Search

This paper addresses the semi-analytical modeling and stability analysis of coupled slosh-tank dynamics within a multi-body system framework using the Homotopy Perturbation Method (HPM). The sloshing motion of the liquid inside the tank is represented using an equivalent pendulum model, which allows for a more accurate depiction of the dynamics involved. Nonlinear equations of motion are derived using the Lagrangian approach to account for lateral and longitudinal excitations, explicitly focusing on compressive oscillations. Our model investigates the influence of critical parameters, including viscous damping, amplitude, and excitation frequency. These parameters are examined at two specific points, one within and one outside the stability regions, to understand their effects on the overall system behavior. The study demonstrates that viscous damping is particularly significant in moving points from unstable to stable regions compared to other principal parameters. Simulations are conducted to visualize stability phenomena through stability diagrams, phase portraits, and time histories of sloshing amplitude. The results obtained using HPM are compared to those from the numerical Runge-Kutta method, validating the analytical approach. This comparison highlights the effectiveness of HPM in accurately capturing the dynamics and stability characteristics of coupled slosh-tank systems, offering valuable insights into the design and control of such systems. [ABSTRACT FROM AUTHOR]

This paper addresses the semi-analytical modeling and stability analysis of coupled slosh-tank dynamics within a multi-body system framework using the Homotopy Perturbation Method (HPM). The sloshing motion of the liquid inside the tank is represented using an equivalent pendulum model, which allows for a more accurate depiction of the dynamics involved. Nonlinear equations of motion are derived using the Lagrangian approach to account for lateral and longitudinal excitations, explicitly focusing on compressive oscillations.Our model investigates the influence of critical parameters, including viscous damping, amplitude, and excitation frequency. These parameters are examined at two specific points, one within and one outside the stability regions, to understand their effects on the overall system behavior. The study demonstrates that viscous damping is particularly significant in moving points from unstable to stable regions compared to other principal parameters.Simulations are conducted to visualize stability phenomena through stability diagrams, phase portraits, and time histories of sloshing amplitude. The results obtained using HPM are compared to those from the numerical Runge-Kutta method, validating the analytical approach. This comparison highlights the effectiveness of HPM in accurately capturing the dynamics and stability characteristics of coupled slosh-tank systems, offering valuable insights into the design and control of such systems.

Forced convection heat transfer in metal foams in the presence of radiation heat transfer is studied using the homotopy perturbation method (HPM). To see wall effects, Darcy-Brinkman model for the flow in porous media is used. A constant heat flux is imposed at the wall and the radiation heat transfer is modeled by a temperature-dependent conductivity. In the present study the case of conjugate convection and radiation heat transfer is analyzed by a semi-analytical approach for the first time. Effects of the radiation parameters (λ, Tr) and porous medium shape parameter (s) on the Nusselt number and dimensionless temperature profile are investigated. Moreover, a discussion on the accuracy and limitations of the HPM method will be presented.

In this paper, considering all the linear and nonlinear inertia terms of moving masses on a flexible beam, the dynamic response and dynamic stability of the beam are studied. Homotopy perturbation method is used to perform the analysis and results are provided in a stability map for the different values of mass and velocity of the moving masses. It is concluded that there is a borderline in the diagram that separates the stable and unstable regions. For the first time, this borderline is determined semi-analytically. Results of the stability analysis are validated using the Floquet theory. In addition to this borderline, it is also concluded that the Homotopy perturbation method is capable of evaluating the new critical values for mass and velocity which cause vibration resonance in the beam. The locus of these resonant points, which is totally a new finding in dynamic analysis of beam-moving mass problem, is determined semi-analytically. Finally, the effect of the friction between the beam and the moving mass is studied on the stability of the system and resonant conditions. Accuracy of the results for this case is also evaluated with a numerical simulation.