George Herrmann

Destabilizing effect of velocity-dependent forces in nonconservative continuous systems.

Cantilevered continuous pipe conveying fluid at constant velocity, showing that internal and external damping and Coriolis forces may have destabilizing effect

Dispersion of free harmonic waves in fiber- reinforced composites.

Abstract : A set of displacement equations of motion is proposed that is suitable for the dynamic analysis of fiber-reinforced composites. In deriving the equations, representative elastic moduli are used for the binder, and the elastic and geometric properties of the fibers are combined into effective stiffnesses. With the aid of certain assumptions regarding the deformation of the fibers, and by employing a smoothing operation, approximate kinetic and strain energy densities for the fiber-reinforced composite are obtained. Application of Hamiltons principle yields the displacement equations of motion. The proposed set of equations is employed to study the propagation of plane harmonic waves propagating in the direction of the fibers and normal to the fiber direction. Plane transverse waves propagating in the direction of the fibers are dispersive, and dispersion curves are shown. By proper choice of the representative elastic moduli of the binder, the phase velocity at infinite wave length for transverse waves propagating in the direction of the fibers, and the constant phase velocities for longitudinal waves and waves propagating in the other directions, agree with the values predicted by the effective modulus theory. (Author)

Some general considerations concerning the destabilizing effect in nonconservative systems

ZusammenfassungEs wird ein lineares System mitN Freiheitsgraden untersucht, beansprucht durch eine Gruppe nichtkonservativer Kräfte, welche linear von den verallgemeinerten Koordinaten abhängen. Mehrere Sätze bezüglich die labilisierende Wirkung von kleinen Kräften, die von den verallgemeinerten Geschwindigkeiten abhängen, werden aufgestellt. Diese Kräfte können von der Dämpfung oder von gyroskopischen Einflüssen herrühren.

The usefulness of adjoint systems in solving nonconservative stability problems of elastic continua

Abstract The general linearized problem of stability of equilibrium of an elastic continuum subjected to follower-type surface tractions is formulated and it is indicated how an adjoint system may be constructed. It is proved that the two sets of eigenvalues of the original and adjoint systems are identical and that each member of the set is a stationary value for a variation of the displacement functions. These properties are then exploited to establish an approximate method of stability analysis which is shown to be more powerful than the commonly used Galerkin method. An illustrative example concludes the presentation.

Applications of Theories of Generalized Cosserat Continua to the Dynamics of Composite Materials

It is shown that the Cosserat continuum and the theory of elasticity with micro-structure can be interpreted as analytical models describing the dynamic behavior of a composite material. The nonclassical material constants are simply functions of the geometry and the classical constants of the two materials constituting the composite. The study of wave propagation in a laminated composite reveals that a more complex micro-structure needs to be introduced in a continuum in order to describe adequately the dispersive character of (essentially) longitudinal waves.

Buckling of a long cylindrical shell surrounded by an elastic medium

Abstract A long, thin, circular, cylindrical shell is subjected to uniform external pressure exerted by a surrounding elastic medium. The stability of equilibrium of the shell is examined by considering possible neighboring equilibrium states. The loading exerted by the elastic medium on the shell in the deformed state is found by solving an associated boundary value problem of the linearized theory of elasticity in the presence of initial stress. Expressions are derived which give the critical pressure for the cases of a bonded and a smooth interface.

Instability modes of cantilevered bars induced by fluid flow through attached pipes.

Abstract A cantilevered bar of uniform cross-section with flexible pipes conveying fluid attached to it is considered. It is shown that for certain cross-sections of the bar stability may be lost by either torsional divergence (torsional buckling) or torsional flutter, depending upon the location of the pipes with respect to the center of gravity of the cross-section. In addition, transverse flutter can also occur, but not transverse buckling. It is shown further that the Coriolis forces, which are present due to the motion of the fluid in vibrating pipes, may have either a stabilizing or a destabilizing effect, depending upon the parameters of the system.

Stability of an Elastic Ring in a Rigid Cavity

A thin, elastic circular arch, clamped at its ends and constrained in a rigid cavity, is subjected to a uniformly distributed parallel loading. Stability of equilibrium in the large “snap-through” is investigated both analytically and experimentally and good agreement is found to exist between the two modes of investigation. It is concluded that the set of simplifying assumptions introduced in the analysis is justified. Simple analytical results obtained in the paper allow the design of underground shelters under this type of loading.

Energy considerations in the analysis of stability of nonconservative structural systems.

Energy considerations are introduced into the analysis of discrete, linear structural systems subjected to nonconservative (circulatory) forces. Various formulations of energy balance permit to establish stability criteria and acquire further insight into several features associated with the stability of nonconservative systems, e.g., the destabilizing effect of damping and gyroscopic forces. A simple example is used to illustrate the general considerations.

Torsional instability of cantilevered bars subjected to nonconservative loading.

Torsional instability of cantilevered bars, describing effects of distributed nonconservative compressive load at free end