Torsional vibration usually occurs in the working process of machines and equipment such as in transmission drive and working shaft of machine tool. To reduce this vibration, the dynamic balancing method and dual mass flywheel systems are applied. There are fewer researches that used the dynamic vibration absorber for reducing the torsional vibration. However, an analytical solution for designing the optimal parameters of dynamic vibration absorbers attached to the damped main system is found to be difficult and complicated. This paper proposes a novel idea to approximately replace an original damped main system by an equivalent undamped system using the least squares estimation of equivalent linearization method. An explicit closed-form expression of the optimal damping ratio and tuning parameters of dynamic vibration absorber are determined for the undamped main system under torsional excitation. The expressions are quite simple and have effective practical applications. Numerical results for time and frequency responses of the system are presented to reveal stronger effect and accuracy of the proposed solution on the damped main system. It is observed that the torsional vibration of the damped main system has been reduced significantly also in the resonant region. The proposed expressions of the optimal parameters are powerful tools for design dynamic vibration absorber to reduce the torsional vibration of rotary system such as the transmission and working shafts, etc.

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The paper formalizes, in a rigorous manner, the concept of information externalities, by modeling R&D activities as the process of searching for a drug to treat a disease, with R&D activities being modeled from the perspective of the theory of optimal search. In conventional models of patent design, only one brand -the brand with the highest quality -is available on the market at any time. Furthermore, demand is completely inelastic: each consumer, regardless of income and regardless of the price of the brand offered on the market, buys exactly one unit of the brand. In this model, which is a dynamic model in continuous time, several differentiated products -the products whose patents are still in force and the products whose patents have expired -are available at any time on the market. Furthermore, the demand for a brand depends on income, its own price, and the prices of the other brands. The analyses of R&D as well as the impact of the cost and the quality of newly discovered drugs on the market are represented under this framework, when the pharmaceutical firms with an active drug discovery program behave strategically in both R&D and in the product market.

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