Below are some examples of 3D printing, used in both teaching and research. The 3D printer is especially useful in rapid-prototyping in structures. For example, students can design and print slender plane frames that exhibit specific buckling phenomena.
Flat or curved panels are often stiffened with the use of ribs. The overall stiffness can be enhanced with only a relatively modest increase in weight and thus this is a popular approach in aeropsace engineering where weight minimization is a paramount design consideration. The 3D printer is a useful means of producing relatively high resolution iso/othergrids, which can then be tested in the lab.
A small ball-bearing rolls within a contained peanut-shaped tunnel. This is a somewhat unusual nonlinear oscillator since the ball is constrained to follow a specific path, however, its velocity provides the other important component of phase trajectories.
It's motion is tracked by a video camera that is attached to the frame as it is subject to periodic shaking and tilting. A couple of slides are contained here.
Highly deformed elastic members can be useful in a vibration isolation context:
Deep space exploration is limited by (among other things) fuel for the propulsion system. Solar sails is a concept whereby photons from the sun propel a large-area but lightweight kite-like structure. The supporting structure is necessarily slender and susceptible to vibration and buckling problems. The material below describes a related study in which a cantilever is pulled by a cable attached to its end:
Shallow arches and panels are prone to snap-through instability. It is especially a problem in slender structural components used in the hostile operating environment of aerospace applications. Snap-through can be caused by the application of a lateral load, or through a change in the thermal environment:
In the lower diagram the arch is repeatedly heated and then allowed to cool, resulting in a snap-buckling (the dns of the bent beam are clamped):
But snap-through also occurs in deep arches, and a couple of slides briefly describing such a system are contained here.
Rigid bodies with corners may rock when shaken laterally. In some cases this will lead to overturning. Motivation for this work originated in the desire to understand the likelihood of overturning of slender statues in a museum during an earthquake. Below is an example in which the block is placed on a foundation that undergoes a seesawing (tilting) motion.
Conventional structural analysis focuses on structures in which the elastic bending stiffness dominates. But for very slender structures the effect of weight can be important. This section describes a few systems in which gravity competes with flexural stiffness to determine equilibrium configurations:
This is a 'heavy' beam on an inclined foundation, polycarbonate provides a convenient material to illustrate highly flexible behavior.
and we can extend the analysis to large amplitude motion, for example if the root of the upright cantilever is subject to horizontal harmonic excitation:
and an animation corresponding to this (undamped) motion can be found here.
