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Rain-wind-induced vibrations of cables

Non-linear vibrations and instabilities of orthotropic cylindrical shells with internal flowing fluid

Nonlinear vibrations and imperfection sensitivity of a cylindrical shell containing axial fluid flow

This work investigates the influence of physical and geometrical system parameters uncertainties and excitation noise on the nonlinear vibrations and stability of simply-supported cylindrical shells. These parameters are composed of both deterministic and random terms. Donnell's non-linear shallow shell theory is used to study the non-linear vibrations of the shell. To discretize the partial differential equations of motion, first, a general expression for the transversal displacement is obtained by a perturbation procedure which identifies all modes that couple with the linear modes through the quadratic and cubic nonlinearities. Then, a particular solution is selected which ensures the convergence of the response up to very large deflections. Finally, the in-plane displacements are obtained as a function of the transversal displacement by solving the in-plane equations analytically and imposing the necessary boundary, continuity and symmetry conditions. Substituting the obtained modal expansions into the equation of motion and applying the Galerkin's method, a discrete system in time domain is obtained. Several numerical strategies are used to study the nonlinear behavior of the shell considering the uncertainties in the physical and geometrical system parameters. Special attention is given to the influence of the uncertainties on the parametric instability and escape boundaries.

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Influence of physical and geometrical system parameters uncertainties on the nonlinear oscillations of cylindrical shells

This paper presents an analytical solution to predict the nonlinear forced vibrations of elastic thin-walled cylindrical shells under suddenly applied loads. Interest in this problem is motivated by effects due to explosions on fluid-storage metal tanks. The model is based on the energy criterion due to Lagrange, in which the kinematic nonlinear relations are assumed using Donnell's simplified shell theory. Solution is achieved as a series summation in terms of trigonometric functions in the axial and circumferential directions, whereas the degrees of freedom depend on time. A blast load is assumed to represent effects due to explosions on the shell as time-dependent pressures with a given circumferential distribution (a cosine square distribution in terms of the central angle). The procedure is validated by comparison with a nonlinear finite element model under the same load conditions. The influence of load level and shell geometry on the transient response is investigated by mean of parametric studies. Good accuracy is found in the results for the range of shells which are representative of horizontal, fuel storage tanks in the oil industry.

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Simplified Analytical Approach to Evaluate the Nonlinear Dynamics of Elastic Cylindrical Shells Under Lateral Blast Loads

Introduction This chapter addresses the linear (small amplitude) and nonlinear (large amplitude) vibrations of circular cylindrical panels. Simply and doubly curved panels are structural elements largely used in engineering applications, such as aeronautics, aerospace, cars, boats, buildings, trains and many others. The linear vibrations of simply supported circular cylindrical panels are studied by using the Flugge-Lur'e-Byrne theory. Nonlinear vibrations of circular cylindrical panels with different boundary conditions (including flexible rotational constraints) under radial harmonic excitations are studied by using Donnell's shell theory with in-plane inertia, as this gives practically the same results as for other refined classical theories for very thin isotropic shells (Amabili 2005). The solution is obtained by using the Lagrange equations of motion and up to 39 degrees of freedom (dofs). Numerical results show that a simply supported panel for mode (1,1) presents a significant softening nonlinearity, which turns to the hardening type for vibration amplitude larger than the shell thickness; a similar behavior is observed for the panel with fixed edges and free rotations; on the other hand, the same panel with free in-plane edges or clamped edges presents hardening nonlinearity. A peculiar aspect of nonlinear vibrations of curved panels is the asymmetric oscillation with respect to the initial undeformed middle surface. In fact, the oscillation amplitude inward (i.e. in the direction of the center of curvature) is significantly larger than the amplitude outward.

Marco Amabili

Papers

Nonlinear Vibrations and Stability of Shells and Plates: Vibrations of Circular Cylindrical Panels with Different Boundary Conditions