identification of boundary conditions of tapered beam-like structures using static flexibility measurements

the integrity and reliability of the beam-like structures are dependent in part on their boundary conditions, which can vary with time due to damage or aging, thus the identification of boundary conditions might be one of the most significant aspects for damage detection of such structures. this paper investigates a direct method for identifying the boundary conditions of tapered beam-like structures using static flexibility measurements. the beam is modeled by a flexible tapered beam, which is constrained at one end by translational and rotational springs. the translational and rotational springs are utilized to simulate the boundary conditions of the tapered beam, and the purpose of this paper is to identify the stiffnesses of the translational and rotational springs, i.e. translational root stiffness and rotational root stiffness. it is theoretical proved that the static flexibility measured on the beam can be expressed as a function of the flexural rigidity of the beam at its constrained end, translational root stiffness and rotational root stiffness. then, a set of linear equations for identifying the translational and rotational root stiffnesses are formed by three or more different static flexibility measurements. finally, the proposed method is validated using both simulative and experimental examples.