Vibration Analysis of Cracked Plates
Summary
Vibration analysis of cracked plates encompasses the study of how discrete flaws impact the dynamic behaviour of planar structural elements. Cracks—ranging from through‐thickness and edge cracks to breathing and irregular geometries—alter stiffness, induce stress singularities and redistribute modal energy. Investigations address both linear free vibration and strongly nonlinear dynamic responses under harmonic or transient excitation. Key factors include crack depth, orientation and location, as well as material heterogeneity in isotropic, composite and functionally graded plates. Theoretical formulations draw on elasticity and plate theories (classical, first‐order shear deformation and three‐dimensional), while advanced numerical techniques—finite element, extended finite element, Ritz and differential quadrature—enable accurate resolution of displacement discontinuities and local stress fields. Nonlinear phenomena such as bifurcation, quasi‐periodicity and chaos emerge in breathing‐crack models, emphasising the need for robust computational tools. Experimental validation via modal testing and spectral response measurement underpins model reliability and informs structural health monitoring strategies. Practical applications span aerospace panels, civil infrastructure decks and mechanical components, where early crack detection and accurate prediction of frequency shifts are critical for safety and lifetime assessment.
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Vibration Analysis of Cracked Plates publication trend
The graph below shows the total number of articles in vibration analysis of cracked plates across all publications each year (not limited to Nature Index journals).
Technical terms
Natural frequency: The inherent vibration frequency of a structure when disturbed and left to oscillate freely.
Mode shape: The characteristic deformation pattern assumed by a structure at a specific natural frequency.
Functionally graded material (FGM): A composite whose composition and hence properties vary continuously in one or more dimensions.
Breathing crack: A crack that periodically opens and closes during vibration, introducing strong nonlinearity.
Extended finite element method (XFEM): A computational technique that enriches standard finite element approximations to model internal discontinuities without mesh fitting.
Differential quadrature method: A numerical scheme that approximates derivatives by weighted linear sums of function values at discrete points.
References
- Effects of edge-crack orientation and depth on non-linear dynamics of laminated nanocomposite single-variable-edge plates. Engineering Structures (2024).
- Bifurcation Study of Thin Plate with an All‐Over Breathing Crack. Advances in Materials Science and Engineering (2016).
- Vibration Analysis of Plate with Irregular Cracks by Differential Quadrature Finite Element Method. Shock and Vibration (2017).
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