On the identification of the elastic modulus and axial force of beam members with unknown boundary conditions using modal information

Abstract

The axial force of beam members with unknown boundary conditions can be estimated by using vibration measurements, and this method necessitates the real elastic modulus of the members to produce accurate estimations. However, in engineering practice, the value of the elastic modulus of such members differs from the designed value owing to material degradation and structural damage. In addition, the elastic modulus of the beam structure may have a significant impact on the identification accuracy of axial force. Therefore, this study develops a methodology for simultaneously estimating axial force and elastic modulus within axial force members of structural systems, based on measurements of multiple natural frequencies and mode shapes. First, an improved vibration formula for the Timoshenko beam under axial load is obtained using the energy approach. Then, based on the proposed dynamic equation, the axial force and elastic modulus of the beam are discovered to have a linear relationship when the modal information of the structure is known. Further, using this linear relationship, a method to identify the axial force and elastic modulus of the beam member under unknown boundary constraints is proposed. Finally, the applicability and accuracy of the proposed method are validated by many numerical and experimental tests, and excellent estimates of the axial forces and elastic modulus are achieved.