Bounded invariant verification for time-delayed nonlinear networked dynamical systems

We present a technique for bounded invariant verification of nonlinear networked dynamical systems with delayed interconnections. The underlying problem in precise bounded-time verification lies with computing bounds on the sensitivity of trajectories (or solutions) to changes in initial states and inputs of the system. For large networks, computing this sensitivity with precision guarantees is challenging. We introduce the notion of input-to-state (IS) discrepancy of each module or subsystem in a larger nonlinear networked dynamical system. The IS discrepancy bounds the distance between two solutions or trajectories of a module in terms of their initial states and their inputs. Given the IS discrepancy functions of the modules, we show that it is possible to effectively construct a reduced (low dimensional) time-delayed dynamical system, such that the trajectory of this reduced model precisely bounds the distance between the trajectories of the complete network with changed initial states. Using the above results we develop a sound and relatively complete algorithm for bounded invariant verification of networked dynamical systems consisting of nonlinear modules interacting through possibly delayed signals. Finally, we introduce a local version of IS discrepancy and show that it is possible to compute them using only the Lipschitz constant and the Jacobian of the dynamic function of the modules.     

Acoustic topology optimization of sound power using mapped acoustic radiation modes

An efficient approach for acoustic topology optimization to minimize the radiated sound power from a vibrating structure is described. The topology optimization is implemented by modifying the local stiffness at discrete locations on the surface of the structure. The radiated sound power level from the structure is directly chosen as the objective function to be minimized. A sensitivity analysis is then implemented to further optimize the layout of the locations of the modified local stiffness. To speed up the computational process, the radiated sound power is computed based on mapped acoustic radiation modes. To demonstrate the acoustic topology optimization using mapped acoustic radiation modes, the radiated sound power of a compressor housing is examined. Based on results from the numerical model, the local stiffness of a compressor housing was experimentally modified. Good agreement in sound power reduction obtained both numerically and experimentally was observed for the overall trend for the sound power levels as a function of one-third octave frequency bands.     

Optical image asymmetric cryptosystem using fingerprint based on iterative fraction Fourier transform

A novel asymmetric cryptosystem for optical image is proposed using fingerprint based on iterative fractional Fourier transform. To enhance the security, a hyperchaotic phase generated by a 4D Lorenz system is considered as the public key in the proposed encryption system, while the private key is emerged by the retrieved phase and fingerprint. In the encryption process, the secret information is hid into the hyperchaotic phase. Subsequently, the private key can be obtained by a reversible operation. To decrypt the original image, the ciphertext and private key are imported into the input plane of fractional Fourier system. This system is also applicable for information authentication because the fingerprint is used both in encryption and decryption approach. Some numerical simulations have been done to test the validity and capability of the encryption system.     

Energy harvesting from a magnetic levitation system

Numerical and experimental studies of a magnetic levitation harvester are presented in the paper. The idea is based on the motion of permanent cylinder magnet in a coil exploited for energy harvesting. The novel model is based on a new definition of the coupling coefficient (inductive coefficient) which relates mechanical and an electrical components. The performed static and dynamics experimental tests show that this coefficient is a nonlinear function of the magnet position, and highly depends on the magnet coordinate in the coil, in such a way that the maximum energy is obtained in a coil ends. The comparison between classical – fixed value model – and novel nonlinear model of the inductive coefficient is presented for selected cases. The most essential differences are presented.     

Bipartite flocking for multi-agent systems

This paper addresses the bipartite flock control problem where a multi-agent system splits into two clusters upon internal or external excitations. Using structurally balanced signed graph theory, LaSalle’s invariance principle and Barbalat’s Lemma, we prove that the proposed algorithm guarantees a bipartite flocking behavior. In each of the two disjoint clusters, all individuals move with the same direction. Meanwhile, every pair of agents in different clusters moves with opposite directions. Moreover, all agents in the two separated clusters approach a common velocity magnitude, and collision avoidance among all agents is ensured as well. Finally, the proposed bipartite flock control method is examined by numerical simulations. The bipartite flocking motion addressed by this paper has its references in both natural collective motions and human group behaviors such as predator–prey and panic escaping scenarios.     

