This paper presents a fixed-end Two-mass system (TMS) with end constraints that permits uncoupled solutions for different masses. The coupled nonlinear models for the present fixed-end TMS were solved using the continuous piecewise linearization method (CPLM) and detailed investigation on the effect of mass-ratio on the TMS response was conducted. The investigations showed that increased mass-ratio leads to decreased oscillation frequency and an asymptotic response was obtained at very large mass-ratios. Theoretical solutions to determine the asymptotic response were derived. Also, it was observed that distinct responses can be obtained for the same mass-ratio depending on the mass combination in the TMS. The present fixed-end TMS and the analyses presented give a broader understanding of fixed-end TMS.

Design of a robust controller via single objective constrained optimization using differential evolution (DE) is presented in this paper. A set robust feedback controller gain is optimized based on plant’s linear model having structured parametric uncertainty such that the closed-loop system would have the maximum stability radius. A wedge region is assigned as the optimization constraint to specify the desired closed-loop poles location which is directly related to the desired time-domain response. The proposed controller design is applied to a Two-mass system which is known as the benchmark problem for robust controller design. The simulation results show that the robustness performance is achieved in the presence of parameter variations of the plant. The proposed controller performs than the conventional LQR (linear quadratic regulator) controller.

In this study, the nonlinear free vibration of conservative Two degrees of freedom systems is analyzed using the homotopy analysis method (HAM). The mathematical model of such systems is described by Two second-order coupled differential equations with cubic nonlinearities. First, novel approximate analytical solutions for displacements and frequencies are established using HAM. Then, the homotopy Padeacute technique is applied to accelerate the convergence rate of the solutions. Comparison between the obtained results and those available in the literature shows that the first-order approximation of homotopy Padeacute technique leads to accurate solutions with a maximum relative error less than 0.068 percent for all the considered cases. 

The attendance of over 1000 people at certain locations and points of time has been defined as mass gatherings (MGs) by the World Health Organization (WHO) (1). Even so, the largest part of reports and articles published in this line typically refer to the number greater than 25000 people to mean such events. In recent times, the WHO further respects the presence of many people as MGs, which can in some way help evaluate the public health resources and performance of societies or countries. MGs, planned socially, culturally, religiously, politically, or in a combined manner, can all together give rise to numerous challenges for the healthcare systems. .