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Exact solutions are obtained for a model of the longitudinal displacement along an elastic tapered bar due to a force applied at its blunt end. A formula for velocity amplification is given; it specifies the velocity of the pointed end of the bar shortly after it feels the influence of the force. For a bar with an exponentially decreasing cross-sectional area, the velocity is magnified by twice an exponential function of length. This result has applications in the design of piezoelectric drills. In addition, we discuss the differences between the motions of rigid and elastic bars during the transient before one complete reflection of the wave induced by a force applied to an end of the bar. In this regime, force is proportional to velocity for elastic bars with constant cross-sectional areas. While the force-velocity relationship is more complicated for tapered elastic bars, their exact relationship is determined. [DOI: 10.1115/1.2424719]

A model has been developed for describing the stresses that arise during binder burnout in three-dimensional porous bodies. The pressure gradient that arises from the decomposition of binder in the pore space is treated as an equivalent body force. For input into the mechanics model, the pressure distribution is obtained from the analytical solution for three-dimensional porous bodies with anisotropic permeability. The normal and shear stresses are then calculated from finite element analysis for bodies of parallelepiped geometry. In general, the normal stresses occur at the center of the body and are an order of magnitude larger than the shear stresses. Both the normal and shear stresses depend on the body size, the body geometry, and on the permeability. [DOI: 10.1115/1.1460908]

Research describes the three-dimensional elasticity solutions of conical shell panel with cantilevered and clamped boundary conditons and its validation by convergence and comparison analysis. Data show that in conical shells, the frequencies of transverse bending modes increase with the increase in thickness.

We propose a mathematical model for pendelluft flow in a single airway bifurcation. The model is motivated by an apparatus used in an experimental study of the pendelluft by Ultman et al. (1988). We derive differential equations governing the fluid flow, which directly connect physiological parameters to the variables determining the pendelluft; this approach allows us to include nonlinearity in the model. If nonlinearity is neglected, our model is identical to the R-I-C circuits used by previous investigators. If nonlinearity is retained, we show that pendelluft can occur even in perfectly symmetric airway bifurcations. For the specific apparatus used in the experiments of High et al. (1991), we demonstrate that two qualitatively different pendelluft flows can occur in the system.

A method for analytically solving the amplitude equations governing the vibration of an inextensional beam, in special cases, is presented. Some terms of the amplitude equations are non-linear and require numerical solutions. However, in two limiting cases, symmetry considerations allow elimination of the non-linear terms, producing closed analytical solutions.