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Motion-induced oscillations of the flexible single link and its payload at the tip have negative impact on the anticipated performance of the flexible manipulators and thus should be suppressed to achieve tip positioning accuracy and high-speed operation. Because of the structural flexibility, the dynamics of the flexible manipulator can be described by coupled Duffing oscillators when considering the inherent structural nonlinearity of the flexible link into the dynamic modeling. However, little research has been focused on addressing the dynamic coupling issue in the nonlinear modeling of flexible-link manipulators using coupled Duffing oscillators. This article presents coupled Duffing oscillators for the nonlinear modeling of flexible single-link manipulators and then proposes a control method for suppressing the nonlinear vibrations of the coupled Duffing oscillators. Simulated and experimental results obtained from a flexible single-link manipulator test bench are in good agreement with the proposed nonlinear modeling and also demonstrate the effectiveness of the proposed control techniques for vibration suppression of the flexible manipulator. [ABSTRACT FROM AUTHOR]

This paper investigates the weighted coordinated motion of coupled harmonic oscillators over weighted cooperative–competitive interactions. First, the traditional synchronisation and containment control concepts are extended to the weighted synchronisation and weighted containment control for the new cooperative–competitive networks. Then, weighted synchronisation problem and weighted containment tracking motion are respectively solved for the coupled harmonic oscillators. Compared with some existing results, the frequency parameters of coupled harmonic oscillators are unknown in this paper and some novel networked structures are introduced in order to make the harmonic oscillator followers converge to the convex hull spanned by leaders' weighted states. Particularly, if the topologies formed by every leader group and follower group are interactively balanced and every follower is weight-product balanced, or if some leader groups are not interactively balanced but satisfy some conditions, the coupled harmonic oscillators can all realise the weighted containment tracking motion. Simulation results are given to demonstrate the effectiveness of the proposed control schemes. [ABSTRACT FROM AUTHOR]

Topology optimization is an effective method in the design of acoustic media. This article presents optimization for graded damping materials to minimize sound pressure at a reference point or sound power radiation under harmonic excitation. The Helmholtz integral equation is used to calculate an acoustic field to satisfy the Sommerfeld conditions. The equation of motion is solved using a unit dynamic load method. Formulations for the sound pressure or sound power radiation in an integral form are derived in terms of mutual kinetic and strain energy densities. These integrals lead to novel physical response functions for solving the proposed optimization problem to design graded damping materials. The response function derived for individual frequency is utilized to solve the multi-objective optimization problem of minimizing sound pressure at the reference point for excitations with a range of frequencies. Numerical examples are presented to verify the efficiency of the present formulations. [ABSTRACT FROM AUTHOR]

Hermetic digital scroll compressor has been widely used as a small-scale organic Rankine cycle application in the heating, ventilation, and air conditioning systems. A clunking noise issue is recently found in an air conditioning outdoor unit, and the main cause of the noise is experimentally identified to be the impact of the scrolls in the compressor unit during the switching process. The semi-active control methods are thus designed to greatly reduce the noise level by using additional valves to adjust the pressure changing rate within the modulation chamber. The response time for the impact of the scrolls can then be controlled by the added valves. The additional release valve with a smaller diameter pipe parallel to the main valve is tested firstly for its performance. Slower flow rate is produced and the pipe can extend the response time and decrease the speed of the impact process by reducing the pressure changing rate. The use of a discharge valve is also tested for controlling the pressure changing rate inside the chamber. The discharge valve with an opposite effect to the release valve is found useful for solving the noise issue. Both noise and vibration results confirm that the impact noise in the frequency range of interest can be reduced by using the proposed semi-active control methods. [ABSTRACT FROM AUTHOR]

This paper studies the solution behaviour of a general delayed predator-prey model with discontinuous prey control strategy. The positiveness and boundeness of the solution of the system is firstly investigated using the comparison theorem. Then the sufficient conditions are derived for the existence of positive periodic solutions using the differential inclusion theory and the topological degree theory. Furthermore, the positive periodic solution is proved to be globally exponentially stable by employing the generalized Lyapunov approach. The global finite-time convergence is also discussed for the system state. Finally, the numerical simulations of four examples are given to validate the correctness of the theoretical results. [ABSTRACT FROM AUTHOR]

