The Piezoelectric Shunting Vibration Absorber (PSVA) has garnered attention for its effectiveness in vibration control. This paper aims to propose a novel PSVA capable of simultaneously amplitude reduction and vibration isolation under various conditions. The PSVA consists of a butterfly-shaped link component and a piezoelectric stack, connected to the structure to be damped via bolts. Subsequently, an equivalent schematic diagram of the PSVA is established, and its equivalent stiffness is determined. Taking a single-degree-of-freedom structure as an example, considering the dynamic stiffness of the shunting circuit, a dynamic model of the electromechanical coupled system is developed, obtaining the system’s acceleration response and force transmissibility frequency response functions. Following this, experimental equipment is designed and fabricated, and the performance of the PSVA is tested under various excitation conditions. Finally, inspired by the experimental results, a segmented inductance circuit is designed and tested for its capability to broaden the vibration control bandwidth.

Ensuring rotor stability is a major concern in engineering, as instabilities can lead to catastrophic failures. Existing literature shows that anisotropic boundary conditions significantly affect the parametric instability characteristics of rotors under periodical axial loads. However, there is little literature systematically analyzing the formation mechanism of parametric resonance under these boundary conditions or providing a detailed classification of the parametric instability regions. Therefore, this paper presents a comprehensive parametric instability analysis of a rotor subjected to periodic axial loads under anisotropic boundary conditions. A novel approach based on the multiple scales method is proposed to address anisotropy in the boundary conditions. Using this approach, the analytical boundaries of the parametric instability regions are derived, and a proof regarding the absence of certain parametric resonances is presented. These analytical solutions are validated by numerical results obtained from the discrete transition matrix method, which form the basis for systematically investigating the effects of anisotropy in direct or cross-coupling stiffness/damping coefficients on the rotor instability. The key scientific contributions of this work include: Deriving analytical instability boundaries, providing a more efficient alternative to purely numerical methods while maintaining high accuracy; Demonstrating the absence of parametric resonance of difference type under both isotropic or anisotropic boundary conditions; Discovering that anisotropy in stiffness coefficients can induce self-interaction within a given forward or backward whirl mode, as well as interaction between two forward or two backward whirl modes, leading to additional instability regions; Reducing anisotropy in direct damping coefficients may increase critical dynamic load coefficients, potentially enhancing rotor safety; If the cross-coupling stiffness coefficients exceed the threshold for triggering intrinsic instability, the rotor may become unstable in all operating conditions. All these findings offer insights into the stability management of rotors under various operating conditions and provide valuable guidance for designing and operating safer, more efficient rotor systems.

This research aims to seek a suitable way for analyzing the time-varying characteristics of some engineering phenomena such as the fuel consumption of flying rockets, the movement process of control rods used to regulate the reaction rate in nuclear reactors, etc. To address this problem, a simulated procedure containing modeling and response solving is proposed. A common variable cross-section pipeline with time-varying mass is designed as a practical time-varying system. A simplified segmented beam model with a moving interface is proposed to simulate the pipe's time-varying behavior. Then the Wentzel-Kramers-Brillouin (WKB)-recursive method is proposed to solve this time-varying problem. A two-segmented beam example is used to verify its computability. The computational efficiency is greatly improved in comparison with the conventional numerical integration methods. To validate this proposed procedure, numerical simulation is carried out and an experiment is specially designed and implemented. In the experiment, many cases of different rates of mass variation and excitation forces are carried out. Overall, the numerical dynamic responses match well with the experimental ones, which indicates that the proposed procedure is suitable for analyzing the system's time-varying characteristics.

Engineering structures are generally designed based on linear elasticity assumptions. However, it is difficult to describe the connected structures using a simple linear system, due to factors such as sliding and friction at interfaces, and variations in contact areas during vibration processes. Therefore, it is necessary to develop an approach to tackle such systems with interface nonlinearities. In this paper, we proposed an extended free-interface component mode synthesis method. According to the proposed method, the substructures are separated at the nonlinear interfaces. Then the component mode synthesis procedure is carried out. By reasonably neglecting the contributions of higher order modes to the damping and inertia terms, it is demonstrated that the nonlinear interface forces and their time derivatives can be expressed as functions of themselves, as well as modal displacements and velocities. This characteristic facilitates the synthesis of the reduced order models for substructures in the state space. Also owing to this operation, the original properties of nonlinear interface forces can be preserved as much as possible, without any linearization. This method is suitable for non-proportionally damped structures with local nonlinearities such as mechanical structures with nonlinear spring and dashpot connections, rotor-bearing systems and so on. It also may be an alternative for the dynamic analysis of jointed structures with contact nonlinearities. Two numerical examples are presented to demonstrate the capability of the proposed method: (1) an eighteen degrees of freedom spring-dashpot-mass system with cubic spring and cubic dashpot interface connections is studied and (2) a more complex mechanical structure: a dual-rotor system with deep-groove ball bearing inter-shaft support. The numerical simulation results indicate that the dynamic responses of the reduced order model match very well with that of the full model, revealing the high accuracy of the proposed method with low computational costs.

