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This article investigates the impact of three harmonically external moments on the motion of a four-degrees-of-freedom (DOF) nonlinear dynamical system composed of a double rigid pendulum connected to a nonlinear spring with linear damping. In light of the system's generalized coordinates, the governing system (GS) of motion is derived using Lagrange's equations. With the use of the multiple-scales method (MSM), the approximate solutions (AS) of the equations of this system are obtained up to a higher order of approximation, maybe the third order. Within the framework of the absence of secular terms, the conditions of solvability are obtained. Accordingly, the different resonance cases are categorized, and three of them are investigated simultaneously. Thus, these conditions are updated in preparation for achieving the modulation equations (ME) for the examined system. The numerical solutions (NS) of the GS are achieved using the algorithms of fourth-order Runge–Kutta (4RK), which are compared with the AS, which displays their high degree of consistency and demonstrates the precision of the MSM. The motion's time history, steady-state solutions, and resonance curves are graphed to demonstrate the influence of various system physical parameters. All relevant fixed points at steady-state situations are identified and graphed in accordance with the Routh–Hurwitz criteria (RHC). Therefore, the zones of stability/instability of are checked and analyzed. Numerous real-world applications in disciplines like engineering and physics attest to the significance of the nonlinear dynamical system under study such as in shipbuilding, automotive devices, structure vibration, developing robots, and analysis of human walking. [ABSTRACT FROM AUTHOR]

Background: Mini-fluid challenge is a well tested and effective tool to predict fluid responsiveness under various clinical conditions. However, mini-fluid challenge has never been tested in patients with end-stage liver disease. This study investigated whether infusion of 150 ml albumin 5% can predict fluid responsiveness in cirrhotic patients following liver transplant., Methods: Fifty patients receiving living donor liver transplant were included in the analysis. Mini-fluid challenge composed of 150 ml of albumin 5% administered over 1 min in three consecutive 50-ml fluid boluses. An additional 350 ml was then infused at a constant rate over 15 min (for a total of 500 ml). Stroke volume (SV) was measured as the product of the subaortic velocity time integral (VTI) and left ventricular outflow tract (LVOT) area. Fluid responsiveness was defined as an increase in SV by ≥15% after the infusion., Results: Fifty patients were enrolled in the study. Fourteen patients were classified with Child A, 15 patients with Child B, and 21 patients with Child C cirrhosis. Thirty four patients were fluid responders and 16 patients were fluid non-responders. After 150 ml of albumin 5%, the SV increased significantly in our cohort. The area under receiver operating curve (AUROC) was 0.7 (95% confidence interval [CI] 0.5-0.8, P = 0.005). In subgroup analysis, the SV increased significantly after mini fluid challenge in the Child A group (P = 0.017) but not Child B or C groups (P = 0.3 and 0.29, respectively). The AUROC for mini-fluid challenge in the Child A group was 0.86 (95% confidence interval [CI] 0.6-0.9, P = 0.0004), while mini-fluid challenge failed to discriminate between responders and non-responders in Child B and C groups., Conclusion: A mini-fluid challenge of 150 ml albumin 5% can predict fluid responsiveness in liver transplant patients with fair sensitivity and specifiicty. Subgroup analyis revealed that minifluid challenge can predict fluid responsiveness in patients with Child A cirrhosis but not patients with Child B or C cirrhosis., Trial Registration: NCT03396159 . (Prospective registered). Initial registration date was 10/01/2018.