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A structural model is significant for the verification of structural control algorithms. However, for nonlinear behavior, experiments are mostly destructive tests that are costly, and conducting repetitive structural experiments is difficult. Therefore, a repetitive structural vibration model is important for structural vibration control. In this study, a smart platform to realize different structural behaviors is developed based on the backstepping control algorithm. Lyapunov functions are used to derive the control law. Simulations show that the designed model can track the structural responses of different arbitrary linear structures very well. In addition, the proposed platform can track responses of different piecewise linear structures and desired models with various hysteresis very well. Numerical results verify the effectiveness of the proposed tracking controller through the backstepping method for the established platform.

Tuned mass dampers （TMDs） have been widely used in recent years to mitigate structural vibration. However, the damping mechanisms employed in the TMDs are mostly based on viscous dampers, which have several well-known disadvantages, such as oil leakage and difficult adjustment of damping ratio for an operating TMD. Alternatively, eddy current damping （ECD） that does not require any contact with the main structure is a potential solution. This paper discusses the design, analysis, manufacture and testing of a large-scale horizontal TMD based on ECD. First, the theoretical model of ECD is formulated, then one large-scale horizontal TMD using ECD is constructed, and finally performance tests of the TMD are conducted. The test results show that the proposed TMD has a very low intrinsic damping ratio, while the damping ratio due to ECD is the dominant damping source, which can be as large as 15% in a proper configuration. In addition, the damping ratios estimated with the theoretical model are roughly consistent with those identified from the test results, and the source of this error is investigated. Moreover, it is demonstrated that the damping ratio in the proposed TMD can be easily adjusted by varying the air gap between permanent magnets and conductive plates. In view of practical applications, possible improvements and feasibility considerations for the proposed TMD are then discussed. It is confirmed that the proposed TMD with ECD is reliable and feasible for use in structural vibration control.

Similitude design plays a vital role in the analysis of vibration and shock problems encountered in large engineering equipment. Similitude design, including dimensional analysis and governing equation method, is founded on the dynamic similitude theory. This study reviews the application of similitude design methods in engineering practice and summarizes the major achievements of the dynamic similitude theory in structural vibration and shock problems in different fields, including marine structures, civil engineering structures, and large power equipment. This study also reviews the dynamic similitude design methods for thin-walled and composite material plates and shells, including the most recent work published by the authors. Structure sensitivity analysis is used to evaluate the scaling factors to attain accurate distorted scaling laws. Finally, this study discusses the existing problems and the potential of the dynamic similitude theory for the analysis of vibration and shock problems of structures.

Uncertainty is inherent and unavoidable in almost all engineering systems. It is of essential significance to deal with uncertainties by means of reliability approach and to achieve a reasonable balance between reliability against uncertainties and system performance in the control design of uncertain systems. Nevertheless, reliability methods which can be used directly for analysis and synthesis of active control of structures in the presence of uncertainties remain to be developed, especially in non-probabilistic uncertainty situations. In the present paper, the issue of vibration control of uncertain structures using linear quadratic regulator (LQR) approach is studied from the viewpoint of reliability. An efficient non-probabilistic robust reliability method for LQR-based static output feedback robust control of uncertain structures is presented by treating bounded uncertain parameters as interval variables. The optimal vibration controller design for uncertain structures is carried out by solving a robust reliability-based optimization problem with the objective to minimize the quadratic performance index. The controller obtained may possess optimum performance under the condition that the controlled structure is robustly reliable with respect to admissible uncertainties. The proposed method provides an essential basis for achieving a balance between robustness and performance in controller design of uncertain structures. The presented formulations are in the framework of linear matrix inequality and can be carried out conveniently. Two numerical examples are provided to illustrate the effectiveness and feasibility of the present method.