Parametric resonance can amplify vibrations to levels far beyond what the rotor system would experience under normal operating conditions. This results in excessive wear and tear, reduced operational lifespan, increased maintenance requirements, and even catastrophic failures. Therefore, it is urgently needed to figure out the instability regions of parametrically excited rotors and develop effective methods to control or regulate them. In this paper, our focus is on a damped single-span rotor with periodic axial load, a representative example of a parametrically excited system. The method of multiple scales is applied to solve the governing equations, and then the analytical instability regions' boundaries and forced vibration responses are derived. Based on these analytical results, the instability region classification is carried out. The absence of certain instability regions is rigorously demonstrated. It is found that the primary difference type does not exist, no matter whether the rotor system has isotropic or orthotropic supporting structures. If the supporting structures are isotropic, the secondary difference type also does not exist. In this case as well, the primary and secondary sum types, which are exclusively associated with either forward or backward whirling frequencies, do not manifest. After the instability region classification, the feasibility analysis of introducing piezoelectric shunt damping to stabilize the rotor system is proceeded. In the numerical simulation, it is seen that as the electrical resonant frequency is tuned to a targeted critical speed, the starting points (critical dynamic load coefficients) of instability regions associated with that critical speed are raised with the increase of piezoelectric shunt damping. This means a higher threshold of triggering the uncontrolled parametric resonance.

The rotor unbalance is a major source of rotor vibrations. Rotor vibrations often produce many undesired effects like noise, wear and fatigue, etc. In this paper, we try to seek the benchmark solutions for the unbalance responses of complex rotor-bearing system. The presented approach could be seen as the extension of transfer matrix method (TMM) in some sense. For the TMM, a disk or supporting structure cut off one uniform shaft el-ement into two and someone must use the compatibility condition between these two new elements to derive the transitive matrix. However, for the presented approach, it di-rectly solves the governing equations of uniform shaft elements with consideration of the effects of disks and supporting structures. Thus, this analytical approach is advantageous in reducing the times of matrix multiplication between state matrices and field matrices. One only needs to calculate the inversion of 16 x 16 dynamic stiffness matrix to find the steady state response. It saves the computer memory and is easy to be programmed. In addition, this analytical approach avoids the problems of selecting optimal discretization mesh densities in the case of FEM applications. For arbitrary linear boundary condition, the benchmark solutions are always easy to be obtained. The numerical simulation is car-ried out and two numerical examples are given to validate the new solutions. In which the finite element method is used as the numerical approach. Simulation results show that the benchmark solutions match very well with the FEM results. The effects of anisotropy in the supporting structures on the rotor's dynamic behavior, which are observed in this work, are also in accordance with many references. This validates the benchmark solutions further.(c) 2023 Elsevier Inc. All rights reserved.

Piezoelectric shunting vibration absorber (PSVA) has attracted considerable attention in recent years. Nonlinearity widely exists in practice although a linear host system is the original design intention. What would happen when the predesigned PSVA under the linear host system assumption is applied to those nonlinear vibration systems? To address this issue, a nonlinear host system with a PSVA is constructed. The nonlinear responses of the electromechanical-coupled system are obtained by using the incremental harmonic balance method. Semi-analytical solutions demonstrate that the predesigned shunting circuit under linear host system assumption does not only work effectively but also makes the stability of the host system worse. To suppress the resonant peak of the host system efficiently, the particle swarm algorithm is applied to determine the proper shunting circuit of the PSVA. The performances of the proper PSVA, such as the suppression effects on the resonant peak, and its influence on the stability of the host system are investigated by numerical examples. Together with the parametric analysis, the tuning rule of the shunting circuit is given which can be the guide in the practical application.

当多跨结构受到横向载荷产生振动时,支承与基座衔接处往往产生较大的支反力.针对该问题,以双支承的梁系统为例,基于压电换能原理,采用柱状压电陶瓷支承作为减振元件,并对其减振效果进行了理论分析.利用Hamilton原理推导了压电机电耦合边界条件下该系统的振动微分方程.结合有限元法和偏微分方程数值计算方法,对不同种类压电材料的机电耦合系统进行了模态分析和动力学响应计算.计算结果表明,压电陶瓷支承可以有效抑制多跨结构中支承传递到基座的振动和支反力.

