## 1 Introduction  
It is routine to obtain vibration measurements in the structural health monitoring of suspension bridges, railway tracks, high-rise buildings etc. Vibrations near a railway track can be a matter of concern [1]. Especially due to the high speed trains [2] travelling at speeds in excess of 200 km/h or even 300 km/h, nearby buildings are likely to be affected. When the train tracks are built in cities, whether they are above ground or underground, they generate a certain amount of vibration in nearby buildings and structures [3; 4]. Such vibrations at low levels can be acceptable unless there is resonance. Resonance causes damage to buildings and can make them unsafe or unstable. Thus, certain international standards have recommended regular quantification and management of these vibrations [5], especially those up to 250 Hz. It is important to monitor the vibration frequencies as they often act a benchmark for normal operations. However, it may be difficult to attach electrical or bulky sensors to railway tracks due to safety concerns. Assembling equipment or accessories near the tracks for obtaining measurements is also a challenge. Hence, fiber Bragg grating (FBG) sensors have been found to hold great promise in this area [6; 7] since the fiber cables can run for several meters and allow for continuous and remote monitoring. In particular, in train tunnels, there is very little space for workers to conduct checks with conventional accelerometers when the lines are in operation. However, with fiber sensors, the system can be used without disrupting normal operations.  
Fiber Bragg gratings (FBG) have been used as vibration sensors for nearly two decades. The conventional use of FBGs for vibration measurements involves gluing the bare FBG directly on to the vibrating object [8; 9]. Since the FBG is fragile and establishing good contact is crucial, this method is most suitable in laboratory conditions. Some alternate, packaged designs of FBG-based vibration sensors are also commercially available [10; 11]. The FBG sensor has the main advantage of intrinsic sensitivity without additional complex packaging or design. In this paper, we present a sensor that is configured as a simple rectangular beam with a uniform FBG and extrapolates the concept of a cantilever. Cantilever vibration and modal studies with a FBG sensor have been reported by several groups [12; 13]. The modal frequency varies depending on the configuration and dimensions of the cantilever. The results in literature have mainly focused on the shift in modal frequencies.  
However, the objective of this study is to detect the vibration frequencies, apart from the modal frequencies, that affect the beam at a given time. This paper presents the results from a passive vibration sensor. The sensor design includes a rectangular metal beam of low stiffness bearing a fiber Bragg grating, which detects vibration frequencies from the vibrating object that it is coupled to. It is based on the principle of the coupling of forced vibrations. The FBG measures two types of frequencies due to the beam vibration: (a) the modal frequencies of the beam, which can be calculated numerically and (b) other frequencies from the periphery due to forced vibrations. A rectangular beam of a certain mass and dimension has a fixed set of vibration modes and is likely to exhibit those modal frequencies [14; 15]. However, other frequencies measured by this sensor are likely to be from its peripheral environment or nearby sources of vibration. This sensor relies on the coupling of vibrations from one metallic object to the other. Measuring vibration frequencies is a proven method of detecting structural integrity. This vibration sensor can be used to conduct intermittent checks on various types of structures and machinery by passively conducting the vibrations from them.