Identification of the coefficients of equation for a vibrating rod in acoustic diagnostics

Abstract

The work is devoted to the study solving some inverse problem of identifying the coefficients of Sturm-Liouville operator. Inverse problems in vibration are concerned with constructing a vibrating system of a particular type, e.g., a string, a rod, that has specified properties. During the operation of the technical design, the dynamic characteristics can be changed by changing the boundary connection. Often these compounds are not directly accessible and their states can be judged from indirect information. In acoustic diagnostics, often the available information is the natural frequencies. Thus, by the set of natural frequencies it is necessary to estimate the state of the boundary connections. In this work an algorithm for constructive determination of coefficients of Sturm-Liouville operator is given. A straightforward solution of the inverse problem for Sturm-Liouville equation in a rod is presented.

Keywords

• sturm-liouville equation
• inverse problems
• natural frequency
• identification of the coefficients
• acoustic diagnostics
• longitudinal vibrations
• oscillator equation