Machine and structural safety and reliability are important issues in engineering. Since self-looseness is one of the most frequent causes of failure in bolted joint structures, it is highly desirable to detect bolted joint looseness early. The focus of this study is to model the structure natural frequency variation as the bolted joint is loosened. A virtual spring approach, incorporating finite element analysis, is proposed to model bolted structure assemblies. The spring constant estimation based on the Hertz theory is addressed, and the relationship between the spring constant and structure natural frequency is presented. An experimental study is used to verify the analytical model. A load bolt is used to measure the existing force in a bolted joint. The changes in the natural frequency of fixed-fixed beams due to the presence of joint looseness were investigated both analytically and experimentally.

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