Flow‐Induced Vibrations

A constitutive model is developed to characterize a general class of polymer and polymer-like materials that displays hyperelastic orthotropic mechanical behavior. The strain energy function is derived from the entropy change associated with the deformation of constituent macromolecules and the strain energy change associated with the deformation of a representative orthotropic unit cell. The ability of this model to predict nonlinear, orthotropic elastic behavior is examined by comparing the theory to experimental results in the literature. Simulations of more complicated boundary value problems are performed using the finite element method. ©2002 ASME

A microstructurally based orthotropic hyperelastic constitutive law

Recent development of the passive vibration control method

Introduction The theory of liquid sloshing dynamics in partially filled containers is based on developing the fluid field equations, estimating the fluid free-surface motion, and the resulting hydrodynamic forces and moments. Explicit solutions are possible only for a few special cases such as upright cylindrical and rectangular containers. The boundary value problem is usually solved for modal analysis and for the dynamic response characteristics to external excitations. The modal analysis of a liquid free-surface motion in a partially filled container estimates the natural frequencies and the corresponding mode shapes. The knowledge of the natural frequencies is essential in the design process of liquid tanks and in implementing active control systems in space vehicles. The natural frequencies of the free liquid surface appear in the combined boundary condition (kinematic and dynamic) rather than in the fluid continuity (Laplace's) equation. For an open surface, which does not completely enclose the field, the boundary conditions usually specify the value of the field at every point on the boundary surface or the normal gradient to the container surface, or both. The boundary conditions may be classified into three classes (Morse and Fesbach, 1953): the Dirichlet boundary conditions , which fix the value of the field on the surface; the Neumann boundary conditions , which fix the value of the normal gradient on the surface; and the Cauchy conditions , which fix both value of the field and normal gradient on the surface. Each class is appropriate for different types of equations and different boundary surfaces.

Liquid Sloshing Dynamics: Fluid field equations and modal analysis in rigid containers

In this paper, a new method for investigation of dynamics of fluid-filled rotor systems is presented. The method consists of development of finite degrees-of-freedom (discrete) models for the rotor systems. The discrete models are physically justified and demonstrative. Being described by the system of ordinary differential equations, they allow one to employ powerful tools of the theoretical mechanics and oscillation theory. The method is applied to the case of the plane model of the rotor system partly filled with incompressible liquid. Both the continuous and discrete models are considered. The main attention is paid to the latter model. The discrete model consists of a disk symmetrically fixed on the shaft (Laval scheme), the ends of which are in viscoelastic bearings, and a ring sliding over the disk with friction. The centers of the disk and ring are elastically connected. The disk models the rotor while the ring describes the liquid filling. When the ring is sliding over the disk surface, an interaction force arises that is diverted from the direction of the relative velocity at the contact points. It is demonstrated that an appropriate choice of the parameters of the discrete model allows one to determine the stability domain of the steady-state rotation of the rotor in the plane of the parameters of the shaft bearings with an excellent accuracy. It is found out that when the parameters overstep the limits of the stability domain, the Andronov-Hopf bifurcation occurs: a periodic motion of a kind of a circular precession arises from the steady-state rotation regime either "softly" or "hardly."

Stability and Andronov-Hopf Bifurcation of Steady-State Motion of Rotor System Partly Filled With Liquid: Continuous and Discrete Models

Whirl Dynamics of a Rotor Partially Filled With Liquid

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Whirl Dynamics of a Rotor Partially Filled With Liquid