Preface Introduction 1. Fluid field equations and modal analysis in rigid containers 2. Linear forced sloshing 3. Viscous damping and sloshing suppression devices 4. Weakly nonlinear lateral sloshing 5. Equivalent mechanical models 6. Parametric sloshing (Faraday's waves) 7. Dynamics of liquid sloshing impact 8. Linear interaction of liquid sloshing with elastic containers 9. Nonlinear interaction under external and parametric excitations 10. Interactions with support structures and tuned sloshing absorbers 11. Dynamics of rotating fluids 12. Microgravity sloshing dynamics Bibliography Index.

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Liquid Sloshing Dynamics

Review of studies on geometrically nonlinear vibrations and dynamics of circular cylindrical shells and panels, with and without fluid-structure interaction

A higher order beam finite element for bending and vibration problems

Bending, buckling and free vibration of laminated composite and sandwich beams: A critical review of literature

The authors review theoretical and experimental studies of the influence of modal interactions on the nonlinear response of harmonically excited structural and dynamical systems. In particular, they discuss the response of pendulums, ships, rings, shells, arches, beam structures, surface waves, and the similarities in the qualitative behavior of these systems. The systems are characterized by quadratic nonlinearities which may lead to two-to-one and combination autoparametric resonances. These resonances give rise to a coupling between the modes involved in the resonance leading to nonlinear periodic, quasi-periodic, and chaotic motions.

Modal Interactions in Dynamical and Structural Systems

Amplitude frequency relations of nonlinear vibrations in uniform beams with various boundary conditions using perturbation method

Nonlinear vibrations of beams with various boundary conditions.

The non-linear flexural vibrations of thin circular rings are analyzed by means of the appropriate "shallow shell" equations. These partial differential equations are reduced to non-linear ordinary differential equations by assuming vibration modes and applying Galerkin's procedure. Vibrations involving primarily a single bending mode are investigated for three distinct cases, and the results indicate that the basic features of the problem are exhibited by an inextensional analysis.

This information is then applied to simplify the analysis of vibrations in which several modes participate. A study of "self-coupled" bending modes shows that the single mode solution is valid only for certain combinations of amplitude and frequency: when the single mode exceeds a "critical amplitude", its companion mode is parametrically excited and participates in the motion.

The general inextensional case (involving an infinite number of modes) is examined for two important sets of forces, and possible solutions are shown to be the excitation of primarily one or two bending modes. Stability analyses of these solutions indicate that when certain restrictions are met, all other bending modes play only a minor part in the vibration.

An experimental study of the problem was also conducted. Theory and experiment both indicate a non-linearity of the softening type, the presence of ultraharmonic responses, and the appearance of the companion mode. Measurements of the steady-state response are in good agreement with the calculated values, and the experimentally determined mode shapes agree with the form of the assumed deflection.

The analytical and experimental results exhibit several features that are common to the non-linear vibration of axisymmetric systems in general and to circular cylindrical shells in particular.

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Nonlinear Flexural Vibrations of Thin Circular Rings

Nonlinear flexural vibrations of thin walled circular cylinders, and buckling of shallow, conical and spherical shells subjected to uniform, impulsive pressures

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David A. Evensen

Papers

Nonlinear vibrations of beams with various boundary conditions.

Nonlinear Flexural Vibrations of Thin Circular Rings

Some Studies on the Nonlinear Dynamic Response of Shell-type Structures