Damage Identification Of Cracked Functionally Graded Structures Based On Vibration And Power Flow

Functionally graded materials(FGMs)are inhomogeneous materials whose composition or/and microstructures change continuously along the spatial location.FGMs possess the ability to reduce the stress/heat concentration,control the deformation and resist the contact damage due to their gradual change in material properties of FGMs.In view of their excellent mechanical performance,FGMs have found a wide range of applications in many fields,such as aerospace,energy,civil engineering,medical,optoelectronics,etc.However,it is inevitable that small damages will emerge in FGM structures which even become significant failure in severe working environments of vibration,corrosivity and high temperature,etc.Hence,it is very important for safety operation in FGM structures to detect the damage locations and estimate the severity of damages.The occurrence of the damage in the structure reduces the local stiffness and changes the global dynamic responses of the structure.The damage identification methods based on structural dynamic response can efficiently detect damage.Among them,the method based on wavelet transform is an effective baseline-free method and has robustness against noise.This paper aims to develop an effective damage identification method based on the the analysis of vibration and power flow of cracked FGM structures by using the continuous wavelet transform(CWT).The main contents and conclusions of the paper include:(1)The free vibration and damage identification of cracked FGM beams are investigated.A new damage index(DI)is proposed to study the damage identification of cracked FGM beams by using the CWT.The damage index is defined based on the position of the wavelet coefficient modulus maxima in the scale space.The crack is assumed to be an open edge crack and is modeled by a massless rotational spring.It is assumed that the material properties follow the exponential distribution along the beam thickness direction.The Timoshenko beam theory is employed to derive the governing equations which are solved analytically to obtain the frequency and mode shape of cracked FGM beams.Then,we apply the CWT to analyze the mode shapes of the cracked FGM beams and calculate the damage index.An intensity factor,which relates to the size of the crack and the wavelet transform coefficient,is employed to estimate the crack depth.The experiment validation of the present method is carried out in a homogeneous cracked beam.The results indicate that the present method is very effective and can reduce the edge effect in the tranditional damage identification method based on the CWT.(2)The vibrational power flow and damage identification of cracked FGM beams are investigated.Based on the Timoshenko beam theory,the governing equations of cracked FGM beam are derived by using the neutral plane as the reference plane.The input power flow and the transmitted power flow of cracked FGM beams subjected to a harmonic concentrated transverse force are solved by the wave propagation approach.The damage index of FGM beams is obtained by using the CWT to analyze the transmitted power flow distribution along the longitudinal direction.The results indicate the input power flow reduces as the Young’s modulus ratio increases.The input power flow and transmitted power flow of cracked FGM beams produce the fluctuation with the variation of the frequency due to the reflection wave between the crack location and driving force position.The peak of DI has the ability to detect the crack location in FGM beams with small crack depth.(3)The free vibration and damage identification of cracked FGM plates are investigated.The material properties of the FGM plates change continuously with the power law distribution along the plate thickness direction.The crack is simulated as a massless rotational spring and the plate is divided into two sub-plates at the crack location connected by the spring.By using ABAQUS,the stress intensity factors(SIFs)in the FGM strip is calculated to determine the stiffness of the spring.The governing equations of cracked FGM plates are derived from the Mindlin plate theory and solved by the differential quadrature method(DQM)to obtain modal parameters.The mode shape of the cracked FGM plate is analyzed by utilizing the CWT.A novel damage index is developed based on the wavelet coefficients to localize the crack in FGM plates.This method can localize the crack accurately and reduce the edge effect even with the measurement noise.(4)The vibrational power flow and damage identification of cracked FGM plates are studied.The material properties of FGM plates change continuously with the power function with respect to the plate thickness direction.The crack is simulated as a massless rotational spring.The governing equations of cracked FGM plates are derived by using the Kirchhoff plate theory and solved by the Lévy method and the wave propagation approach.The transmitted power flow of cracked FGM plates is analyzed by utilizing the CWT.The damage index is obtained according to the wavelet coefficients.The results indicate the input power flow and critical frequency reduce as the graded index increases.The input power flow and transmitted power flow produce the fluctuation with the variation of the frequency.The crack can be localized accurately by the peak of DI.The present investigation has a positive contribution to study of vibration,power flow and wavelet-based damage identification method of cracked FGM structures,and is also important for the safety of FGM structures in practical applications.