Added mass and wave radiation damping for flow-induced rotational vibrations of skinplates of hydraulic gates

One observed vibration mode for Tainter gate skinplates involves the bending of the skinplate about a horizontal nodal line. This vibration mode can be approximated as a streamwise rotational vibration about the horizontal nodal line. Such a streamwise rotational vibration of a Tainter gate skinplate must push away water from the portion of the skinplate rotating into the reservoir and draw water toward the gate over that portion of the skinplate receding from the reservoir. The induced pressure is termed the push-and-draw pressure. In the present paper, this push-and-draw pressure is analyzed using the potential theory developed for dissipative wave radiation problems. In the initial analysis, the usual circular-arc skinplate is replaced by a vertical, flat, rigid weir plate so that theoretical calculations can be undertaken. The theoretical push-and-draw pressure is used in the derivation of the non-dimensional equation of motion of the flow-induced rotational vibrations. Non-dimensionalization of the equation of motion permits the identification of the dimensionless equivalent added mass and the wave radiation damping coefficients. Free vibration tests of a vertical, flat, rigid weir plate model, both in air and in water, were performed to measure the equivalent added mass and the wave radiation damping coefficients. Experimental results compared favorably with the theoretical predictions, thus validating the theoretical analysis of the equivalent added mass and wave radiation damping coefficients as a prediction tool for flow-induced vibrations. Subsequently, the equation of motion of an inclined circular-arc skinplate was developed by incorporating a pressure correction coefficient, which permits empirical adaptation of the results from the hydrodynamic pressure analysis of the vertical, flat, rigid weir plate. Results from in-water free vibration tests on a 1/31-scale skinplate model of the Folsom Dam Tainter gate are used to demonstrate the utility of the equivalent added mass coefficient.

The Resilience of Self-Esteem in Late Adulthood

OBJECTIVE: The authors examined the resilience of self-esteem after loss in the lives of older adults. Specifically, the authors investigated the relationship between loss and change in self-esteem during a 3-year period. METHOD: A subsample of older adults (n = 1,278) from the Americans' Changing Lives Study was used to examine loss in the domains of health, financial security, or work and career and self-esteem before and after the loss. RESULTS: There was a small but significant decrease in self-esteem between Wave I and Wave II of the study. Loss in one of the domains explained less than 1% of the variance in self-esteem change. DISCUSSION: The low incidence of loss and small change in high levels of self-esteem are further evidence of resilience in older adults' psychological well-being. The implications for older adults' use of cognitive strategies to manage losses and promote gains are discussed.