To obtain approximate probability density functions for a class of axially moving viscoelastic plates under external and parametric white noise excitation

The probability density function plays an essential role to investigate the behaviors of stochastic linear or nonlinear systems. This function can be evaluated by several approaches but due to its analytical theme, the Fokker–Planck–Kolmlgorov (FPK) approach is preferable. FPK equation is a nonlinear PDE gives the probability density function for a stochastic linear or nonlinear system. Many researches have been done in literature tried to specify the conditions, in which the FPK equation gives an exact solution. Although, the exact probability density function can be achieved by solving the FPK equation even for some nonlinear systems, many types of systems cannot satisfy the conditions for exact solution. In this article, the axially moving viscoelastic plates under both external and parametric white noise excitation as one of the newest and applicable research areas are studied. Due to strong nonlinearities recognized in the governing equation of the system, the exact probability density function cannot be obtained, however, via an approximate method; some precise approximate solutions for different but comprehensive case studies are evaluated, validated, and discussed.     

Dynamic stability recognition of cylindrical shallow shells in Kelvin–Voigt viscoelastic medium under transverse white noise excitation

Nonlinear Dynamics - This paper investigates the problem of delay-dependent dissipativity for a class of Markovian jump neural networks with a time-varying delay. A generalized integral inequality...     

Some flower-like gaits in the snakeboard’s locomotion

The snakeboard is a modified version of the skateboard in which the front and back pairs of wheels can pivot freely about a vertical axis (see Fig. 1). The rider can generate motion by coupling a turning of his/her feet which lie on wheel platforms with an appropriate twisting of his/her body without kicking off the ground. The snakeboard was first presented in details by [Lewis et al., in Proceedings of the 1994 IEEE International Conference on Robotics and Automation, San Diego, CA, USA, May 1994, pp. 2391–2400]. In literature, it also has been studied as a prototype of the symmetrical nonholonomic locomotion systems. Geometrical modeling, finding the gaits, presenting the controllability ideas and designing desired trajectories are the subjects that can be found in the literature of the snakeboard. In this paper, we present some symmetric sensitive flower-like gaits for the snakeboard by suitable tuning of the input parameters. The highly symmetric patterns generated by these gaits, besides their inherent beauty, sensitivity to parameter variations and coherency; exemplify the rich information content of the underlying nonlinear system.