The control objectives in this paper are to move the gantry of a container crane to its target position and to suppress the transverse vibration of the payload. The crane system is modeled as an axially moving string equation, in which control inputs are applied at both ends, through the gantry and the payload. The dynamics of the moving string are derived using Hamilton’s principle for systems...

In this study, the effect of small-scale of both nanostructure and nano-fluid flowing through it on the natural frequency and longitudinal wave propagation are investigated. Here, the stationary and axially moving single-walled carbon nanotube conveying fluid are studied. The boundary conditions for the stationary nanotube is considering clamped-clamped and pined-pined and for the axially movin...

We study the small vibrations of an axially travelling string with a dashpot damping at one end. The is modelled by wave equation in time-dependent interval two endpoints moving constant speed v. For undamped case, we obtain conserved functional equivalent to energy solution. derive precise upper and lower exponentially decaying estimates for explicit constants. These do not seem be reported li...

In this paper, we are interested to stabilize an axially moving string subject external disturbances. We assume that the disturbance may increases exponentially. employ active rejection control (ADRC) approach estimate disturbance. design a observer has time-varying gain so can be estimated with exponential way. order closed loop system, use constructed through high-gain adaptive velocity feedb...

Based on classical plate theory, standard and spectral finite element methods are extended for vibration and dynamic stability of axially moving thin plates subjected to in-plane forces. The formulation of the standard method earned through Hamilton’s principle is independent of element type. But for solving numerical examples, an isoparametric quadrilateral element is developed using Lagrange ...