Showing papers in "Journal of Applied Mechanics in 1973"

Conservation Laws and Energy-Release Rates

Abstract: New path-independent integrals recently discovered by Knowles and Sternberg are related to energy-release rates associated with cavity or crack rotation and expansion. Complex-variable forms are presented for the conservation laws in the cases of linear, isotropic, plane elasticity. A special point concerning plastic stress distributions around cracks is discussed briefly.

On the Contact Problem of an Inflated Spherical Nonlinear Membrane

Abstract: The contact problem of an inflated spherical nonlinear elastic membrane between two large rigid plates is formulated in terms of three first-order ordinary differential equations for the region where the spherical membrane is not in contact with the rigid plates. The constraint condition introduced by the rigid plate on part of the spherical membrane reduces the number of governing equations to two for the contact region. A general stress-strain relation for the spherical membrane is used in the formulation. The results presented in this paper assume that the material behavior of the spherical membrane is that described by the Mooney model. Nonlinear spring characteristics and the instability phenomena of the inflated membrane are discussed.

Nonlinear Vibrations of a Hinged Beam Including Nonlinear Inertia Effects

Abstract: This investigation treats the large amplitude transverse vibration of a hinged beam with no axial restraints and which has arbitrary initial conditions of motion. Nonlinear elasticity terms arising from moderately large curvatures, and nonlinear inertia terms arising from longitudinal and rotary inertia of the beam are included in the nonlinear equation of motion. Using a Galerkin variational method and a modal expansion, the problem is reduced to a system of coupled nonlinear ordinary differential equations which are solved for arbitrary initial conditions, using the perturbation procedure of multiple-time scales. The general response and frequency-amplitude relations are derived theoretically. Comparison with previously published results is made.

Applications of the Theory of Impulsive Parametric Excitation and New Treatments of General Parametric Excitation Problems

Abstract: In this paper the stability theory of impulsive parametric excitation developed in [1] is first applied to three mechanical systems. Explicit and exact stability conditions are easily found and some typical stability charts are presented. Also presented in the paper is the use of this theory and a parallel theory involving step functions as approximate methods for treating periodic parametric excitations of more general nature. Exploratory studies along this line have led us to believe that these approximate methods have promise to be very powerful and practical tools for dealing with the stability of general high-order periodic systems.

Lateral Bending-Torsion Vibrations of a Thin Beam Under Parametric Excitation

Abstract: : A thin plate-like cantilever beam, well below static lateral buckling under gravity, is subjected to vertical harmonic excitation of its base. The governing equations reduce to systems of two Mathieu equations coupled mainly by symmetric, off-diagonal parametric excitation terms. For such cases, the primary instability regions are shown to occur near forcing frequencies (omega sub F) = (omega sub i) + (omega sub j), with each mode oscillating at its own natural frequency, omega sub i. Experiments performed on an actual beam confirm this behavior. Since the beam had nonlinear damping, the instability regions settled down to steady limit cycles whose frequencies and amplitudes were well predicted by theory. The simultaneous excitation of two modes, each oscillating at its own natural frequency, may be of considerable interest in vibration testing of actual structures. (Author)

Elastic Analysis of a Skull

Abstract: : A finite element elastic analysis is made of a skull. Measurements were made of the geometry and thickness of a skull. The skull was then idealized with a doubly curved and arbitrary triangular shell element. Results suggest that the skull is well built for resistance to front loads. The importance of using a composite material through the thickness of the shell was established. On the basis of tensile cracking at maximum elastic stress, loads of 3,500 lbs. and 1,400 lbs. were predicted for the first cracking of the skull due to front and side loading respectively.

Stress Redistribution and Rupture Due to Creep in a Uniformly Stretched Thin Plate Containing a Circular Hole

Abstract: A uniaxial theory of low-stress, high-temperature creep rupture has been shown to predict the results of uniaxial creep rupture tests. By including the creep rupture relationships into the accepted multiaxial deformation laws and following the numerical procedure outlined in a previous publication, a lower bound on the rupture time has been obtained for the case of a biaxially loaded plate containing a small hole at its center. It has been shown that the rupture behavior of the structure is controlled by a single stress whose magnitude is independent of the form of the constitutive relationship. The results of the prediction method agreed well with the experimentally determined values for aluminum plates tested at elevated temperatures.

A Continuum Theory for Wave Propagation in Laminated Composites—Case 1: Propagation Normal to the Laminates

Abstract: A continuum theory with microstructure for wave propagation in laminated composites, proposed in a previous work concerning normal propagation, is extended herein to the case of propagation parallel to the laminates.