Bianchi type–I Model with Time Varying Λ and G: The Generalized Solution

In this paper, we have investigated the homogeneous and anisotropic Bianchi type–I cosmological model with a time-varying Newtonian and cosmological constant. We have analytically solved Einstein’s field equations (EFEs) in the presence of a stiff-perfect fluid. We show that the analytical solution for the average scale factor for the generalized Friedman equation involves the hyper-geometric function. We have studied the physical and kinematical quantities of the model, and it is found that the universe becomes isotropic at late times.

A 3-R(SRS)RP Multi-Loop Mechanism for Space Manipulation: Design, Kinematics, Singularity, and Workspace

Space manipulation has great prospects in aerospace applications. In this work, a multiloop robot, namely 3-R(SRS)RP multiloop mechanism, is presented. Its design, kinematics, singularity, and workspace are studied. The novel design is mainly reflected in the robot’s structure, variable section, and novel compound hinge. Given these features, the forward-displacement undertaken with a closed-loop method leads to a complex mapping diagram. Only numerical solutions are obtained in this model due to the variable section parameter λ. This variable affects kinematic performances such as bending and folding properties. Moreover, the node differential kinematics and the Jacobian matrix are solved to analyze singular configurations of the mechanism. The workspace is then evaluated via a numerical method with varying λ. The bending and folding properties and the continuous workspace of the given robot vary while changing λ. Hence, the robot has great potentials of good performances in various applications. With this robot, a multimodule manipulator with a wide range of operations, increased mobility and rigidity, variable geometry, and adaptable shape based on mission requirements can be constructed.

Transient Dynamics of Harmonic Devices Under Thermal Loading

Curved beams are an essential structural form widely used in the engineering industry. When loaded past a critical point, they may buckle in a bifurcation or snap-through mode. Studies have shown that structural buckling problems are highly sensitive to slight changes in thermal properties. A shallow curved beam model subjected to a harmonic excitation is considered in this paper. A simplified, dimensionless one degree of freedom model is obtained following the works of [1]. Using this model, the transient dynamics of the system is analyzed for varying forcing parameters. The effect of the arch rise (λ) is also examined as the varying thermal properties effect the geometry of the beam system. Dynamic and transient dynamic responses of the system are obtained in the time domain for both constant and linearly varying λ. Wavelet analysis is utilized to analyze this data in the frequency domain and it provided an effective representation of the system responses that are localized in both time and frequency.

Plane Symmetric Inflationary Universe with Hybrid Expansion Law and Time Varying Λ

Plane symmetric inflationary cosmological model using Hybrid Expansion Law (HEL) with flat potential and time varying in General Theory of Relativity has been studied. The solution of the Einstein’s field equations is obtained under the assumption of HEL which yields a time-dependent deceleration parameter presenting transition of the universe from the early decelerating phase to the recent accelerating phase. The physical and kinematical parameters of the models have been studied and discussed.