Dynamical instability of laminated plates with external cutout

A method to study dynamical instability and non-linear parametric vibrations of symmetrically laminated plates of complex shapes and having different cutouts is proposed. The first-order shear deformation theory (FSDT) and the classical plate theory (CPT) are used to formulate a mathematical statement of the given problem. The presence of cutouts essentially complicates the solution of buckling problem, since the stress field is non-uniform. At first, a plane stress analysis is carried out using the variational Ritz method and the R-functions theory. The obtained results are applied to investigate buckling and parametric vibrations of laminated plates. The developed method uses the R-functions theory, and it may be directly employed to study laminated plates of arbitrary forms and different boundary conditions. Besides, the proposed method is numerical-analytical, what greatly facilitates a solution of similar-like non-linear problems. In order to show the advantage of the developed approach, instability zones and response curves for the layered cross- and angle-ply plates with external cutouts are constructed and discussed.     

Dynamic modeling and analysis of wind turbine drivetrain considering the effects of non-torque loads

With the increase of the rotor diameter and the deterioration of operating conditions, modern wind turbines suffer from more and more significant time-varying non-torque loads, which increases the burden of turbine structures especially the gearbox. Based on an aeroelastic loose coupling approach and assembly of the finite element method, an integrated drivetrain coupling analysis model including blade module, aerodynamic module, and gearbox module is established in this study. This proposed model is validated by comparing the calculation results with previous literature. Taking National Renewable Energy Laboratory 5-MW wind turbine as the research object, the gearbox vibration responses, gear meshing forces and bearing forces under non-torque loads caused by blade gravity, wind shear (WS), tower shadow (TS) and yawed inflow are studied in detail. Results show that the y-direction displacements of the gearbox, sun gear 1, sun gear 2 and gear are larger than those in x-direction because F_y or M_x generated by blade gravity, WS and TS dominates the non-torque loads. The non-torque loads lead to a non-uniform planet load sharing especially for the planetary gear stage 1. Because of the fluctuations of non-torque loads, not only the rotation frequencies of the corresponding carrier but also the multiple frequencies of the carrier 1 are observed in the frequency spectrums. The non-torque loads are mainly borne by carrier 1 bearings. Except for the blade gravity, the bearing forces caused by other unsteady inflows have obvious fluctuations.     

Leader-following formation control for second-order multiagent systems with time-varying delay and nonlinear dynamics

In this paper, the leader-following formation control problem for second-order multiagent systems with time-varying delay and nonlinear dynamics is considered. Two different cases of coupling topologies, fixed topology and switching topology, are analyzed. Based on the Lyapunov theory combined with the linear matrix inequality (LMI) method, sufficient conditions in terms of LMIs are given to ensure the multiagent systems can reach and maintain the desired formation. The simulation results are provided to demonstrate the effectiveness of the obtained theory results.     

Opinion dynamics in networks with heterogeneous confidence and influence

We propose a discrete-time model of opinion dynamics. The neighborhood relationship is decided by confidence radius and influence radius of each agent. We investigate the influence of heterogeneity in confidence/influence distribution on the behavior of the network. The simulations suggest that the heterogeneity of single confidence or influence networks can promote the opinions to achieve consensus. It is shown that the heterogeneous influence radius systems converge in fewer time steps and more often in finite time than the heterogeneous confidence radius systems. We find that heterogeneity does not always promote consensus, and there is an optimal heterogeneity so that the relative size of the largest consensus cluster reaches maximum in heterogeneous confidence and influence networks.     

Mutual diffusion in dense supercritical fluids

An expression for the mutual diffusion coefficient of a dense binary system of hard spheres, derived by using the Percus-Yevick approximation for the contact radial distribution function, together with Thorne's extension of the Enskog theory, is used to study the variation of the mutual diffusion coefficient with pressure, composition and ratio of the molecular diameters. Applications are made to real systems.