In this paper, the problem of random vibration of geometrically nonlinear MDOF structures is considered. The solutions obtained by application of two different versions of a stochastic linearization method are compared with exact (F-P-K) solutions. The formulation of a relatively new version of the stochastic linearization method (energy-based version) is generalized to the MDOF system case. Also, a new method for determination of nonlinear stiffness coefficients for MDOF structures is demonstrated. This method in combination with the equivalent linearization technique is implemented in a new computer program. Results in terms of root-mean-square (RMS) displacements obtained by using the new program and an existing in-house code are compared for two examples of beam-like structures. ~~ Introduction Resurgent interest in high speed fight vehicles and the daily operation of the aging commercial and military aircraft fleets necessitate the further development of sonic fatigue technology to understand the fatigue mechanisms and to estimate the service life of aerospace structures subjected to intense acoustic and thermal loads. Efforts to extend the performance and flight envelope of high speed aerospace vehicles have resulted in structures which may behave in a geometrically nonlinear fashion to the imposed loads. Such behavior can have a significant effect on fatigue life. Further improvements in vehicle performance and system design are hampered by the limited understanding of the physical nature of geometrically nonlinear *NRC Postdoctoral

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Discontinuous system is playing an increasingly important role in terms of both theory and applications. In this paper, we are concerned with discontinuous BAM (bidirectional associative memory) neural networks with time-varying delays. Under the basic framework of Filippov solution, by means of differential inclusions theory, inequality technique, fundamental solution matrix of coefficients and the non-smooth analysis theory with Lyapunov-like approach, some new sufficient criteria are given to ascertain the existence and globally exponential stability of the anti-periodic solutions for the considered BAM neural networks. Simulation results of two topical numerical examples are exploited to illustrate the improvement and advantages of the established theoretical results in comparison with some existing results. Some previous known results are extended and complemented.

This study focuses on mixed time delayed, both leaderless and leader-follower problems of nonlinear multi-agent systems. Here, we find the stability criteria for multi-agent systems (MASs) by utilizing a proposed lemma, the Lyapunov–Krasovskii functions, analytical techniques, Kronecker product, and some general specifications to obtain the asymptotic stability for the constructed MASs. Furthermore, the criteria to establish the synchronization of leader-follower multiagent systems with linear feedback controllers are discussed. Finally, we provide two numerical calculations along with the computational simulations to check the validity of the theoretical findings reported for both leaderless and leader-follower problem in this study.

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