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The dynamic properties of an existing structure are altered when the mass and stiffness properties of the structure are modified. In some cases it can be desired that a specific natural frequency of the structure should not change after modifications. In case of adding a number of masses on the structure, one of the pre-specified natural frequencies can be preserved by attaching a grounded spring on it. In the present study, a new method is developed based on the ShermanMorrison formula in order to determine the necessary spring coefficient. The performance of the developed method for damped structures is also investigated. Furthermore, an approach based on minimization of the described objective function is introduced for prediction of the best spring location.

The angular velocity of the input link of a mechanism fluctuates due to the inertia of links and the external forces, although it is generally assumed constant in design. The control of the crank angular velocity of a four-bar mechanism driven by a DC motor by moving sliding mode control is considered in this study. A time-varying slope is proposed based on the error state. The mathematical model of the motor-mechanism system is derived using Eksergian's equation of motion. First, the state space equations are solved numerically for constant motor voltage to show the velocity fluctuations of the crank. Then both the conventional sliding mode control method and the proposed moving sliding mode control method are applied to obviate this unwanted velocity fluctuation. The method is verified by numerical simulations as well as experimental studies. The results of both the sliding mode control and the moving sliding mode control methods are compared. It is shown that a moving sliding surface in the sliding mode control increases the robustness of conventional sliding mode control by decreasing the reaching time. Also, the performance of the moving sliding mode control against parametric variations and external disturbances is experimentally investigated by adding a mass and applying an unexpected force on one of the links of the mechanism.

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