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The dynamic vibration absorber (DVA) has attracted attention since its invention. This paper deals with the optimization problems of the standard DVA and two other models of DVA called three-element DVA and non-traditional DVA for damped primary structures. Unlike the standard configuration, the three-element DVA contains two spring elements in which one is connected to a dashpot in a series and the other is placed in parallel. Meanwhile the non-traditional DVA has a linear viscous damper connecting the absorber mass directly to the ground. There have been some studies on the design of three-element and non-traditional dynamic vibration absorbers in the case of undamped primary structures. These studies have shown that both three-element and non-traditional DVAs perform better than the standard DVA. When the primary structure is damped, there are very few studies on the three-element and non-traditional DVAs in the literature. This article proposes a global-local approach to give approximate analytical solutions of the [Formula: see text] optimization for all standard, three-element and non-traditional DVAs attached to damped primary structures. The main idea of the study is based on the global-local criterion of the equivalent linearization method in order to replace approximately the original damped structure by an equivalent undamped one. Afterwards, the already derived expressions of the optimal parameters for the undamped primary system case are used with the equivalent undamped structure that was just obtained. The numerical simulations are carried out to verify the effectiveness of the obtained results. Additionally, design aids, which show the variation of the optimal design quantities for various DVA mass ratios and inherent structural damping ratios are also provided.

The indirect medical education (IME) and disproportionate share hospital (DSH) adjustments to Medicare's prospective payment rates for inpatient services are generally intended to compensate hospitals for patient care costs related to teaching activities and care of low income populations. These adjustments were originally established based on the statistical relationships between IME and DSH and hospital costs. Due to a variety of policy considerations, the legislated levels of these adjustments may have deviated over time from these "empirically justified levels," or simply, "empirical levels." In this paper, we estimate the empirical levels of IME and DSH using 2006 hospital data and 2009 Medicare final payment rules. Our analyses suggest that the empirical level for IME would be much smaller than under current lawabout one-third to one-half. Our analyses also support the DSH adjustment prescribed by the Affordable Care Act of 2010 (ACA)-about one-quarter of the pre-ACA level. For IME, the estimates imply an increase in costs of 1.88% for each 10% increase in teaching intensity. For DSH, the estimates imply that costs would rise by 0.52% for each 10% increase in the low-income patient share for large urban hospitals.

Objective: This study estimates the effects of generic competition, increased cost-sharing, and benefit practices on utilization and spending for prescription drugs. classes with practically no generic competition. All variables were constructed to measure each drug relative to its class at a specific plan sponsor. Data and Methods: Results:We estimated that the shift toward generic utilization had cut in half the rate of increase in the price of a prescription during [2007][2008][2009]. Specifically, the results showed that (1) rapid generic penetration had significantly held down costs per prescription, (2) copayment and other benefit practices shifted utilization to generics and favored brands, and (3) price increases were generally greater in less competitive classes of drugs. Conclusion: In many ways, Part D wasimplemented at a fortuitous time; since 2006, there have been relatively few new blockbuster drugs introduced, and many existing high-volume drugs used by beneficiaries were in therapeutic classes with multiple brands and generic alternatives. Under these conditions, our paper showed that plan sponsors have been able to contain costs by encouraging use of generics or drugs offering greater value within therapeutic classes. It is less clear what will happen to future Part D costs if a number of new and effective drugs for beneficiaries enter the market with no real competitors.

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