Dynamical Characterization of Plates Containing Plane Cracks with Functional Gradient Materials
Year: 2025
Type: article
Abstract: This study develops a vibration model for functionally graded material (FGM) plates with embedded planar cracks. Based on thin plate theory and von Kármán-type geometric nonlinear strain assumptions, the kinetic and potential energies of each region are derived. Displacement field trial functions are constructed according to boundary conditions, and the Ritz method is employed to determine natural frequencies and vibration modes under small deformation conditions. The investigation focuses on how crack parameters and material gradient coefficients affect vibration characteristics in exponentially graded FGM plates. The results show that natural frequencies decrease with increasing crack length, while crack presence alters nodal line patterns and mode symmetry. During free vibration, the upper and lower surfaces of the crack region exhibit relative displacement. Material gradient effects induce thickness-direction asymmetry, causing non-uniform displacements between the plate's upper and lower sections.
Source: Materials
DOI: 10.3390/ma18163868
Authors: Gen Liu, An Xi, Yunchao Qi, Wenju Han
Language: English
Subfield: Mechanics of Materials
Field: Engineering
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $3,137
OpenAlex ID: W4413283118