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

Introduction. 1. Nonlinear theories of elasticity of plates and shells 2. Nonlinear theories of doubly curved shells for conventional and advanced materials 3. Introduction to nonlinear dynamics 4. Vibrations of rectangular plates 5. Vibrations of empty and fluid-filled circular cylindrical 6. Reduced order models: proper orthogonal decomposition and nonlinear normal modes 7. Comparison of different shell theories for nonlinear vibrations and stability of circular cylindrical shells 8. Effect of boundary conditions on a large-amplitude vibrations of circular cylindrical shells 9. Vibrations of circular cylindrical panels with different boundary conditions 10. Nonlinear vibrations and stability of doubly-curved shallow-shells: isotropic and laminated materials 11. Meshless discretization of plates and shells of complex shapes by using the R-functions 12. Vibrations of circular plates and rotating disks 13. Nonlinear stability of circular cylindrical shells under static and dynamic axial loads 14. Nonlinear stability and vibrations of circular shells conveying flow 15. Nonlinear supersonic flutter of circular cylindrical shells with imperfections.

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Nonlinear Vibrations and Stability of Shells and Plates

A review of the recent developments in the analysis of laminated beams and plates with an emphasis on shear effects and buckling is presented. A discussion of various shear-deformation theories for plates and beams is given. The available theories are derived assuming a variation of either the in-plane displacement components or the stress components or both in the thickness coordinate. A review of the recently developed finite elements to analyze thin and thick laminated beams and plates is given next. These elements have been derived using the displacement methods, or the mixed methods or the hybrid methods. Recent studies on the buckling and postbuckling behavior of perfect and geometrically imperfect plates are described next. These behaviors have been studied using analytical, numerical, and experimental techniques. Finally, a review of the various studies on the delamination buckling and growth in beams and plates is given. Once again, the studies have been conducted using analytical, numerical, and experimental techniques. The energy release rates have been determined using closed-form solutions or using numerical differentiation. Mention also is made of studies on multiple delaminations and on dynamic response of composite laminates under impact loads.

Recent advances in analysis of laminated beams and plates. Part I - Sheareffects and buckling.

Recent Advances in Liquid Sloshing Dynamics

A summary of the recent developments in the analysis of laminated beams and plates with an emphasis on vibrations and wave propagations in presented. First, a review of the recent studies on the free-vibration analysis of symmetrically laminated plates is given. These studies have been conducted for various geometric shapes and edge conditions. Both analytical (closed-form, Galerkin, Rayleigh-Ritz) and numerical methods have been used. Because of the importance of unsymmetrically laminated structural components in many applications, a detailed review of the various developments in the analysis of unsymmetrical ly laminated beams and plates also is given. A survey of the nonlinear vibrations of the perfect and geometrically laminated plates is presented next. It is seen that due to the bending-stretching coupling, the nonlinear behavior of the unsymmetrically laminated perfect and imperfect plates, depending upon the boundary conditions, may be hardening or softening type. Similar behavior also is observed for imperfect isotropic and laminated plates. Lastly, the developments in studying the wave propagation in laminated materials are reviewed. It is seen that a significant effort has been spent on developing appropriate continuum theories for modeling the composite materials. Some recent studies on the linear and nonlinear transient response of laminated materials also are described.

Recent Advances in Analysis of Laminated Beams and Plates, Part II: Vibrations and Wave Propagation

Theoretical analyses are presented for nonlinear vibrations of a clamped rectangular plate under a uniformly distributed periodic load, with the effect of both initial deflection and initial edge displacement taken into consideration The dynamic analog of the Marguerre equations is used and the steady-state solutions are obtained by first applying the Galerkin method and then the harmonic balance method Actual calculations are carried out for the square plate under the assumption of the three degrees-of-freedom system and the frequency response characteristics and typical waveforms are determined under various initial edge displacements including initially buckled cases Effects of both initial deflection and initial edge displacement on the static deflection as well as the lower natural frequencies are also clarified

Nonlinear vibrations of a clamped rectangular plate with initial deflection and initial edge displacement— Part II: Experiment

Theoretical analyses are presented for the linear free vibration of a clamped-free cylindrical shell partially filled with an incompressible, inviscid liquid. For the vibration of the shell itself, the dynamic version of the Donnell equations was used and the problem was solved with the modified Galerkin procedure, taking the effect of the axisymmetric deformation due to the static liquid pressure into consideration. Concerning the vibration relevant to the liquid motion, the solution for the velocity potential was assumed as a sum of two sets of linear combinations of the suitable harmonic function, the unknown parameters of which were imposed to satisfy both boundary conditions along the wetted shell wall and the free liquid surface in a sense of appropriate series expansions. The procedure stated in the foregoing leads to a determinantal equation for the determination of the natural frequencies of the present shell-liquid system. To compare with the experimental results which will be stated in a companion paper, 14 detailed numerical results will be presented in another companion paper 13 on the free vibration characteristics of the two test cylinders partially filled with water.

Free vibration of a clamped-free circular cylindrical shell partially filled with liquid—Part I: Theoretical analysis

Non-linear vibrations of a clamped circular plate with initial deflection and initial edge displacement, part I: Theory

To compare with the theoretical results presented in Parts I and II, 1,2 detailed experimental results have been obtained on the free vibration of a clamped-free cylindrical shell partially filled with liquid. Two polyester test cylinders with radius 100 mm, thickness 0·25 mm, and lengths 114 and 227 mm were used, and the filling ratio of the contained water was varied from 0 to 1·0 stepwise by 0·25 increments. Experiments were carried out by exciting the shell wall with two small shakers located at diametrically opposite positions and by observing the resonant responses of the shell with a noncontacting proximeter utilizing fiberglass optics. Excellent agreement between theory and experiment was demonstrated for the natural frequencies and the corresponding wave numbers concerning the lower-order natural vibrations dominated by the shell wall response. Variations of the mode shape with the circumferential wave number and the liquid depth were also examined, and were found to compare favourably with those predicted theoretically.

M. Chiba

Papers

Nonlinear vibrations of a clamped rectangular plate with initial deflection and initial edge displacement— Part II: Experiment

Free vibration of a clamped-free circular cylindrical shell partially filled with liquid—Part I: Theoretical analysis

Non-linear vibrations of a clamped circular plate with initial deflection and initial edge displacement, part I: Theory

Free vibration of a clamped-free circular cylindrical shell partially filled with liquid—part III: Experimental results

Non-linear vibrations of a clamped circular plate with initial deflection and initial edge displacement, part II: Experiment