Jim Papadopoulos

Buckling of regular, chiral and hierarchical honeycombs under a general macroscopic stress state.

An approach to obtain analytical closed-form expressions for the macroscopic ‘buckling strength’ of various two-dimensional cellular structures is presented. The method is based on classical beam-column end-moment behaviour expressed in a matrix form. It is applied to sample honeycombs with square, triangular and hexagonal unit cells to determine their buckling strength under a general macroscopic in-plane stress state. The results were verified using finite-element Eigenvalue analysis.

Self-similar hierarchical honeycombs

Hierarchical structures are observed in nature, and can be shown to offer superior efficiency. However, the potential advantages of structural hierarchy are not well understood. We extensively explored a bending-dominated model material (i.e. transversely loaded hexagonal honeycomb) which is susceptible to improvement by simple iterative refinement that replaces each three-edge structural node with a smaller hexagon. Using a blend of analytical and numerical techniques, both elastic and plastic properties were explored over a range of loadings and iteration parameters. A wide variety of specific stiffness and specific strengths (up to fourfold increase) were achieved. The results offer insights into the potential value of iterative structural refinement for creating low-density materials with desired properties and function.

On-road measurements of high speed bicycle shimmy, and comparison to structural resonance

This paper first presents original data records of the linear accelerations, along with angular velocities and forward velocity, for a high-speed hands-on bicycle shimmy. These describe the oscillation in terms of duration, magnitude, correlation with forward speed, and related danger for the rider. Then additional experimental data are reported which support the conjecture that the shimmy while riding occurs essentially at the same frequency as the lateral resonance of the head tube when the saddle of a stationary bicycle is laterally constrained.

Comment on ‘On the stability of a bicycle on rollers’

In their paper ‘On the stability of a bicycle on rollers’, Patricia A Cleary and Pirooz Mohazzabi (2012 Eur. J. Phys. 32 1293) incorrectly assert that two key differences exist between riding a bicycle on pavement and riding on rollers. The first is that riding a bicycle on rollers somehow tests the role of the centrifugal force and the second is that a lack of inertia or forward momentum on rollers somehow decreases stability. The most straightforward explanation for why these differences do not exist is Galilean invariance. Although it is true that the steer and yaw angles, and thus the magnitude of any lateral acceleration, are limited because of the narrow width of a treadmill or rollers, which certainly can make balancing more difficult, the accelerations that do occur are identical to those which would be found by riding within a similarly narrow path of fixed pavement. In fact, even though a bicycle on rollers or a treadmill has no forward momentum in a frame of reference that is stationary with respect to the ground, it has the same balance dynamics, and thus stability, as the same bicycle on fixed pavement.