The vibration characteristics of bridge structures can be used as evaluation indicators for accurately diagnosing their deterioration. Damage detection methods of existing bridge structures also require effective management methods to reduce labor and their maintenance costs. In this paper, a digital three-axis acceleration sensor MPU6050 capable of measuring static (gravity) and dynamic (vibration) accelerations based on MEMS devices can be operated in a simple sensor network, a low cost, low weight and small size measurement system is designed and evaluated for the vibration characteristics of the bridge. We also consider the logarithmic damping characteristic for vibrations, one of the important dynamic parameters characterizing the bridge behavior. The logarithmic decrement for vibrations is usually evaluated by the vibration recording by digital signal processing. Among the processing procedures band-pass filtering is commonly used to extract spectral components of interest. We analyze the case when two very close spectral components are present in the acceleration records. We show that construction of the filter is non-trivial in such a situation and failing to choose optimal filter’s parameters leads to significant logarithmic decrement estimation errors. Therefore we propose a method that does not require band-pass filtering but utilizes knowledge of amplitude beat presence. Simulation of the method indicated errors by an order less than using filtering