Fatigue crack is an important rotor fault, which can lead to catastrophic failure if undetected properly and in time. Study and Investigation of dynamics of cracked shafts are continuing since last four decades. Some review papers were also published during this period. The aim of this paper is to present a review on recent studies and investigations done on cracked rotor. It is not the intention of the authors to provide all literatures related with the cracked rotor. However, the main emphasis is to provide all the methodologies adopted by various researchers to investigate a cracked rotor. The paper incorporates a candid commentary on various methodologies. The paper further deals an extended Lagrangian formulation to investigate dynamics of cracked rotor.

Fatigue cracks have great potential to cause catastrophic failures in rotating shaft. This fault may interrupt smooth, effective and efficient operation and performance of the machines. This problem has attracted the attention of researchers. Through various researches methodology investigation of dynamics of cracked rotor has been done, and work in this area is still continuing. Review papers are presented from time to time on this subject. The study and investigation in the last few decades on cracked rotors are presented in a review paper by Wauer [

Study of cracked rotor is continuing since last four decades. Different modeling techniques are used by various researchers. These approaches can be presented in the next subsections.

Guo and Peng [

Many researchers have analyzed the dynamics of cracked rotor by the approaches based on crack breathing. The crack gradually opens and closes during each revolution, in other words breaths during the revolution of the shaft; however, it is not yet entirely clear how partial closure interacts with key variables of the problem. Hence there is a need for a model that accounts for the crack breathing mechanism and for the interaction between external loading and dynamic crack behavior concluded by Bachschmid et al. [

Wavelets method may be used to detect the damage location and depth by considering modal frequencies, modal shape, and modal damp, and so forth. Zheng et al. [

Traditional FEM has some limitation, such as low efficiency, insufficient accuracy, slow convergence to correct solutions, and so forth, in case of complex problem with high gradient or strong nonlinearity. In order to overcome these difficulties, wavelet spaces have been employed as approximate spaces and then wavelet finite element methods (WFEM) have been derived by Ma et al. [

Three-dimensional (3D) FEA has attracted the researchers as an investigative tool for the study of crack breathing mechanism. Due to ease in simulation, many researchers applied finite element technique for analysis of crack in a rotating shaft. Papadopoulos and Dimarogonas [

Darpe et al. [

Müller et al. [

Qin et al. [

Besides the above mentioned techniques, there are few techniques and methodologies developed by few researchers to analyze the dynamics of cracked rotor. Shulzhenko and Ovcharova [

Since the last two years, few papers have appeared in various archives, where few new methods and tools have been applied for analysis of dynamics of rotor and its correct prediction. Chang et al. [

Among the various analytical techniques used by various researchers, Lagrangian mechanics are one of the area, where few works have been reported in literature. It is a well-known phenomenon that asymmetric rotating component produces nonpotential and dissipative forces, and classical Lagrange's equation cannot analyze the dynamics of such system with nonholonomic constraints, nonpotential forces, dissipative forces, gyroscopic forces, and general class of systems with time fluctuating parameters, as such Lagrangian cannot be worked out due to nonconservative forces involved in the system. So some additional information of system interior and exterior is needed in generating extended Lagrangian equations through bond graphs [

To enlarge the scope of Lagrangian-Hamiltonian mechanics, a new proposal of additional time like variable “umbra-time’’ was made by Mukherjee [

After an exhaustive survey of literature, the potential researchers in this field have various tools and methodologies to be applied to detect and proper identification of a crack. The methodologies have some specific advantages over the other. Now, there is a choice before the dynamics people to adopt proper techniques. The paper may be concluded as follows.

Crack breathing mechanism plays an important role in analysis of dynamic behavior of a cracked rotor. This breathing phenomena must be modeled accurately to detect the crack in a rotor.

Wavelet transform method was used by various researchers to predict the generation and propagation of a crack in rotating shaft. This propagation mechanism may be modeled so that the early failure of the rotor shaft may be detected.

Finite element method is a better choice and applied by various researchers to analyze the dynamic behavior of a shaft having different kind of cracks, for example, transverse crack, two cracks, slant crack, and so forth. The crack element must be accurately discretized to depict the real behavior of a cracked rotor.

Wavelet along with finite element method is also a good choice to have advantages of both techniques. Recently wavelet along with genetic algorithm analysis is also finding place in the various Literature.

The proposal of extended lagrangian-Hamiltonian formulation provides the invariants of motion of the dynamical system. It provides a great insight of the dynamics of a cracked rotor through extended Noether’s theorem.