Frank L. DiMaggio

Transient response of submerged spheroidal shells

Abstract The transient response of an elastic prolate spheroidal shell to a uniform pressure suddenly applied to its surface, and the pressure field in the surrounding acoustic fluid are obtained. By appropriate transformations of response functions and a geometric variable the problem is reduced to the simultaneous numerical integration, in a finite domain, of partial differential equations on functions which are regular in the space variables. An approximate relation is established to represent the fluid field, which, together with the plane wave approximation, is then used to obtain approximate solutions for the shell response. Extensive numerical results are presented for steel shells in sea water.

Dynamic response of a fluid-filled spheroidal shell--an improved model for studying head injury

Abstract The human head is modelled by considering the skull to be an elastic prolate spheroidal shell enclosing an acoustic medium which represents the brain. A suddenly applied, uniformly distributed, pressure is applied to the shell surface. Time histories of the distribution of stress in the shell and pressure in the fluid are obtained for material and geometrical parameters representative of a human head. It is found that there is a significant difference in the results obtained using this model from those obtained when the assumption of zero eccentricity, i.e. spherical geometry, is made, but not in the important maximum negative pressure developed in the fluid.

Doubly asymptotic approximations as non-reflecting boundaries in fluid-structure interaction problems

Abstract Acoustic approximations are differential relations between induced fluid pressure and velocity in an acoustic medium. The plane wave approximation (PWA) is valid for high frequency response while doubly asymptotic approximations (DAA) are valid at very high and very low frequencies and, in advanced versions, at selected intermediate frequencies. These relations have been applied extensively on the wet surface of submerged structures to completely uncouple the equations of motion of the structure from those of the surrounding fluid. If DAA are used, a different virtual mass matrix and, in the advanced versions, fitting matrices must be evaluated for each structural geometry. In this paper, the approximations are used on a fluid surface which encloses the structure and has a geometry for which virtual mass and fitting matrices are known. The response is obtained by solving numerically the coupled fluid-structure equations within this approximation to a non-reflecting boundary. A numerical example of the dynamic response of a spheroidal shell is solved using a sphere as the absorbing boundary and the response obtained is compared to exact results.

Interactive approximations for a cavitating fluid around a floating structure

Abstract A method is investigated for determining the response of floating structures to underwater explosions strong enough to cause bulk cavitation. In such problems the difference between the actual and free field pressures on any surface surrounding the structure and cavitated region is related to the corresponding velocity differences by a linear functional relation. In this paper, it is proposed that approximate functionals, called interactive approximations, be applied on these surfaces, called interaction horizons. In the limit, the interaction horizon can be taken as the wet surface of the structures, eliminating the consideration of fluid field equations. The technique is applied to the two-dimensional problem of a rigid rectangular structure, floating on a fluid with a bilinear constitutive relation, subjected to a plane, exponentially decaying wave having an angle of incidence. First the exact solution of the nonlinear, steady state, free field problem, including determination of the cavity, is obtained by the method of characteristics. Then the interaction problem is solved by finite differences, using both plane wave and doubly asymptotic interactive approximations, at interaction horizons and on the wet surface. When an interaction horizon is used, Laxs one-dimensional scheme is modified to discretize the fluid equations. It is found that, for this example, the plane wave approximation applied directly to the wet surface is sufficiently accurate to determine structural response.

Pressures in a submerged fluid-filled cylindrical shell subjected to a step wave

Abstract The response of a submerged, fluid-filled, infinitely long, cylindrical shell (plane-strain ring) subjected to a step shock wave is studied to determine the effect of shell parameters (moduli, thickness, radius) on the shape of the pressure pulse transmitted inside the shell. The results show that the shell is transparent if thin enough, but, as the thickness increases, strong shell vibrations become important and distort the pulse.

Dynamic response of a containment vessel to fluid pressure pulses

Abstract Two methods, one of which is a very simple approximation, are proposed for the dynamic analysis of the response of the wall of a nuclear containment vessel to the fluid pressure exerted on it when the relief valve discharge piping is cleared.

Transient response of submerged shells using improved acoustic approximations

Abstract The Doubly Asymptotic Approximation (DAA) has been widely used to uncouple the equations of motion of an infinite acoustic medium from those of the structure it surrounds. Recently, two new schemes. The Improved Doubly Asymptotic Approximation (DAA2) and the Inertial-Damping Collocation Approximation (IDCA) have been proposed. All three give exact steady state responses at very low and very high frequencies, but the newer ones contain fitting matrices which may be chosen to give exact results for intermediate frequencies. In this paper, the transient response of a spherical shell to a plane step shock wave is computed by means of the Fast Fourier Transform, using each of the approximations, and the results are compared with the exact solution.

Effect of bending on the axisymmetric vibrations of a spheroidal model of the head

Abstract The head is modelled as an elastic prolate spheroidal shell filled with an inviscid, compressible fluid. Bending effects are included, and the free vibration frequency spectrum obtained is compared with that of an earlier spheroidal model using extensional (membrane) shell theory and with a spherical model including bending. The differences between the present results and those reported previously are significant.

Transient response of shells with internally attached structures

Abstract Equations of motion are derived for the transient response, to a shock wave, of a submerged shell with internal structures. A substructuring procedure, which does not require calculation of a system stiffness matrix, is employed to obtain these equations in a general manner for arbitrary internal structures approximated by finite elements.

Routes to chaos of a pendulum with vertically rotating pivot

Abstract Each blade of a mechanical shredder may be modeled by a pendulum whose pivot rotates in a vertical circle with angular speed Ω. It is well known from field tests that small oscillations about radial lines, which are stable at high operating speed, degenerate into disordered motion when speeds become low enough after the machine is shut off. The transition to chaos of small periodic motion about radial lines as the driving speed of the pivot is reduced is investigated for several values of the system parameters. Numerical methods are used to obtain time histories, Poincare maps, response curves and frequency spectra. The harmonic balance method is used to obtain response curves for oscillatory periodic solutions, whose stability is determined by the Floquet method. In the undamped case, instability associated with pitchfork or tangent bifurcations precedes chaos. When damping is introduced, additional routes involving intermittency and period-doubling cascades may precede chaotic motion characterized by strange attractors.