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For three-dimensional (3-D) vibration suppression of flexible beams, the most commonly used method is the boundary-controlled strategy, which is challenging to employ in general environments. In this study, a novel strategy by employing planned-motion flywheel assembly is designed to suppress 3-D vibration of flexible beams, which is easier to implement and more widely applicable than the boundary-controlled strategy. First, the dynamic equations of flexible beams with flywheel assembly are derived based on the Lagrange equation, where the Euler-Bernoulli beam theory and the geometric nonlinearity are employed. Subsequently, the phase delay method is employed to plan the motion of the flywheel assembly, while the optimal parameters in the expressions of flywheel assembly's motion are derived through the analysis of system energy. Theoretical results suggest that the flywheel assembly with planned motion enables the beam stable rapidly in free vibration and decreases displacement in forced vibration. Experimental results also demonstrate this strategy can enable the beam stable rapidly in free vibration under various initial conditions. The proposed control strategy can provide effective 3-D vibration suppression in flexible beams. [ABSTRACT FROM AUTHOR]

• An effective theoretical dynamics model of BFJDSs is proposed. • Vibration experiment of BFJDSs is conducted. • Experiment validates the present theoretical model. • Present model is applicable for bolt looseness and no-looseness conditions. Bolted flange joint disk-drum structures (BFJDSs) are key components in aero-engines, in which fatigue damage often occurs due to structural vibration. However, no study has so far given an effective theoretical dynamic model of BFJDSs. In this study, an effective dynamic model of BFJDSs is proposed. The present model considers the flange effect, non-uniform contact pressure of bolted joint, and bolt mass. The theoretical expression for describing the stiffness variation of bolted joints is presented. During the modeling process, the energy functions of disk, drum, and flange are obtained according to the Kirchhoff plate, Sanders' shell, and Euler-Bernoulli beam theories, respectively. The non-uniform artificial spring technique is adopted to simulate the pressure distribution of bolted joint. This method is capable of taking into account the contact pressure, which is closer to real contact situation. The displacement functions of disk and drum are expanded by using the Chebyshev orthogonal polynomials, and the motion equations are obtained by employing the Lagrange equation. Then, the experimental studies are performed on BFJDSs to illustrate the effectiveness of the theoretical model. Finally, the frequency veering and coupling vibration phenomena are revealed. The comparison studies indicate that the established theoretical model can well predict the vibration characteristics of BFJDSs under both bolt looseness and no-looseness conditions. The maximum error can be reduced from 46.81% to 3.61% by using the present dynamic model. [Display omitted] [ABSTRACT FROM AUTHOR]

• Dynamic model of shaft-disk rotors in axial non-uniform temperature field is developed. • Three-dimensional displacement fields for both shaft and disk are considered. • Temperature-dependent material properties are considered. • Present model can effectively predict vibrations of shaft-disk rotors in axial non-uniform temperature field. • Effect of non-uniform temperature field is related to the rotational speed and disk location. Research on vibrations of shaft-disk rotors in non-uniform thermal field is essential for the design of rotating machinery. In this paper, the dynamic model of axially loaded thin-walled shaft-disk rotors in axial non-uniform temperature field is developed, considering three-dimensional displacement fields of the shaft and disk. This model introduces the temperature-dependent properties of materials, and gyroscopic and centrifugal effects. Based on the Euler-Bernoulli beam theory and the Kirchhoff plate theory, Lagrange's equation is used to derive the differential equations of motion. By comparing with the results of the existing reference and finite element results, the accuracy of the present model is verified. The effects of the axial displacement of shaft, temperature-dependent material property, temperature difference, temperature distribution, disk position and axial preload on the free vibration of shaft-disk rotors are discussed. Results show that the present model can effectively predict free vibrations of shaft-disk rotors in axial non-uniform temperature field. The effect of thermal field on vibrations of shaft-disk rotors is affected by the rotational speed and disk location as well. [ABSTRACT FROM AUTHOR]

• A new strategy is proposed for vibration control of flexible pendulums. • We introduce a flywheel to control flexible pendulum vibration. • The control method has robustness and is effective for nonlinear forced vibration. • An experiment platform is built to validate the proposed control strategy. Flexible inverted pendulums have found wide applications in mechanical systems, but their stability is susceptible to external disturbances. In this study, a new strategy that employs a flywheel to suppress vibration of flexible inverted pendulums is proposed. We develop the theoretical dynamic model of flexible pendulums with a flywheel by the Euler-Bernoulli beam theory, where the axial displacement of the pendulum and geometric nonlinearities are considered. An active control method based on the Bézier trajectory is proposed, where the acceleration of the flywheel is set as the input. Additionally, the equivalent damping ratio of the system including flywheel's motion is derived. The relationship between the parameters in the control equation and the suppression effect is obtained through the simulation of the equivalent damping ratio. Then, an experimental platform is built. The experimental results show that the present control strategy has good suppression effect on the vibration of the flexible inverted pendulums when selecting appropriate parameters. Meanwhile, the results of anti-disturbance test show that the present method has a certain robustness. Finally, the simulation results show that this strategy is also effective for nonlinear forced vibration under different excitation frequencies. [ABSTRACT FROM AUTHOR]

• The piezo-actuated beam model considering the neutral surface offset caused by the piezoelectric actuator is established and the LADRC algorithm is designed. • Modal experiment and AVC experiment of the piezo-actuated beam are carried out. • The AVC of the piezo-actuated beam is studied by using theoretical and experimental methods. • The vibration suppression performance of the LADRC algorithm on piezo-actuated beams is studied, and the adaptability and anti-noise ability of the LADRC algorithm are explored. The active vibration control (AVC) of lightweight thin-walled structures on spacecraft has been a proven solution for vibration suppression. In this study, a linear active disturbance rejection control (LADRC) algorithm is presented for vibration suppression of piezo-actuated beams. Firstly, the governing equation of a piezo-actuated beam is obtained by using the Euler–Bernoulli beam theory and the Lagrange equation. The LADRC algorithm is designed for the piezo-actuated beam based on the governing equation. Then, the accuracy of the piezo-actuated beam model is confirmed by comparison with ANSYS and experiments. Finally, numerical simulations and experiments are carried out on the active vibration suppression of the piezo-actuated beam under the fixed harmonic excitation, variable harmonic excitation, and fixed harmonic excitation with measuring noise, respectively. The results show that the LADRC algorithm has an excellent control effect on structural vibration suppression, strong adaptability to various external excitations, and anti-noise ability. [ABSTRACT FROM AUTHOR]