Influence of initial imperfections on nonlinear free vibration of elastic bars

Summary Nonlinear free vibration of elastic bars possessing initial imperfections is studied. This generalizes the problem of a perfect bar studied previously by Woinowsky-Krieger and Burgreen. For the vibration frequency the differential equation is solved exactly in terms of complete elliptic integrals. Numerical results demonstrate that the initial imperfections usually reduce the frequency of nonlinear free vibration of elastic bars subjected to moderate compression, but there are exceptions with the opposite effect. Such an effect of incerease in frequency was observed previously in unstiffened and cylindrical shells by Singer et al. The exact solution is contrasted with timewise single-term and two-term Galerkin approximations. It turns out that while the single-term treatment fails to show the increase, the two-term treatment brings it out with attendant close agreement with the exact solution.With 3 Figures     

Application of Thermography to Detection of Matrix Cracks in Transverse Layers and Yarns of Ceramic Matrix Composites

An approach to the estimate of the surface temperature in ceramic matrix composites tested for matrix cracks using thermography is presented. The solution deals with the case of damage in transverse layers or yarns where matrix cracks are parallel to the general fiber direction. The method used to correlate the surface temperature to the density of matrix cracks utilizes the energy balance and yields an explicit expression for the surface temperature.     

Effect of temperature on stresses and delamination failure of z-pinned joints

Although z-pins have been shown effective in preventing delaminations in adhesively bonded and co-cured joints, their applicability depends on a reliable assessment of the strength of a z-pin-composite assembly. In particular, high residual thermal stresses that have been found in experiments dictate the necessity in a local stress analysis. Elevated temperature applied to the joint during its lifetime may also affect its effectiveness in preventing delaminations. The present paper illustrates an approach to determining local residual stresses confirming the observations regarding a possible delamination and cracking in the composite structure due to high post-processing transverse stresses. The analysis of the effect of elevated temperature applied at one of the surfaces on the response of a z-pinned joint is conducted using the concept of a double cantilever beam with an “insulated” crack. In addition, it is illustrated that an elevated temperature may actually benefit the integrity of the joint if it causes an increase in the z-pin-composite interfacial strength.