Structural health monitoring systems have a great potential for cost saving and safety improvement in different types of structures. One of the most important tasks of these systems is to identify damage at an early stage of its development. A variety of methods may be used to identify, locate, or quantify the extent of damage or fault in a structural or mechanical component. However, the preferable method is the one which maximises the probability of detecting the flaw, while also considering feasibility of in-situ testing, ease of use and economic factors. Cracks are one of the common defects in structural components that may ultimately lead to failure of structures if not detected. The presence of cracks in a structure brings about local variations in the stiffness of the structure. These variations cause the dynamic behaviour of the cracked structure to be different from that of a healthy one. Vibration-based damage detection methods have attracted considerable attention over the past few decades. These methods generally use changes to the physical properties of structures for the purpose of crack detection. In this thesis, two new vibration-based methods have been developed for damage detection in beam-like and rotor-type structures. The first method performs the entire signal processing required for crack detection in time domain. It is based on assessing the normality of vibration responses using the normal probability plot (NPP). The amount of deviation between the actual and normal distribution of measured vibration responses was calculated along the length of the structure to localise the crack. The second proposed method converts the vibration responses into frequency domain for further processing. Excitation of the cracked structure at a given frequency always generates higher harmonic components of the exciting frequency due to the breathing of the crack. This method uses the operational deflection shape of the structure at the exciting frequency and its higher harmonics to identify the crack location. Avoiding complicated signal processing in frequency domain is the main advantage of the first method. However, more precise identification of crack locations can be obtained through the second method. Generally, both methods have the advantage of being easy, reference-free and applicable to in-situ testing for any structure. The concept and computational approach of both methods along with their validations through numerical and experimental examples have been presented. Moreover, different input excitations have been used to evaluate the capability of the developed methods in detecting the crack location(s).

One of the key areas that have attracted attention in the construction industry today is Structural Health Monitoring, more commonly known as SHM. It is a concept developed to monitor the quality and longevity of various engineering structures. The incorporation of such a system would help to continuously track health of the structure, indicate the occurrence/presence of any damage in real time and give us an idea of the number of useful years for the same. Being a recently conceived idea, the state of the art technique in the field is straight forward - populating a given structure with sensors and extracting information from them. In this regard, instrumenting with too many sensors may be inefficient as this could lead to superfluous data that is expensive to capture and process. This research aims to explore an alternate SHM technique that optimizes the data acquisition process by eliminating the amount of redundant data that is sensed and uses this sufficient data to detect and locate the fault present in the structure. Efficient data acquisition requires a mechanism that senses just the necessary amount of data for detection and location of fault. For this reason Compressive Sensing (CS) is explored as a plausible idea. CS claims that signals can be reconstructed from what was previously believed to be incomplete information by Shannon's theorem, taking only a small amount of random and linear non - adaptive measurements. As responses of many physical systems contain a finite basis, CS exploits this feature and determines the sparse solution instead of the traditional least - squares type solution.As a first step, CS is demonstrated by successfully recovering the frequency components of a simple sinusoid. Next, the question of how CS compares with the conventional Fourier transform is analyzed. For this, recovery of temporal frequencies and signal reconstruction is performed using the same number of samples for both the approaches and the errors are compared. On the other hand, the FT error is gradually minimized to match that of CS by increasing the number of regularly placed samples. Once the advantages are established, feasibility of using CS to detect damage in a single degree of freedom system is tested under unforced and forced conditions. In the former scenario, damage is indicated when there is a change in natural frequency of vibration of the system after an impact. In the latter, the system is excited harmonically and damage is detected by a change in amplitude of the system's vibration. As systems in real world applications are predominantly multi-DOF, CS is tested on a 2-DOF system excited with a harmonic forcing. Here again, damage detection is achieved by observing the change in the amplitude of vibration of the system. In order to employ CS for detecting either a change in frequency or amplitude of vibration of a structure subjected to realistic forcing conditions, it would be prudent to explore the reconstruction of a signal which contains multiple frequencies. This is accomplished using CS on a chirp signal. Damage detection is clearly a spatio-temporal problem. Hence it is important to additionally explore the extension of CS to spatial reconstruction. For this reason, mode shape reconstruction of a beam with standard boundary conditions is performed and validated with standard/analytical results from literature. As the final step, the operation deflection shapes (ODS) are reconstructed for a simply supported beam using CS to establish that it is indeed a plausible approach for a less expensive SHM. While experimenting with the idea of spatio-temporal domain, the mode shape as well as the ODS of the given beam are examined under two conditions - undamaged and damaged. Damage in the beam is simulated as a decrease in the stiffness coefficient over a certain number of elements. Although the range of modes to be examined heavily depends on the structure in question, literature suggests that for most practical applications, lower modes are more dominant in indicating damage. For ODS on the other hand, damage is indicated by observing the shift in the recovered spatial frequencies and it is confirmed by the reconstructed response.