This study addresses the problem of an elastically anisotropic elliptical inhomogeneity bonded to an infinite elastically anisotropic matrix through a linear viscous interface. Our results show that uniform, as well as time-decaying stresses, still exist inside the elliptical inhomogeneity when the interface drag parameter, which is varied along the interface, is properly designed, and when the matrix is subjected to remote uniform antiplane shearing. Interestingly, the internal stresses decay with not one but two relaxation times. Some special cases are discussed in detail to demonstrate the obtained solutions.

Prediction of a rigid body falling through water column with a high speed (such as Mk-84 bomb) needs formulas for drag/lift and torque coefficients, which depend on various physical processes such as free surface penetration and bubbles. A semi-empirical method is developed in this study to determine the drag/lift and torque coefficients for a fast-moving rigid body in a water column. The theoretical part is to derive the relationships (called diagnostic relationships) between (drag, lift, and torque) coefficients and (position and orientation) of the rigid body from the three momentum equations and the three moment of momentum equations. The empirical part is to collect data of trajectory and orientation of a fast-moving rigid body using multiple high-speed video cameras (10,000 Hz). Substitution of the digital photographic data into the theoretical relationships leads to semi-empirical formulas of drag/lift and torque coefficients, which are functions of the Reynolds number, attack angle, and rotation rate. This method was verified by 1/12th Mk-84 bomb strike experiment with various tail configurations (tail section with four fins, two fins, and no fin and no-tail section) conducted at the SRI test site. The cost of this method is much lower than the traditional method using the wind tunnel. Various trajectory patterns are found for different tail configurations.

The effects of small vibrations on particle motion in a viscous fluid cell have been investigated experimentally and theoretically. A steel particle was suspended by a thin wire at the center of a fluid cell, and the cell was vibrated horizontally using an electromagnetic actuator and an air bearing stage. The vibration-induced particle amplitude measurements were performed for different fluid viscosities ( 58.0 cP and 945 cP ), and cell vibration amplitudes and frequencies. A viscous fluid model was also developed to predict the vibration-induced particle motion. This model shows the effect of fluid viscosity compared to the inviscid model, which was presented earlier by Hassan et al. (2004, “The Effects of Vibrations on Particle Motion in an Infinite Fluid Cell,” ASME J. Appl. Mech., 73(1), pp. 72–78) and validated using data obtained for water. The viscous model with modified drag coefficients is shown to predict well the particle amplitude data for the fluid viscosities of 58.5 cP and 945 cP . While there is a resonance frequency corresponding to the particle peak amplitude for oil ( 58.0 cP ) , this phenomenon disappeared for glycerol ( 945 cP ) . This disappearance of resonance phenomenon is explained by referring to the theory of mechanical vibrations of a mass-spring-damper system. For the sinusoidal particle motion in a viscous fluid, the effective drag force has been obtained, which includes the virtual mass force, drag force proportional to the velocity, and the Basset or history force terms.

An analytical solution to the virtual mass of a rotating fluid or solid sphere is obtained. The solution is valid at Reynolds number < 10 . The solution was based on integrating the kinetic energy of the fluid round the rotating sphere. The value of the virtual mass coefficient of the rotating sphere was found to be equal to 5.

The phenomenon of three-dimensional (3D) steady-state motion of a string traveling along an invariant curve in a flowing medium is studied. Existence conditions are found using a perturbation scheme where a known two-dimensional (2D) solution is used as an initial approximation.

The flow past a bluff body can be controlled significantly by placing small rotating cylinders at appropriate locations. Computational results for control of Re = 10 4 flow past a circular cylinder are presented. Two control cylinders of one-twentieth the diameter of the main cylinder rotate at a rate such that their tip speed is five times the free-stream speed of the flow. Computations are carried out for various values of the gap between the main and control cylinders. A stabilized finite element method is utilized to solve the incompressible Navier-Stokes equations in the primitive variables formulation. A gap value of one-tenth the diameter of the main cylinder is found to be close to the optimal value. Compared to the flow past an isolated cylinder a very significant reduction in the drag and unsteady forces is observed for the flow with control.

Aerodynamic interactions between parachute canopies can occur when two separate parachutes come close to each other or in a cluster of parachutes. For the case of two separate parachutes, our computational study focuses on the effect of the separation distance on the aerodynamic interactions, and also focuses on the fluid-structure interactions with given initial relative positions. For the aerodynamic interactions between the canopies of a cluster of parachutes, we focus on the effect of varying the number and arrangement of the canopies.

The paper examines the phenomenon of steady-state motion for a string traveling with constant velocity along an invariant curve under gravity in a viscous medium. This technically important phenomenon has been known in the literature for about 120 years and may be applied in high-speed turbines, the textile industry, etc. The conditions for the phenomenon’s existence are found. Concepts of two critical string velocities as well as sub, super, and hypercritical domains are introduced. The analytical solutions for the nonlinear differential equations and arbitrary constants for the general boundary conditions are found. The theoretical results are very close to the experimental ones.