Free and forced vibration analysis of multiple cracked FGM multi span continuous beams using dynamic stiffness method

Abstract In the present paper, the free and forced vibration of multiple cracked multi span continuous beams made of functionally graded material (FGM) is investigated by the dynamic stiffness method. First, there are constructed dynamic stiffness matrix and nodal load vector of multiple cracked FGM beam element using Timoshenko beam theory and massless double spring model of crack. Then, effect of cracks parameters on free and forced vibration of the FGM continuous beams is examined. The theoretical developments are validated by numerical examples. The obtained results provide an efficient method to analyze free and forced vibration of multiple cracked FGM framed structures and assessment of the behavior of damaged structures.