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The dynamical motion properties of the variable mass infinitesimal body are investigated under the effects of the gravitational forces of the kerr-like oblate heterogeneous primaries which are situated at the vertices of an equilateral triangle. The effects of the coriolis as well as centrifugal forces are also considered. Under the effects of the above perturbations we evaluate the equations of motion, and then we perform the important dynamical properties of motion such as the locations of parking points, their stability, first return map (i.e. Poincaré surfaces of section), regions of motion by evaluating quasi-Jacobian integral and trajectory allocations by well-known software Mathematica. This study will show the effects of perturbations on these motion properties in various cases such as classical case and for different values of perturbations. One can compare these results from the results available in the literature.

Forces defined in the framework of optical reference geometry are introduced in the case of stationary and axially symmetric Kerr black hole and naked-singularity space–times with a repulsive cosmological constant. Properties of the forces acting on test particles moving along circular orbits in the equatorial plane are discussed, whereas it is shown where the gravitational force vanishes and changes its orientation and where the centrifugal force vanishes and changes its orientation independently of the velocity of test particles related to the optical geometry; the Coriolis force does not vanish for the velocity being nonzero. The space–times are classified according to the number of circular orbits where the gravitational and centrifugal forces vanish.

This paper reviews several innovative techniques that have been developed in our labs to overcome the shortages of conventional sol-gel techniques, and discusses the technical details of preparing these ceramic coatings with controllable thickness, microstructure, composition and improved properties.

Electromechanical nanocantilevers are promising for using as sensors/detectors in centrifugal-fluidic systems. For this application, the presence of angular speed and electrolyte environment should be considered in the theoretical analysis. Herein, the pull-in instability of the nanocantilever incorporating the effects of angular velocity and liquid media is investigated using a size-dependent continuum theory. Using d’Alembert principle, the angular speed is transformed into an equivalent centrifugal force. The electrochemical and dispersion forces are incorporated considering the corrections due to the presence of electrolyte media. Two different approaches, i.e., the Rayleigh–Ritz method (RRM) and proposing a lumped parameter model (LPM), were applied to analyze the system. The models are validated with the results presented in literature. Impacts of the angular velocity, electrolyte media, dispersion forces, and size effect on the instability characteristics of the nanocantilever are discussed.

A steady Newtonian fluid flow through annular region in curved pipes is studied in this paper. The flow takes place due to an axial pressure gradient and it is three-dimensional in nature. The equations governing the flow are highly coupled and nonlinear. The solutions are obtained, analytically, using a regular perturbation method. The effects of curvature ratio $(\delta )$, Reynolds number (Re) and the radius ratio $(l)$ on the axial velocity and stream function are presented graphically. It is observed that, along with curvature ratio and Reynolds number, radius ratio highly affects the fluid flow in annular curved pipes.

In this study, an experimentally validated spatial analysis method for the vehicle–bridge interaction system was modified to include the features of vehicle braking and accelerating. The effect of braking or accelerating was considered as external force acting on the vehicular center of gravity and was quasi-statically distributed to every tandem, for which the formulae of load redistribution were derived. The effect of centrifugal force was also incorporated in the model. Based on the modified spatial analysis method, the dynamic responses of a three-span continuous concrete box girder bridge due to vehicle braking and accelerating were studied. Impact factors, including deflection, bending moment, torsional moment and shear force, were examined. The results show that vehicle braking has considerable effect on dynamic responses and the impact factors are related to braking rise time and braking position, but cases of vehicle braking do not always cause larger effects. While the increase in initial speed can produce higher maximum dynamic responses and corresponding impact factors, the dynamic responses in the first span of a multi-span bridge are smaller than those in other spans due to vehicle accelerating.

The spatial-varying frequency of a vehicle-bridge interaction (VBI) system subjected to a moving mass is theoretically derived and numerically investigated through a three-dimensional VBI model, in which the effects of moving mass are introduced through the inertial force and centrifugal force in the equation of motion of the bridge. For a large vehicle-to-bridge mass ratio, it has been known that the frequency of a VBI system could change with respect to the location of a moving vehicle. As such, this study derives the analytical solution based on a moving mass-beam system to account for frequency variation and further builds the numerical model with detailed implementation for practical applications. The numerical results show the following findings: (1) The frequency of a VBI system is a function of velocity and location of a moving vehicle. (2) The reduction of spatial-varying frequency ratio for a particular mode decreases with respect to the mode of higher order. (3) The maximum reduction of spatial-varying frequency ratio of the first mode in a moving mass-beam system occurs in the location where the bridge has the maximum deflection as a result of local mode excitation. (4) For the VBI system with high suspension stiffness and large vehicle-to-bridge mass ratio, the absolute variation of spatial-varying frequency ratio of the first mode can be up to 30–40%.

This work performs a topology optimization of the interior structure of engine blades in compressors with any given geometry of the desired outer-surface shape that may be determined by CFD and aerodynamic design software for the desired performance for thermal and fluid flows. A lofted compressor airfoil surface from the aerodynamic design was used to create a three-dimensional (3D) solid in SolidWorks. This was converted to an .IGS file that would be imported into HyperMesh® for the meshing and submitted to OptiStruct® for optimization. An optimization process is designed to produce an optimal interior structure, considering both pressure on the outer surface and centrifugal forces produced by rotational movements. The optimized blade becomes hollow in an optimal pattern with minimum materials needed for the pressure loading on outer skin and the distributed centrifugal forces. The final design was compared to the initial design using finite element method (FEM) to confirm that the mass, stress, strain, and displacement were reduced. The mass was reduced by 59.8% and the stresses reduced by a factor of 3.66! These results were validated by conducting a mesh independence study. 3D printers were used to produce the optimized blades in both plastic and metal.

If a Slinky suspended in a U-shape is rotated horizontally, it will have the shape of an upside-down $\mathrm{\Omega }$, like $\mathrm{\Omega }$, due to the centrifugal force in the horizontal direction acting on each point of the Slinky. In this paper, we discuss the shape of a rotating Slinky in both theoretical and experimental aspects. The rotating Slinky has the shape described by a multi-valued function if the angular velocity of the rotation satisfies $\omega >\pi \sqrt{K/M}$. Our theoretical results are in good agreement with experimental observations. The video of the experiments can be viewed at https://youtu.be/rpu9Ol2jdAM.