Abstract
Variable cross-section rods are used in many parts and mechanisms. For example, conical rods are widely used in percussion mechanisms. The strength of such parts directly depends on the natural frequencies of vibrations. Oscillations and vibration are also used in diagnostics, for example in acoustic diagnostics of defects. The paper presents a method that allows numerically finding a variable cross section of an elastic rod from the natural frequencies of longitudinal vibrations. It is assumed that the cross-sectional area varies along the axis and is described by an exponential function of a polynomial of degree n. The boundary condition on the left end is hard, on the right-elastic. It is shown that to determine n unknown coefficients of the cross section function, n natural frequencies are required.
Highlights
The problem of determining the natural frequencies and forms of longitudinal vibrations of rods with a variable cross-sectional area is well studied [1, 2, 3, 4]
Conical rods are widely used in percussion mechanisms
Oscillations and vibration are used in diagnostics, for example in acoustic diagnostics of defects
Summary
The problem of determining the natural frequencies and forms of longitudinal vibrations of rods with a variable cross-sectional area is well studied [1, 2, 3, 4]. This direction is relevant, because rods of various configurations are elements of many structures and machines. By formulation, the problem considered in this paper is the inverse, because it is not necessary to find the natural frequencies, but the law of changing the cross-sectional area by natural frequencies. In [9], an identification procedure is given for determining the characteristics of a crack (location and size of a crack) based on dynamic measurements
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