A recently emerging family of smart materials, photostrictive materials, exhibit large photostriction under uniform illumination of high-energy light. This photostriction mechanism arises from a superposition phenomenon of photovoltaic and converse piezoelectric effects. A photostrictive type of opto-electromechanical actuator activated by high-energy lights can introduce actuation and control effects without hard-wired connections. The control light intensity applied to the actuator is proportional to the transverse velocity at a positioned point, which is measured by a laser vibrometer. In this paper, photostrictive films are numerically analyzed to evaluate their use as wireless actuators for future remote vibration control of flexible structures. A novel opto-electromechanical solid shell finite element formulation is developed for accurate analysis of the multiple physics effects of photovoltaic, pyroelectric and thermal expansion of photostrictive materials. Available experimental data and analytical solutions have been used to verify the present finite element results. The simulation in this study demonstrates that the present formulation is very reliable, accurate and also computationally efficient and that the use of photostrictive actuators can provide good controllability of structural vibration.

For a variable speed large scale wind turbine, the vibration issues become a key problem that cannot be ignored in the turbine’s life cycle. Wind turbine tower vibration will cause superfluous mechanical loads. To resolve the vibration issue, a method for constructing the energy function V is proposed to meet the demands of safe operation. The Lyapunov theorem has been embedded in a wind turbine control algorithm, proving the theoretical feasibility of stability control based on function V. According to an analysis of this complex nonlinear model for the wind turbine, the general method of constructing an energy function suitable for a wind turbine is presented explicitly. The feasibility of applying an energy function to wind turbine vibration control is verified experimentally using a 3.0-MW direct drive wind turbine model. The experimental results indicate that the dynamic performance of the tested wind turbine model with energy function control is significantly better than that of the uncontrolled structure in terms of the reduction of nacelle acceleration, velocity, and displacement response.

In this paper, how to compute the eigenfrequencies of the structures composed of a series of inclined cables is shown. The physics of an inclined cable can be complicated, so solving the differential equations even approximately is difficult. However, rather than solving the system of 4 first-order equations governing the dynamics of each cable, the governing equations are instead converted to a set of equations that the exterior matrix satisfies. Therefore, the exterior matrix method (EMM) is used without solving the original governing equations. Even though this produces a system of 6 first-order equations, the simple asymptotic techniques to find the first three terms of the perturbative solution can be used. The solutions can then be assembled to produce a 6 × 6 exterior matrix for a cable section. The matrices for each cable in the structure are multiplied together, along with the exterior matrices for each joint. The roots of the product give us the eigenfrequencies of the system.

In order to extend the statistical energy analysis (SEA) method to predict the vibration and sound radiation of underwater structures, we mainly analyze the effect of water loading on the key parameters in SEA and propose the approximate expressions of modal density and mean square velocity of submerged plates. With the radiation efficiency of submerged plates previously proposed by us, the modified SEA solutions of the radiated sound power and mean square velocity of submerged stiffened rectangular plates are established. Numerical examples show that the modified SEA solutions are more close to the theoretical solutions than the present SEA solutions, and reflect the mean value or trend of the theoretical solution much better, especially at lower frequencies. An experiment of point-exciting submerged plates was done in a lake. The experiment values show that for both un-stiffened and stiffened plates, the modified SEA solutions have a good agreement while the present SEA solution has considerable error, which validates the established statistical model.

Solar sail is a new type of spacecraft for deep space exploration, which flies by the pressure of sunlight. The attitude of the sail determines its orbit, so altitude control plays an important role in the mission. However, the large flexible structure leads to some difficulty in attitude control. This paper establishes the reduced dynamic model of a flexible solar sail with foreshorten- ing deformation, and coupling with its attitude and vibration. As usual, large angle maneuvering will lead to the vibration of flexible structure, so the time optimal control of solar sail maneuvering is considered. Bang-Bang control of the solar sail gen- erates large amplitude and sustained vibration, while the combined control based on input shaping can eliminate the vibration efficiently. With the comparison of two reduced models, it is demonstrated that the choice of two models depends on the attention to the stretching deformation.

This paper analyzes the physical meaning of the active and reactive power flow in the finite L-shaped beams and studies the active vibration control of the structures based on the active and reactive power flow.The traveling wave approach is used to calculate the structural dynamic responses.Because the error of control force is inevitable in practical applications,the effects of the error of control force on the control results are studied.The study indicates that the error of control force has pronounced influence on the control results of the acceleration and reactive power flow.It is obvious that the reactive power flow can represent the vibration strength component of the complex intensity,and the active power flow strongly depends on the structural damping of the finite beams.