Sizing and location of the piezoelectric actuators and sensors for vibration control of flexible structures is usually based on maximum control effectiveness and achieving the maximum output for the vibration in the modes of interests. Integration of piezoelectric patches affects the mass and the original dynamic properties of the parent structure. This is the first part of the two-paper research which presents the theoretical development of the multi-objective fuzzy optimization technique of sizing and location of the collocated piezoelectric actuators and sensors on the thin-walled composite beam. The optimization criteria for the optimal size and location of piezoelectric A/Ss are based on the degree of controllability (DC) for controlled modes. The optimization procedure implies the constraining of the original dynamic properties change and the limitation of the mass increase. A pseudogoal function, derived based on the fuzzy set theory, gives an expression for global objective functions eliminating the use of weighting coefficients and penalty functions. the particle swarm optimization technique is used to find the optimal configuration.

Key words: piezoelectric element, actuator, vibration measurement, composite materials, beam, fuzzy logic, multi-objective optimization, theoretical model.