Analysis reveals significant nonlinear responses in functionally graded material plates with cracks under transverse loads, suggesting complex interactions.
A nonlinear vibration model of functionally graded material (FGM) plates with planar cracks was established. The plate was divided into four sub-regions according to the planar crack area. Based on the Lagrangian dynamics equation, the nonlinear dynamic equation of the FGM plate with cracks considering the contact effect was derived. The nonlinear dynamic response of the FGM plate with cracks was explored. It is found that when the crack length is greater than or equal to 0.4a, the upper and lower sub-plates in the crack region show significant opening and closing during vibration. Under the action of transverse external loads, the contact effect between the upper and lower sub-plates of the planar crack would lead to complex nonlinear dynamic responses.
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Liu et al. (2025) studied this question.
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