# Tension Force Detection of Short Suspender by Using Laser Doppler Vibrometer
## 1 Introduction  
As an important force component, cables with different aspect ratios (those with small aspect ratio are usually called short suspenders) and profiles (strand or steel rod) have been widely used in large-span bridge structures [1; 2; 3; 4]. Maintaining the cable force in design level is key in ensuring structural stability and safety. However, degradation of cable force occurs frequently, due to lack of pretension forces, relaxation of anchor cable, anchor slipping, and environment corrosion, contributing to structural failure and instability [5; 6; 7; 8]. Timely detection of cable tension force can discover problems in time to give early warnings and then ensure the operational safety of structures. There are several methods to measure cable tension force at present, including oil pressure gauge, pressure sensor, magnetic flux, and vibration frequency. The oil pressure gauge method can accurately detect the cable tension force in the construction stage, but it does not function well during the operation stage of cables due to heavy equipment, labor intensity, low efficiency, and high cost [9; 10]. Although the pressure sensor method has a good performance in cable force detection, it can only be used in embedded manner, leading to high cost, complexity construction, and inconvenience of replacement [11]. Magnetic flux method [12] is a new test technology developed in recent years, by which the relationships between the cable tension force/temperature and magnetic flux can be established to detect cable force inreal time. It is worthwhile to note that the calibration process of magnetic flux method is complicated, seriously affecting its large-scale promotion and application. The vibration frequency method is an indirect test method based on the development of tension string vibration theory, and it has been widely studied and applied in cable tension force detection due to its high accuracy and simplicity [11, 13, 14, 15, 16]. It should be noted that two aspects must be guaranteed to implement this method effectively. On one hand, the cable vibration frequency should be picked up accurately; on other hand, a suitable theoretical calculation model between cable force and vibration frequency should be adopted. Because the relationships between natural vibration frequency of slender cables with high aspect ratio and tension force follows string vibration theory, the tension force of slender cables can be calculated according to measured frequency and theoretical calculation model. However, the string vibration theory for short suspenders is easily affected by boundary conditions, stiffness and inclination [17, 18]. When calculating the tension force for short suspender from frequency, it is necessary to solve the simultaneous equations of transcendental equations, and the calculation process is very complicated [19, 20, 21]. A new theory model needs to be established for tension force detection of short suspenders. Meanwhile, the vibration frequency measured by traditional vibration sensors for short suspender easily suffers from service environmental and stress state, reducing the accuracy of tension force detection. Meanwhile, the short suspenders in bridge structure with high stiffness and high vibration frequency are more prone to fracture under the dual influence of dynamic stress and corrosion compared to slender cables, resulting in partial collapse or direct damage to the bridge [22, 23]. There is an urgent need for a fast and accurate measurement for short suspenders. Laser Doppler Vibrometer (LDV) has been proved to be a fast and accurate equipment for testing the vibration frequency of cables [24, 25, 26]. [PERSON] et al. [25] reported that the vibration frequencies of stayed cable obtained by LDV are in good agreement with those obtained by vibration sensors. The maximum relative errors between these two methods are only 5.5% and 1.0%, respectively, as the first order frequency and the high order frequency is used to calculate fundamental frequency.