Traditional metamaterial designs can only be applied to a single medium, such as air or resin. Inspired by the local resonators and Helmholtz resonators, a novel configuration called the local resonance Helmholtz (LRH) lattices is proposed in this paper. This metamaterial is designed to suppress the propagation of both solid-borne and air-borne sound waves simultaneously. Numerical simulations are adopted to obtain the dispersion curves, transmission characteristics, and mechanical properties. The experimental samples are fabricated through the stereo lithography appearance (SLA)-based 3D-printing technology to test the actual vibration isolation and sound insulation performances. The results show that both mechanical vibrations and air sound waves are attenuated, meaning the concept of LRH lattices is feasible. The proposed metamaterial provides new possibilities for the design of advanced material with simultaneous sound and vibration attenuation performances. (C) 2021 Elsevier Ltd. All rights reserved.

The present work investigates the existence/nonexistence of instability regions for a para-metrically excited linear gyroscopic system. To achieve this goal, a new approach is pro-posed to determine the boundaries of parametric instability regions. As long as the gyro-scopic system's undamped equations of motion are derived, one can easily use this ap-proach to determine its instability regions. For convenience, a rotor-bearing system with periodic axial loaded is used as a parametrically excited representative gyroscopic system. The approach rewrites the second order differential equations in the state space form. Then the generalized eigenvalue problem is solved to derive the left and right eigenvectors. They are used to decouple the governing equations and reduce the order. In the subsequent the-oretical derivation, the multiple scale method is applied to obtain the analytical solutions of the boundaries of instability regions. The numerical simulation is also carried out to val-idate the analytical boundaries. Wherein the numerical instability regions are obtained by applying the discrete state transition matrix method. From the theoretical and numerical analysis, we find out: (1) the analytical boundaries match well with the numerical results; (2) only the sum type instability regions can be observed; (3) the primary difference type instability regions do not exist; (4) the secondary or higher order difference type instability regions also may not exist.(c) 2022 Elsevier Inc. All rights reserved.

The parametric instability of an electromechanically coupled single-span rotor-bearing system subjected to periodic axial loads is studied. Here, the rotor system is equipped with two piezoelectric dampers, which has been developed in our previous work. The so-called electromechanically coupled characteristic is namely derived from that damper. By using assumed mode method and Lagrange equation, the equations of motion are derived. The multiple scales method is utilized to obtain the analytical instability boundaries. Numerical simulations based on the discrete state transition matrix method (DSTM) are conducted to verify the analytical results. With the comparison between analytical results and simulated results, we find that the additional combination instability regions are created due to the usage of piezoelectric dampers.

This work proposes a new calculation algorithm of the Wentzel–Kramers–Brillouin (WKB) solution for slow linear time-varying (LTV) systems based on the recursive formulation. For a linear dynamic system with time-varying (TV) mass, damping or stiffness, the recursive relations in real function form among the components of the WKB solution are obtained. The integral terms within the sampling intervals that cannot be solved analytically are approximated by simple algebraic calculations with high precision. Thus, the conventional expression of the WKB solution involving complex numerical integral terms is reduced to an analytical recursive formulation. An explicit function relationship between the TV system parameters and the dynamic response can be obtained when the external excitation is given. In the premise of similar accuracy, the recursive formulation has much higher efficiency than the conventional calculation process, which is verified by applying the proposed method to a particular LTV dynamic system.

A new approach for time-varying (TV) modal parameters identification is proposed in this research. In the identification process, the entire signal is divided into successive short time windows, where the structure response under white noise excitation is transformed into modal coordinates by the Independent Component Analysis (ICA) method. The de coupled time-varying Auto-Regressive Moving-Average (ARMA) model based on the new assumption of "short-time linearly varying" (STLV) is established with the extracted modal coordinates. The TV parameters can be obtained by solving a nonlinear least squares problem. The main motivation of the proposed approach is to simplify the model and reduce the computational difficulty. The effectiveness and accuracy are validated via both the numerical example and experiment. (c) 2021 Elsevier Ltd. All rights reserved.

In this paper, the dynamic behavior of a rotor system with electromechanically coupled boundary condition under periodic axial load is studied, where the boundary condition is derived from a ring-shaped piezoelectric damper which is developed for vibration control of rotor system. This damper is based on the piezoelectric shunt damping technique, which can produce much or little damping performance depends on the selection of shunt circuit parameters. By using assumed mode method and Lagrange equation, the equations of motion are derived. Actually these equations can also be derived from a general forced parametrically excited gyroscopic system. Thus, to analyze such system, a method of multiple scales is developed firstly, where a general procedure is proposed to establish solvability conditions. Subsequently, this procedure is applied to obtain the analytical instability boundaries and forced vibration responses. The analytical results show that the additional combination instability regions are created due to the introduction of shunt circuit. When the parametrically excited eccentric rotor is rotating, the parametric vibrations are superimposed on the unbalanced responses. As the resistance value of shunt circuit is increasing, both parametric vibrations and unbalance vibrations can be significantly suppressed. For the unbalanced responses, both the resonance and anti-resonance phenomena can be observed; whereas for the parametric vibrations, only the resonance phenomena exist. These phenomena indicate that we may achieve great vibration control performance for the rotor parametric vibrations by introducing the piezoelectric shunt damping, as long as the circuit parameters are well adjusted. To validate the obtained analytical expressions, the numerical methods are applied. Specifically, the discrete state transition matrix method (DSTM) is applied to validate the analytical instability boundaries and the Runge-Kutta method is conducted to verify the analytical frequency response functions.

