The main objective of the research is to study the potential application of carbon nanotubes and graphene sheets as nano-resonator sensors in the detection of atoms/molecules with vibration and wave propagation analyses. It is also aimed to develop and examine new methods in the design of nano-resonator sensors for differentiating distinct gas atoms and different macromolecules, such as DNA molecules. The hypothesis in the detection techniques is that atoms or molecules attached on the surface of the nano-resonator sensors would induce a recognizable shift in the resonant frequency of or wave velocity in the sensors. With this regard, a sensitivity index based on the shift in resonant frequency of the sensors in the vibration analysis and/or a shift in wave velocity in the sensors in the wave propagation analysis is defined and examined. In order to achieve the objective, the vibration characteristics of carbon nanotubes and graphenes are studied using molecular dynamics simulations to first propose nano-resonator sensors, which are able to differentiate distinct gas atoms with high enough resolutions even at low concentration. It is also indicated that the nano-resonator sensors are effective devices to identify different genes even with the same number of nucleobases in the structure of single-strand DNA macromolecules. The effect of various parameters such as size and restrained boundary conditions of the sensors, the position of attached atoms/molecules being detected, and environment temperature on the sensitivity of the sensors is investigated in detail. Following the studies on vibration-based sensors, the wave propagation analysis in carbon nanotubes and graphene sheets is first investigated by using molecular dynamics simulations to design nano-resonator sensors. Moreover, a nonlocal finite element model is presented and calibrated for the first time to model propagation of mechanical waves in graphene sensors attached with atoms through a verification process with atomistic results. The simulation results reveal that the nano-resonator sensors are able to successfully detect distinct types of noble gases with the same mass density or at the same environmental condition of temperature and pressure.