Resonance in the Cart-Pendulum System—An Asymptotic Approach

The major objective of this research is to study the planar dynamical motion of 2DOF of an auto-parametric pendulum attached with a damped system. Using Lagrange’s equations in terms of generalized coordinates, the fundamental equations of motion (EOM) are derived. The method of multiple scales (MMS) is applied to obtain the approximate solutions of these equations up to the second order of approximation. Resonance cases are classified, in which the primary external and internal resonance are investigated simultaneously to establish both the solvability conditions and the modulation equations. In the context of the stability conditions of these solutions, the equilibrium points are obtained and graphically displayed to derive the probable steady-state solutions near the resonances. The temporal histories of the attained results, the amplitude, and the phases of the dynamical system are depicted in graphs to describe the motion of the system at any instance. The stability and instability zones of the system are explored, and it is discovered that the system’s performance is stable for a significant number of its variables.

Multiple Slip Impact on the Darcy–Forchheimer Hybrid Nano Fluid Flow Due to Quadratic Convection Past an Inclined Plane

Nowadays, the problem of solar thermal absorption plays a vital role in energy storage in power plants, but within this phenomenon solar systems have a big challenge in storing and regulating energies at extreme temperatures. The solar energy absorber based on hybrid nanofluids tends to store thermal energy, and the hybrid nanofluids involve the stable scattering of different nano dimension particles in the conventional solvent at a suitable proportion to gain the desired thermophysical constraints. The authors focus on the behavior of the inclined plate absorber panel as the basic solution of water is replaced by a hybrid nanofluid, including Cu (Copper) and Al2O3 (Aluminum Oxide), and water is utilized as a base surfactant in the current investigation. The inclined panel is integrated into a porous surface with the presence of solar radiations, Joule heating, and heat absorption. The fundamental equations of the flow and energy model are addressed with the similarity transformations. The homotopy analysis method (HAM) via Mathematica software is used to explore the solution to this problem. Furthermore, the important physical characteristics of the rate of heat transfer, omission and absorption of solar radiation, and its impact on the solar plant are observed.

Influences of Elastic Foundations and Material Gradient on the Dynamic Response of Polymer Cylindrical Pipes Patterned by Carbon Nanotube Subjected to Moving Pressures

Composite materials are frequently used in the construction of rail, tunnels, and pipelines as well as in the construction of aircraft, ships, and chemical pipelines. When such structural elements are formed from new-generation composites, such as CNT-reinforced composites, and their interaction with the ground, there is a need to renew the dynamic response calculations under moving pressures and to create new mathematical solution methods during their design. The aim of this study was to analyze the influences of elastic foundations (EFs) and material gradient on the dynamic response of infinitely long carbon nanotube (CNT)-based polymer pipes under combined static and moving pressures. The CNT-based polymer pipes resting on the EFs were exposed to the axial and moving pressures. The uniform and heterogeneous reinforcement distributions of CNTs, which varied linearly throughout the thickness of polymer pipes, were considered. After setting the problem, the fundamental equations derived to find new analytical expressions for dynamic coefficients and critical velocity, which are dynamic characteristics of cylindrical pipes reinforced by the uniform and linear distributions of CNTs, were solved in the framework of the vibration theory. Finally, numerical computations were performed to examine the effects of EFs on the critical parameters depending on the characteristics of the pipes, the speed of moving pressures, the shape of the distribution of CNTs, and the change in volume fractions.

Design of a Mechatronic Interface with Compliant Manipulator for Robot Assisted Echocardiography

A compliant manipulator with a compound soft actuator is proposed for robot-assisted echocardiography. The target application is devoted to the TOE echo (Trans-oesophageal echocardiography), which is conventionally performed by medical practitioners. The manual manipulation of the echocardiography probe shows significant risks such as human errors, exposure to ionizing radiation, and multitasking complexity. Automation of TOE provides advantages in terms of control, safety, and workload of the operator. This paper proposes a teleoperated robotic system assisting the physician to perform TOE, to be used in cardiac catheterization laboratories as well as hybrid operation theatres. A system containing a holder with master-slave Dynamixel servos and a manipulator with soft actuators has been developed. To alleviate the major lack of the previous designs in conducting the insertion tube, a robotic arm with a soft structure is proposed that has not hazards of conventional robot manipulators. The fundamental equations and relations for quasi-static control of the system are developed in this paper.

Foundations of Engineering Mathematics Applied for Fluid Flows

Based on a brief historical excursion, a list of principles is formulated which substantiates the choice of axioms and methods for studying nature. The axiomatics of fluid flows are based on conservation laws in the frames of engineering mathematics and technical physics. In the theory of fluid flows within the continuous medium model, a key role for the total energy is distinguished. To describe a fluid flow, a system of fundamental equations is chosen, supplemented by the equations of the state for the Gibbs potential and the medium density. The system is supplemented by the physically based initial and boundary conditions and analyzed, taking into account the compatibility condition. The complete solutions constructed describe both the structure and dynamics of non-stationary flows. The classification of structural components, including waves, ligaments, and vortices, is given on the basis of the complete solutions of the linearized system. The results of compatible theoretical and experimental studies are compared for the cases of potential and actual homogeneous and stratified fluid flow past an arbitrarily oriented plate. The importance of studying the transfer and transformation processes of energy components is illustrated by the description of the fine structures of flows formed by a free-falling drop coalescing with a target fluid at rest.