This paper strives to derive the analytical solutions for the dynamic analysis of stepped multi-span rotor system, where the rotating shaft's internal damping effect is also considered. Specifically, the steady-state whirl analysis and free vibration analysis is given herein. For the steady-state whirl analysis, firstly, the stepped shaft is spilt to several uniform segments and their governing equations are established by Hamilton principle. Subsequently, by applying variable separation method and Laplace transform method to each segment's governing equation, their steady-state responses in terms of determinate interpolation functions multiplied by unknown boundary constants are derived. Then based on the transfer matrix method, each segment's boundary constants are determined with consideration of the compatibility conditions of each two adjacent segments and the end boundary conditions. For the free vibration analysis, one only need to remove the forced term in the steady-state form of transfer matrix and the rotor's characteristic equation will be obtained. Through the theoretical derivation, it is found that this analytical approach can be generalized to any isotropic elastic boundary conditions. To validate the proposed method, two case studies are proposed, where the finite element method is used as benchmark method. For the first one, the influence of internal damping on a uniform rotor's damped whirl characteristics and its stability is analyzed. The damped whirl characteristics analysis reveals that viscous internal damping result in the destabilization of forward modes as long as the spinning speed becomes higher than the critical speed. This phenomenon is also demonstrated by the time responses analysis. For the second one, the dynamic responses of a two-span three steps rotor-bearing system with isotropic viscoelastic boundary conditions are determined. All of simulated results show a great agreement between analytical results and FEM results. (c) 2021 Elsevier Inc. All rights reserved.

The parametric instability of a rotor system with electromechanically coupled boundary conditions under periodic axial loads is studied. Based on the current flowing piezoelectric shunt damping technique, the detailed rotor model is established by the finite element (FE) method. In the matrix assembly procedure, a novel simple process is proposed to make the equations of shunt circuits more conveniently to be introduced into the global FE equations. The discrete state transition matrix method which is used for determining the influence of circuit parameters on instability regions in this paper has also been presented. The numerical simulation shows that only the combination instability regions exist when the shaft is rotating. The mechanical damping has different effect on the simple and combined instability regions. These two points are consistent with the previous references, which verifies the obtained FE model. In addition, the simulated results also reveal that the introduction of shunt circuits has little influence on the rotor's original whirling frequencies. It gives rise to the appearance of new synchronous whirl modes. The new whirling frequencies are combined with the original ones to form the new combination instability regions. Furthermore, the resistance of shunt circuits has the same performance as the mechanical damping has. That is, moving up the start points of instability regions and expanding its width.

In this paper, a method based on Green's function is proposed for the dynamic analysis of a rotor-bearing system with electromechanically coupled boundary conditions. The rotor system is supported by two ring-shaped piezoelectric dampers, which has been manufactured in our previous research. Based on the piezoelectric shunt resonant circuits, e.g., current flowing shunt circuit, the rotor system's boundary condition will become complicated and electromechanically coupled. The Laplace transform method is applied to solve the partial governing equations with such boundary conditions and the steady-state whirl Green's function is derived subsequently. Since the Green's functions are fundamental solutions of the system, the steady-state whirl solutions can be obtained by applying the superposition principle. Owing to the solutions' concise form, it is convenient and suitable for analysis and computation. Validation of the proposed method is demonstrated by comparison with the finite element method (FEM). The simulated results show that the analytical solutions possess high accuracy and the piezoelectric damper has significant damping performance. (C) 2020 Elsevier Inc. All rights reserved.

新军事变革开展近20年来,人们的观点从"行动域"——战斗力至上转向"认识域"——新作战模式的兴起,包括部队编制和指挥系统也都在新军事变革之后产生了变化.对于未来战争,各国有了新的利益诉求和军事战略,各种新型科技也在一步步将未来战争推向更高的技术层次.本文从"信息技术主导下的精确作战能力"这一已有结果出发,进一步探究"下一代能力".初步探究目前情况下未来战争在"认识域"上的改变,并进一步分析信息化条件下未来战争发展过程中的内在困境和发展诉求.