FEATURES OF LOW-FREQUENCY NATURAL VIBRATIONS OF A TUBULAR PRODUCT WITH LONGITUDINAL SLOTS

Abstract

Tubular products are widely used in engineering; with a significant portion operating under dynamic vibration loading. In such operational environments, the frequency of exciting factors may coincide with the natural oscillation frequencies of the specified products, leading to significant increases in loads and, sometimes, even their destruction. The object of the research is a cylindrical part with a diameter of 117 mm, a height of 86 mm, and a wall thickness of 2.48 mm. The subject of the research is the frequency and shape of natural oscillations in the frequency range of 0…10 kHz. The aim of the work was to determine the relative frequency of natural oscillations for specific shapes of the object in the presence of four cuts 1 mm wide evenly spaced around the circumference (along the axis of rotation) with a relative height of 0.25 and 0.5. By relative frequency, we mean the ratio of the frequency of natural oscillations of a cylindrical part with cuts to the frequency of natural oscillations of a part without cuts of a similar shape. By relative height, we mean the ratio of the depth of the cuts to the height of the part. The similarity of the shape is determined by the number of nodal lines located along the circumference (along the axis of rotation) n and located along the generator m. Such a classification allows us to more accurately determine the change in the frequency of natural oscillations as a function of the slot depth. To determine the shapes and frequencies of natural oscillations, the finite element method was used, implemented in the SolidWorks software package, along with the real-time speckle interferometry method. The classification of shapes was performed by analyzing the obtained images. The result of the research is the determination of the relative frequency of natural oscillations of specific shapes, so in the presence of slots with a relative height of 0.25 and the absence of nodal lines along the generator, the relative frequency is 0.987…0.862, when the nodal line coincides with at least one of the slots, and 0.918…0.962 when the nodal lines along the circumference are between the slots. For the corresponding cases with one nodal line along the generator, the relative frequency ranges narrow to 905..924 and 924…956, respectively. The largest stratification is observed for a shape with eight nodal lines along the circumference and a relative gap of 0.5 and is 0.491…0.743. Additionally, certain mode shapes cannot be classified by nodal line locations due to severe modal distortion resulting from a significant drop in structural stiffness. The results presented in relative terms can be applied to tubular products of different diameters.