Boundary conditions detection of beam-like structural elements using a test mass

A boundary conditions (BCs) identification technique in uniform beams, using a test mass, is developed in this research. The proposed method is based on changing in natural frequencies of a beam caused by the test mass. The test mass is defined as a stationary mass, which is located in different places of the beam. The boundary conditions of beam are modeled as elastic-spring supports. Solving the differential equations, the eigenfunctions of the problem in the absence of test mass is explicitly derived. Rayleigh’s quotient method is employed to consider the effect of the test mass. As a result, expressions for natural frequencies are derived for arbitrary mode of transverse vibration. Knowing the natural frequencies of beam carrying a test mass at some different conditions, it is possible to estimate constants of the springs’ stiffness. The proposed analytical approach is also validated using numerical studies on different values of stiffness examples. There is quite encouraging agreement between the results of the present study and those computed using the finite element method, numerically.