Dengqing Cao

Further results on asymptotic stability of linear neutral systems with multiple delays

The problem of asymptotic stability of linear neutral systems with multiple delays is addressed in this article. Using the characteristic equation approach, new delay-independent stability criteria are derived in terms of the spectral radius of modulus matrices. The structure information of the system matrices are taken into consideration in the proposed stability criteria, thus the conservatism found in the literature can be significantly reduced. Simple examples are given to demonstrate the validity of the criteria proposed and to compare them with the existing ones.

Stability analysis of neural networks with periodic coefficients and piecewise constant arguments

Abstract Global exponential stability of a class of neural networks with periodic coefficients and piecewise constant arguments is investigated in this paper. A new definition of exponential stability and a novel differential inequality with piecewise constant arguments are introduced to obtain sufficient conditions for the globally exponential stability of the periodic solution of neural networks. The stability criteria are independent on the upper bound of the adjacent element difference of the discontinuous switching moments. According to the new definition of exponential stability and the novel differential inequality, not only it is not necessary to establish any relationship between the norms of the states with/without piecewise constant arguments, but also the stability criteria for the neural networks can be obtained just in terms of the original differential equation, rather than the equivalent integral equation which is widely used in the early works. Typical numerical examples are utilized to illustrate the validity and improvement in less conservatism of the theoretical results.

The vibration transmissibility of a single degree of freedom oscillator with nonlinear fractional order damping

ABSTRACT Motivated by the theoretical analysis of the effects of nonlinear viscous damping on vibration isolation using the output frequency response function approach, the output frequency response function approach is employed to investigate the effects of the nonlinear fractional order damping on vibration isolation based on Volterra series in the frequency domain. First, the recursive algorithm which is proposed by Billings et al. is extended to deal with the system with fractional order terms. Then, the analytical relationships are established among the force transmissibility, nonlinear characteristic coefficients and fractional order parameters for the single degree of freedom oscillator. Consequently, the effects of the nonlinear system parameters on the force transmissibility are discussed in detail. The theoretical analysis reveals that the force transmissibility of the oscillator is suppressed due to the existence of the fractional order damping, but presents different effects on suppressing the force transmissibility of the oscillator over the frequency region by varying the fractional order parameters. Moreover, the fractional order parameters, which affect the force transmissibility, the bandwidth of the frequency region and the resonance frequency, can be used as designing parameters for vibration isolation systems. At last, numerical studies are presented to illustrate the theoretical results.

Vibration characteristics and thermoelastic analysis of the supersonic composite laminated panel with arbitrary elastic boundaries

The novelty of this study is to present a theoretical approach to investigate the dynamic behaviors of the laminated panels under arbitrary elastic boundary conditions. The motion equations of panels considering the first order piston theory are derived using Hamilton principle. A solution of computing the vibration characteristics of a panel with arbitrary elastic boundaries is proposed based on the Rayleigh–Ritz method, in which the admissible functions are constructed by a set of characteristic orthogonal polynomials employing the Gram–Schmidt process; the support boundary is modeled by introducing the technology of artificial springs. The effects of spring stiffness and different boundaries on the dynamic characteristics and thermal aeroelastic behaviors are presented in detail. Numerical results show that the small ply angle and large spring stiffness are helpful to improve the aerodynamic stability. Multiple new phenomena have been observed, e.g. the phenomena of mode jumping and the alterations of coupled mode orders. Moreover, the thermal loads and aerodynamic loads play an opposite effect on the stability of composite panels.

Aero-Elastic Flutter Characteristics of Laminated Composite Panel Embedded with Shape Memory Alloy Wires

The effects of shape memory alloy (SMA) wires on the natural frequency, flutter boundary and amplitude of limit cycle oscillation (LCO) of a laminated composite panel are investigated. The classical plate theory as well as von-Karman strain-displacement relation are used to formulate the nonlinear dynamic model of the smart laminated panel. The aerodynamic loadings are simulated by the third order piston theory. The thermo-mechanical behavior of SMA wires is estimated according to one-dimensional Brinson SMA model. The effects of SMA wires temperature, pre-strain, volume fraction and orientation on flutter boundary and amplitude of LCO of the panel are analyzed in detail.

Random Attractors for Von Karman Plates Subjected to Multiplicative White Noise Loadings

The study on long-time dynamical behaviors of thin plates or panels subjected to random excitations is an important issue. Motivated by problems arising in practical engineering, the dynamics of Von Karman plates without rotational inertia can be described by a partial differential equation driven by multiplicative white noises which can generate a random dynamical system (RDS). According to the estimation of energy function for the vibrations of the plate, it can be proved that there exist random attractors for the corresponding RDS.