used to analytically derive the characteristic functions for an arbitrary axisymmetrical convex container, for which time-consuming and expensive numerical methods have been used in the past. Numerical results show that neglecting the surface tension results in the underestimation of the magnitude of the liquid surface oscillation. The reason for this is explained by the influences of the Bond number and the liquid filling level on the critical value of the coefficient of the excitation term in the modal equation, above which the oscillation is destabilized, and on the characteristic root of the destabilized system. [S0021-8936(00)01502-6]

A Complex Modal Analysis Method for Damped Vibration Systems (The Representation in the Second Order Differential Form of a Modal Equation and its Use for Practical Application)

Second order uncoupled differential equations for the general damped vibration systems are derived theoretically. The equations are written in a form similar to the classical real modal equations by using the natural frequency, the modal damping ratio, and the newly defined complex modal mass. Introducing supplementary variables, the response analysis is carried out in a similar manner to the real modal analysis. By comparing these equations to the classical ones, physical meanings of the derived equations are clarified. For the vibration problems near the resonant point, approximate complex modal equations are derived which have almost the same form as the classical one. Some applications of the proposed method to vibration problems are discussed.