One of the major structural problems in the railroads made of continuous welded rails is buckling in hot weather and breakage or pulling apart in cold weather. Buckling is usually caused by the high compressive stress due to thermal load or weak track conditions, and sometimes vehicle loads. The prevention of track buckling is related to the determination of the temperature, called rail neutral temperature, at which the net longitudinal force in the rail is zero. In the project presented in this thesis we investigated the capability of a novel sensing system to indirectly measure applied stress in rails and predict incipient buckling. This system consists of a simple and cost-effective transducer, recently developed at the University of Pittsburgh, which enables the generation and detection of highly nonlinear solitary waves (HNSWs), which are compact non-dispersive mechanical waves that can form and travel in highly nonlinear systems such as granular, layered, or porous materials, where they are conventionally generated by the mechanical impact of a striker. To prove the feasibility of this novel system to predict buckling temperature or measure applied stress, we investigated numerically and experimentally the interaction between solitary waves propagating along a chain of granular particles and slender beams of different shapes, lengths, and boundary conditions. We found that the geometric and mechanical properties of the beam or thermal stress applied to the beam alter certain features of the solitary waves. Overall, the work presented in this thesis was articulated in four main tasks: 1) literature review; 2) create a semi-analytical model; 3) design and test new transducers; and 4) conduct a series of experiments including a field test at the University of California, San Diego. This HNSWs approach does not require many electronic accessories and shows a good sensitivity to the properties of the material that is at the interface with the chain of particles. Moreover, it only observes the propagation of solitary waves within the transducer without the waves in the rail.