Determination of the Boundary Conditions for String Fastening Using Natural Vibration Frequencies in a Medium with a Variable Asymmetric Elasticity Coefficient

Abstract

This paper considers the inverse problem of identifying the boundary conditions for the problem of vibrations of a string in an elastic external medium, whose elasticity coefficient is described by an asymmetric potential. It is shown that, in contrast to the case of a symmetric potential, the boundary conditions can be uniquely identified, but this requires the use of three, rather than two, natural vibration frequencies. Cases are considered in which unique identification based on two natural frequencies is possible. Methods for determining the boundary conditions using two and three natural frequencies are proposed. The error of the methods is analyzed.