This paper investigates the stochastic synchronization and pinning control in the sense of probability distribution for a general model of complex heterogeneous dynamical networks subjected to stochastic disturbances. Some generic stochastic synchronization criteria are established for both cases of undirected and directed topology by using the ergodic theory on stochastic dynamical systems. Compared with most existing studies on the stochastic synchronization in the sense of mean square, it is demonstrated that the concept of stochastic distribution synchronization can well characterize the realistic structure and essential nature of complex practical stochastic systems. Subsequently, two representative examples of complex heterogeneous dynamical networks, namely coupled stochastic Duffing oscillators and coupled FitzHugh‐Nagumo neuron oscillators, are given to illustrate and numerically verify the theoretical results. [ABSTRACT FROM AUTHOR]

Frequency domain filtered-x least mean square algorithms can reduce the computational complexity of the time domain counterpart with long filters; however, they suffer from large block delay, additional quantization error due to large size transformations and implementation difficulties in existing DSP hardware. In this paper, a time–frequency domain flexible structure is proposed using the partitioned block frequency domain adaptive filtering technique, which has no signal path delay and is well suited for low-cost DSP implementation. The proposed structure divides the long filters into many equal partitions and carries out the control filter update in frequency domain while generating the control signal in both time and frequency domains, thereby eliminating the forward path delay completely while maintaining low computational complexity. The proposed structure has a potential benefit for controlling broadband noise, where the causality constraint is more important. The simulation results using the measured acoustic paths demonstrate that the proposed structure maintains similar control performance as that of the time domain algorithm but with much less computational complexity. Furthermore, the tracking performance of the proposed structure under different levels of measurement noise is investigated. [ABSTRACT FROM AUTHOR]

Undesirable vibrations that occurred in cold rolling mills, widely known as chatter, are studied in this article by considering the interaction of three types of vibrations, namely, the longitudinal vibration of the rolled strip and the torsional and vertical vibrations of the upper work roll. The dynamic component of rolling force is determined using the quasi-static model under the assumption that the changes in roll gap and strip tension produce the variation of rolling force. The coupled vibrations of the work roll and rolled strip are mathematically governed by a set of 3-degree-of-freedom non-linear equations. Under chatter conditions, a new variable is introduced to represent the motion of the quasi-neutral point. A stability criterion for the motion of the quasi-neutral point is developed by studying the eigenvalues of the corresponding characteristic equation of the linearized parts of the non-linear equations. The chatter stability can then be examined by evaluating the determinants of five matrices. Numerical examples are given to show the stable and unstable vibrations in the cold rolling process. The unstable vibration would lead to skidding phenomenon and even break the rolled strip. The results presented in this article provide new insights into the dynamic interaction of the coupled vibrations and the dynamics of the rolling process. [ABSTRACT FROM AUTHOR]

By taking advantage of periodic high-frequency flexure deformation of screen panels, flip-flow vibrating screens (FFVSs) can achieve outstanding sieving performance. As the amplitude of the relative displacement between the main frame and the floating frame of a FFVS exceeds the relaxing length of screen panel, the tensile stress generated from the deformation of screen panel can considerably affect the dynamics and the screening performance of the FFVS. However, there is a research gap in understanding the mechanical properties (especially the stiffness and damping) of screen panels. To address this research issue, the dynamic tests are first conducted to investigate the dynamic behavior of screen panels under harmonic excitations. Then the Kelvin-Voigt (KV) model is adopted to represent the hysteresis feature of the tension force. Furthermore, to characterize the mechanical properties of the screen panels under different stretching lengths, a nonlinear mechanical model is introduced and incorporated into the dynamic model of the FFVS. The effects of the stiffness, damping and relaxing length of screen panel, the shear springs and the eccentric mass moment on the vibration characteristics of the FFVS are numerically studied using a genetic algorithm and Newmark- β algorithm. The obtained results show that the panel tension force can induce the hardening nonlinearity in the relative displacement response of FFVS and the soft type of nonlinearity in the displacement response of the main screen frame in a certain frequency region. Furthermore, at the second-order resonance peak, a small change in frequency can cause a substantial increase in the vibration amplitude of the main frame and a significant decrease in the relative amplitude. This nonlinear phenomenon would induce a large alternating stress on the main frame structure and thus reduce the service life of the FFVS. [Display omitted] • The mechanical properties of screen panels is experimentally investigated. • The stiffness and the damping features of screen panel is obtained. • A integrated nonlinear dynamic model of the flip-flow screen system is proposed. • The effects of screen panels on the dynamics of the screen system is investigated. [ABSTRACT FROM AUTHOR]