Normally , the geometry, boundary condition, material properties plays a vital role in the evaluation of its dynamic response due to their vibration .Further, inclusion of cracks may change their dynamic behavior drastically. There are parameters like crack location, its depth, orietntaion,etc may signifcantly affect the frequency response of the structure.

Also the crack introduces a local flexibility due to strain energy concentration in the vicinity of the crack tip undeer load.

Equation of motion for non-crack system is

[M] {``X} + [K] {X} = {F}

Equation of motion for cracked system is

[M] {``X} + [K- dK ] {X} = {F}; where dK is the additional stiffness matrix due to the crack strain energy concentration.

Few related articles may help you :

Article Vibration of a Beam with a Breathing Crack

Article Free vibration analysis of a cracked beam by finite element method

There is a relatively simple engineering approach, when a crack in a rod or beam is modeled by a softer material (with a smaller Young's modulus); see

Article Natural frequencies of a beam with arbitrary number of cracks

Hi Ankit,

For composite laminates having transverse cracks I think you could try to define a representative volume element with appropriate boundary conditions, as shown in the reference below. This approach could be applicable to homogeneous materials in some cases.

S. Li, C.V. Singh, R. Talreja, A representative volume element based on translational symmetries for FE analysis of cracked laminates with two arrays of cracks, Int. J. Solid Struct. 46 (7-8) (2009) 1793-1804.