# Damage Identification Based on Adding Mass for Liquid-Solid Coupling Structures
## 1 Introduction
[24] identified the mass, damping coefficient, and stiffness of structures based on the correlation between the structural modal information and additional masses. [PERSON] et al. [25] attached a mass to different locations of a composite plate structure to change the dynamic characteristics. This allowed us to obtain the rotational bending mode shapes to identify damage. [PERSON] et al. [26] developed a method to determine the additional mass by a linear response function and the correlation analysis model of the structure. [PERSON] et al. [27] studied the identification and location of additional mass in beams and the influence of additional mass on the rotational freedom of the beam. [PERSON] et al. [28] used the Virtual Distortion Method to assess truss structural strength and summarized the application of the method in dynamics and statics, and so on. [PERSON] et al. [29] identified the damages of a plane frame by analyzing the frequencies of the structure with additional virtual mass and real structure precisely. [PERSON] et al. [30] combined Bayesian and adding virtual mass method to identify structural damage: this approach was proven. As the adding mass method is convenient for operation in practice, and the measured data is often highly reliable, the same approach is adopted in this study to obtain the structural response information. Due to the vibration coupling between liquid and solid, the vibration mechanism is complicated for structures immersed in liquids, which increases the difficulty of damage identification. [PERSON] et al. [31] introduced the model methods and results of the mechanical solid-liquid coupling containing outer slip and inner slip. [PERSON] et al. [32] proposed the water mass and analyzed the dynamic responses of the conical columns in water. [PERSON] et al. [33] derived the solid-liquid coupling vibration equation in the pipe and discussed the influence of solid and liquid dynamic characteristics on natural frequencies. [PERSON] et al. [34] calculated the load of liquid on the hull surface by two coupling methods, considering the ship as elastic. [PERSON] et al. [35] computed the modal information of the liquid oscillations in a spherical container by the singularity method. [PERSON] et al. [36] coupled the fluid loading and structural responses by a new hybrid simulation technique to determine the interaction between tsunami waves and structures. [PERSON] et al. [37] conducted some dynamic tests to study the inertia coefficient and additional hydrodynamic mass, and developed a calculation method. For considering the influence of the liquid-solid coupling vibration on structures, the attached fluid mass method is adopted. The force exerted by the liquid on structures is equivalent to the additional mass effect produced by solid vibration. This paper is structured as follows. First, the basic theory of adding mass method for damage identification is introduced. Then, considering the liquid-solid coupling, the approach of equaling the liquid to the attached fluid mass is proposed. Finally, the effectiveness and reliability of the proposed method are verified by experiments of a submerged cantilever beam and liquid storage tank.