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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]

Bolt connection is commonly used to assemble shell structures in engineering fields. Prolonged external excitation can induce stick, slip, even separation states at the connection interface, leading to complex nonlinear dynamics in bolted shell structures. Understanding the dynamic mechanism of bolted joined shells under stick–slip-separation condition is crucial for the design and application of these structures. In this study, we aim to build the nonlinear dynamic model and reveal the vibration mechanism of bolted joined conical-cylindrical shells with stick–slip-separation behavior. During the development of the mechanical model of the bolt connection, the axial bilinear stiffness characteristics and interface friction behaviors are taken into account simultaneously, which could simulate the transition of the contact state at the connection interface. The rigid joint between the conical and cylindrical shells is realized via successive distributed artificial springs. Donnell's shell theory as well as the displacement assumption of Chebyshev polynomials are employed in theoretical modeling, and the governing equation is obtained by the Lagrange equation. In contrast with existing research and experimental data, the accuracy of the present theoretical model is validated. Both theoretical and experimental results indicate the frequency multiplication and dynamic softening phenomena as the excitation level increases. By the consideration of the stick-slip-separation behavior at the connection interface in the modeling, these nonlinear vibration behaviors can be effectively illustrated. Additionally, hysteresis characteristics are further investigated to explore frictional energy dissipation. The stick–slip-separation contact state at the connection interface under different excitation levels, bolt preloads and cone angles are also analyzed. The present investigation provides a basis for the design and health condition monitoring of bolted shell structures. [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]

• Nonlinear dynamics of bolted JCCSs are studied theoretically and experimentally. • Displacement-dependent characteristics in bolt connection zone are considered. • The developed model is capable of predicting nonlinear vibration of bolted JCCSs. • Experimental results validate the present theoretical model. This paper investigates the nonlinear dynamic characteristics of joined conical-cylindrical shells (JCCSs) with bolt connection for the first time. In the process of developing mechanical model of the bolt connection, the displacement-dependent stiffness and damping are taken into account, which could simulate the change of the contact state at the connection interface under different excitations. Both theoretical and experimental studies are performed to illustrate the nonlinear vibration behaviors of the bolted JCCSs. Successive uniform distributed artificial springs between the conical and cylindrical shells are adopted to simulate the rigid joint of the two shells. Donnell's shell theory is employed in theoretical modeling, and the governing equation is obtained by the Lagrange equation. The displacement admissible function applied in the research is Chebyshev polynomial. By comparison with existing literature and experimental data, the accuracy of present theoretical model is validated. It is found that both theory and experiment show a dynamic softening phenomenon with the increase of excitation level. Taking the displacement-dependent characteristics in bolt connection zone into consideration can effectively illustrate this soft phenomenon. The established model is capable of predicting the nonlinear vibration characteristics of JCCSs with bolt connection. [Display omitted] [ABSTRACT FROM AUTHOR]

• An effective mathematical model for bolted flange joints is proposed. • The proposed model is applicable for both bolt looseness and no-looseness conditions. • Experimental results validate the proposed model. • The soft nonlinearity characteristics of bolted flange joint multi-plate structure under base excitation are revealed. Bolted flange joints are widely used in various engineering structures to combine two or more substructures together. However, the understanding of mechanical mechanism of bolted flange joints is still insufficient due to the lack of efficient mathematical models. This paper proposes an effective mathematical model for bolted flange joints, which is then employed to conduct vibration analysis on bolted flange joint multiple-plate structures. During the modeling process, the flange is modeled by the Kirchhoff plate theory, and the bolted joints are modeled by the two-dimensional face constraint in bolted joint affected region (BJAR). The artificial spring technique is adopted to simulate the face constraint. The friction contact model and equivalent linearization technique are adopted to analyze the stick and slip states of bolted joints. By adopting the Chebyshev orthogonal polynomials as admissible functions, governing equations are derived. Then, the Rayleigh-Ritz method is applied to study the free vibration characteristics, and the Newmark-beta method is employed to study the vibration response under base excitation. The experimental studies are performed on the bolted flange joint two-plate structure (BFJTPS) to illustrate the effectiveness of the proposed theoretical model. The results indicate that the proposed mathematical model can well predict the vibration characteristics of multiple-plate structures under both bolt looseness and no-looseness conditions. The soft nonlinearity phenomenon under bolt looseness condition can be successfully revealed by the model. [ABSTRACT FROM AUTHOR]