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This paper summarizes the results that were obtained from investigations of vibrations of cover- and box-shaped elements that cover assemblies of automobiles and are intended to diminish noise. The problem is that the elements in hand can appear to be the additional source of vibrations. For the elements fastened on the automobile body, the conditions for vibration excitation and recommendations for design are made more precise, at the same time keeping in mind that the main function of mentioned elements is not the reduction of noise. Our approach consists of three main directions: modifying properties of material, changing structure of elements and recommendations for choosing the preparation of its fixation points.