A finite strain ring dynamical model for pneumatic tires
Abstract
In this report, using the most general 'plane sections remain plane' rod theory and the continuum mechanics approach, the exact strain expressions for a shearable, extensible ring are derived. These expressions are nonlinear in terms of both the displacements and the geometry of the ring and are Taylor series approximated after their derivation. A linear viscoelastic stressstrain relationship is assumed. The radial stress is considered negligible. The model includes extension of the neutral axis, transverse shear deformation, and the full complement of inertial forces created by rotation of the ring. A pretensioning force due to pressurizing the tire is included. The tire sidewall (viscoelastic foundation) is considered to act in a completely radial direction. The equations of motion are developed from the free body and inertial force diagrams of a differential element. The membrane forces and bending moment are then substituted to yield three nonlinear equations of motion. The equations of motion are then put into matrix form with the linear and nonlinear portions separated. Chapters 3 and 4 study linear wave propagation, while Chapter 5 provides verifying comparison examples with existing finite element codes, as well as a numerical example for the KC135 transport aircraft tire.
 Publication:

Final Report
 Pub Date:
 August 1993
 Bibcode:
 1993pafb.reptQ....L
 Keywords:

 Aircraft Tires;
 C135 Aircraft;
 Dynamic Models;
 Finite Element Method;
 Pneumatic Equipment;
 Pressurizing;
 Rods;
 StressStrain Relationships;
 Taylor Series;
 Tires;
 Viscoelasticity;
 Bending Moments;
 Deformation;
 Displacement;
 Equations Of Motion;
 Linear Equations;
 Linear Systems;
 Mathematical Models;
 Nonlinear Systems;
 Shear Properties;
 Transport Aircraft;
 Wave Propagation;
 Mechanical Engineering