Nonlinear Vibration Analysis of Cylindrical Shells

Nonlinear vibration analysis of cylindrical shells addresses the dynamic behaviour of curved, slender structures when subjected to large amplitude excitations that render linear assumptions invalid. Starting from classical shell theories—such as Donnell’s or first-order shear deformation models—researchers derive governing equations via Hamilton’s principle, incorporating von Kármán geometric nonlinearity to capture quadratic and cubic coupling between in-plane and transverse motions. Analytical and semi-analytical solution strategies, including Galerkin projection, multiple scales perturbation and numerical continuation, have clarified the emergence of internal resonances, subharmonic responses and chaotic regimes. Advances in material systems—ranging from functionally graded composites to three-phase nanoreinforced shells—and the addition of structural features such as spiral stiffeners, rotation and thermal or electromagnetic fields have expanded application domains. These developments inform the design of aerospace cylinders, marine pipelines, pressure vessels and energy-harvesting devices. By elucidating how geometry, boundary conditions, foundation stiffness and environmental parameters influence stability thresholds and energy transfer between modes, current studies underpin optimisation strategies for vibration mitigation, load-bearing capacity and operational reliability in critical global infrastructure.

Research from Nature Portfolio

No recent Nature Portfolio content available.

Nonlinear Vibration Analysis of Cylindrical Shells publication trend

The graph below shows the total number of articles in nonlinear vibration analysis of cylindrical shells across all publications each year (not limited to Nature Index journals).

Technical terms

Nonlinear vibration: Oscillatory behaviour in which restoring forces vary non-proportionally with displacement, leading to amplitude-dependent frequencies and complex dynamic phenomena.

Cylindrical shell: A curved structural member with a hollow circular cross-section, commonly used in pipelines, rocket bodies and pressure vessels.

Internal resonance: A condition where two or more natural frequencies satisfy a simple integer ratio, facilitating strong energy exchange between vibration modes.

Functionally graded material (FGM): A composite whose properties vary spatially to tailor stiffness, thermal resistance or mass distribution.

Spiral stiffener: A helical reinforcement applied to a shell’s surface to modify its stiffness distribution and vibration characteristics.

von Kármán nonlinearity: A formulation capturing moderate large-amplitude deformations by including quadratic nonlinear strain–displacement terms.

Galerkin method: A projection technique converting partial differential equations into a set of ordinary differential equations by expanding solutions in assumed mode shapes.

Hamilton’s principle: A variational statement that the true motion of a dynamic system minimises the integral of the difference between kinetic and potential energies over time.

References

1. Multiple internal resonances of rotating composite cylindrical shells under varying temperature fields. Applied Mathematics and Mechanics (2022).
2. Nonlinear Vibration Analysis for Stiffened Cylindrical Shells Subjected to Electromagnetic Environment. Shock and Vibration (2021).
3. Influence of Spiral Stiffeners’ Symmetric and Asymmetric Angles on Nonlinear Vibration Responses of Multilayer FG Cylindrical Shells. Symmetry (2024).