Abstract. In this paper, the problem of optimal design for eigen-frequencies of a longitudinal bar using Pontryagin's maximum principle (PMP) considering the influence of concentrated mass is presented. The necessary optimality condition when simultaneously maximizing system's eigen frequencies and minimizing system's weight considering the influence of concentrated mass is established by using Maier objective functional in order to control the final state of the objective functional. By considering eigen frequencies as state variables, the analogy coefficient k in the necessary optimality condition is explicitly determined. Numerical results obtained in this paper include: (1) the bar's optimal configurations as well as frequency responses in different cases of objective functions; (2) the Pareto front for the system's first eigen frequency and weight; (3) the influence of concentrated mass on the bar's optimal configuration.

In this paper, the authors present the sliding mode control problem of a structure using hedge-algebras-based fuzzy controller considering the impact of time delay (de-sHAC). Controlled model is a structure subjected to earthquake excitations. Numerical simulations are implemented in order to show advantages of the proposed controller. Obtained results include: variation of maximum displacement and maximum absolute acceleration versus time delay; time responses of displacement, absolute acceleration and control force of the structure in the uncontrolled case, the controlled case using the hedge-algebras-based fuzzy controller with input time delay (de-HAC) and the de-sHAC.