Narrow Results

This study focuses on the steady-state periodic response and the chaotic behavior in the transverse motion of an axially moving viscoelastic tensioned beam with two-frequency excitations. The two-frequency excitations come from the external harmonic excitation and the parametric excitation from harmonic fluctuations of the moving speed. A dynamic model is established to include the finite axial support rigidity, the material derivative in the viscoelastic constitution relation, and the longitudinally varying tension due to the axial acceleration. The derived nonlinear integro-partial-differential equation of motion possesses space-dependent coefficients. Applying the differential quadrature method (DQM) and the integral quadrature method (IQM) to the equation of the transverse motion, a set of nonlinear ordinary differential equations is obtained. Based on the Runge–Kutta time discretization, the time history of the axially moving beam is numerically solved for the case of the primary resonance, the super–harmonic resonance, and the principal parametric resonance. For the first time, the nonlinear dynamics is studied under various relations between the forcing frequency and the parametric frequency, such as equal, multiple, and incommensurable relationships. The stable periodic response and its sensitivity to initial conditions are determined using the bidirectional frequency sweep. Furthermore, chaotic motions are identified using different methods including the Poincaré map, the maximum Lyapunov exponent, the fast Fourier transforms, and the initial value sensitivity. Numerical simulations reveal the characteristics of the periodic, quasiperiodic, and chaotic motion of a nonlinear axially moving beam under two-frequency excitations.

The aim of this work is to study the hydrostatic pump created under liquid sloshing in a rectangular tank partially filled with liquid. A numerical simulation was performed to predict the liquid motion in the tank. The apparition of the compression and the depression zones due to the liquid motion was presented and analyzed. An experimental setup with sinusoidal movement was developed to study the hydrostatic pump. The hydrostatic pump is created using a mixing element. The experimental results show that the compression and the depression zones can create the hydrostatic pump. The effect of the connecting chamber value was studied for different values of external excitation frequency. The pump depends considerably on the dimension of the connecting zone between the two volumes. For the different connecting chamber values, the pumped quantity increase with the increase of the frequency.