Frequency response of laminated composite plates and shells with matrix cracks type of damage mode

The present study has been designed to tackle a new set of problems for structural composites, as these materials are finding new applications in civil engineering field. An attempt has been made to study the frequency response of laminated polymer composite plates and shallow shells containing matrix cracks type of damage with arbitrary support conditions and free vibratory motions. The shell governing equations are derived using a simplified shallow shell theory based on a first order shear deformation field. The continuum damage mechanics approach has been used to model the matrix cracks in a damaged region within the plates and shallow shells. In such approach, the damage is accounted for in the laminate constitutive equations by using a set of second order tensor internal state variables which are strain-like quantities. The simplified damage model was then used to study the changes in frequency response of laminated composite plates and shallow cylindrical shells. The Ritz method and a finite element method have been proposed and developed as approximate solution procedures to quantify the change in the free vibration frequencies due to matrix cracks type of damage under both material as well as geometrical variables such as size, shape and extent of damage, degree of curvature, ratio of orthotropy, thickness ratio as well as support conditions. The analysis of various plates and shells with a centrally located damaged-zone depicts a typical trend of reduction in the vibration frequencies. This reduction is more pronounced for higher frequency modes and it shows greater sensitivity toward the size of the damaged region and density of cracks. The results also show that the changes in the frequency, especially for the fundamental mode, appear to be less sensitive to the shell boundary conditions as well as small values of curvature.; The investigation of various undamaged plates and shallow shells demonstrates the importance of a first-order shear deformation theory. The present treatment of the effect of matrix cracks is more realistic and economical than the standard ply-discount strategy which under-estimates the residual stiffness of damaged plates and shells.