A hollow circular cylinder rotating with constant angular velocity and partially filled with a viscous incompressible fluid has been analyzed for stability. The analysis can be extended to apply to many different rotor geometries. The results of this analysis predict that over a range of operating speeds, the system is unstable. The extent of this unstable region is determined by the system parameters. The interplay between viscosity of the fluid and damping on the rotor is especially important in determining stability boundaries. A parametric study is presented for a rotor modeled as a cup in the middle of a symmetrically supported massless shaft. The rotor is subject to a linear spring and a linear damper. Rotor unbalance, gravity, and axial effects are considered negligible.

Linear stability methods were applied to a biomechanical model of the human musculoskeletal spine to investigate effects of reflex gain and reflex delay on stability. Equations of motion represented a dynamic 18 degrees-of-freedom rigid-body model with time-delayed reflexes. Optimal muscle activation levels were identified by minimizing metabolic power with the constraints of equilibrium and stability with zero reflex time delay. Muscle activation levels and associated muscle forces were used to find the delay margin, i.e., the maximum reflex delay for which the system was stable. Results demonstrated that stiffness due to antagonistic co-contraction necessary for stability declined with increased proportional reflex gain. Reflex delay limited the maximum acceptable proportional reflex gain, i.e., long reflex delay required smaller maximum reflex gain to avoid instability. As differential reflex gain increased, there was a small increase in acceptable reflex delay. However, differential reflex gain with values near intrinsic damping caused the delay margin to approach zero. Forward-dynamic simulations of the fully nonlinear time-delayed system verified the linear results. The linear methods accurately found the delay margin below which the nonlinear system was asymptotically stable. These methods may aid future investigations in the role of reflexes in musculoskeletal stability.

This paper analyzes the dynamics of a simple rotor mounted on a shaft constructed from a viscoelastic material. The equations are solved using a perturbation technique that is valid whenever viscoelastic time constants are much larger than elastic time constants. Regions of stable and unstable motion are discovered analytically. Several time histories for the rotor motion are presented.

Concrete structures are normally full of cracks, more so than structures of any other material, and the typical mode of failure of concrete is fracture rather than plasticity. Yet, fracture mechanics so far has not been introduced in standard specifications for concrete design. Its applicability has been doubted by concrete engineers, due to the fact that the linear elastic fracture mechanics was shown long ago to disagree with tests of brittle failures almost as much as the plastic limit analysis. Recent research, however, has shown that fracture mechanics formulations which take into account the nonlinear behavior in the fracture process zone and the distributed nature of cracking can be brought in good agreement with the test results. This has led in recent years to a tremendous surge of interest and intensification of research in the fracture mechanics of concrete. The present volume, which summarizes the recent research results, is thus a very welcome addition to the literature. The book consists of six chapters. Chapter 1, written by G. C. Sih, deals with the mechanics of material damage in concrete, which is characterized chiefly by the material strain energy density function. Chapter 2, prepared by A. DiTommaso, discusses the evaluation of concrete fracture, its microscopic aspects as well as the consequences of cracking for stress-strain relations. Chapter 3, authored by S. Mindess, is the largest chapter which treats fracture testing of cement and concrete and discusses the physical phenomena involved in fracture, the rate of loading effects, notch sensitivity, the fracture toughness parameters and their measurement techniques, and the effect of specimen size. A valuable aspect of this chapter is an extensive and detailed summary of the concrete fracture test data available in the literature. An excellent historical review, documented by a set of 175 references, is also given in this chapter. Chapter 4, written by S. P. Shah, analyzes the dependence of concrete fracture toughness on specimen geometry and composition. This chapter presents a lucid and thorough discussion of the resistance curves and their measurement techniques, proposes a theoretical model for the nonlinear fracture process zone, and gives many comparisons with test data. Fracture of fiber reinforced concrete is also discussed and a new model is presented. Chapter 5, by F. O. Slate and K. C. Hover, deals with microcracking in concrete, discussing the microscopic observations of microcracks as well as their effect on the properties of concrete, with particular attention to the differences between high strength and low strength concretes. Finally, Chapter 6, prepared by P. Jacquot, addresses the specialized field of interferometry

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