Modelling of flexible continuous systems under high-frequency loadings using continuum mechanics: a prisma-compliant systematic review
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flexible systems,
high-frequency loading,
Timoshenko–Ehrenfest,
Cosserat rod
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Abstract
Tracking the dynamic response of flexible continuous systems under high-frequency loading poses substantial mathematical and computational challenges because rigid-body assumptions and lumped-parameter methods cannot adequately represent wave propagation, viscoelastic damping, and higher-order modal interactions. This systematic review analyzes publications from 2019–2026 indexed in Scopus, Web of Science, and Google Scholar following the PRISMA 2020 guidelines to identify dominant continuum-mechanics frameworks, mathematical boundary conditions, and computational integration algorithms. Of 365 initial records, 42 studies met the selection criteria and were evaluated using the Model Validation Quality Index (MVQI). The synthesis shows that the Euler–Bernoulli model is less suitable for high-frequency analysis because it neglects rotary inertia and shear deformation. Three dominant approaches are the Timoshenko–Ehrenfest beam theory, geometrically exact Cosserat rod theory, and Eringen nonlocal elasticity. The Principle of Virtual Work is employed to characterize wave-propagation behavior, while non-ideal boundary conditions are addressed using the Artificial Spring Technique and Generalized-? integration. The review highlights the need for fully coupled nonlinear thermomechanical continuum models to improve the accuracy of flexible-structure analysis under extreme dynamic conditions.
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References
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