I am solving a wing structure for normal modes using SOL103 in NASTRAN. Since I am beginner, I started with just the wingskin (lower and upper wingskins) but that results were far from what was expected. Only the local modes of the wingskin was observed. I modelled the spars and ribs then the 1st mode of bending was observed, rest all were the local modes of wingskin. Increasing the number of ribs caused the 2nd mode of bending to appear. Introducing stringers stiffened the structure where the 1st twisting mode and bending in x-y plane (my model has chord along x-axis and span along y-axis) were obtained. However still the local bending modes of the wingskin are seen where seen. So what is the appropriate spar-rib-stringer spacing and their thicknesses and the wingksin thickness so as to obtain the expected normal modes of a wing?

My wing is a sweptback wing with 30deg sweep angle, taper ratio of 0.6, span of 2m, and made of NACA0012 airfoil. I intend to simulate the cruise condition.

  • $\begingroup$ It needs to be stronger than "cruise condition". Combinations of materials good in compression and those good in tension are helpful (starting with wood and cable!). Fiber glass over foam core should also yield some clues. Avoid harmonicly reinforcing bending modes. $\endgroup$ Aug 24 '21 at 15:04
  • $\begingroup$ @RobertDiGiovanni SOL103 is linear eigenmodes so no difference in compression/tension stiffness (let alone strength) can be modelled. The choice of materials is not the main issue here. $\endgroup$
    – Sanchises
    Aug 24 '21 at 18:39
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    $\begingroup$ Why would you combine 30° sweep with a NACA0012? What speed are you designing for? $\endgroup$ Aug 24 '21 at 19:07

It seems like you discovered the inconvenient truth about thin-walled structures. Despite their apparent superiority (all the material is as far away as possible from the bending line) they are extremely flimsy. This is because the ratio of out-of-plane stiffness and mass is very poor: flexural rigidity $D\propto t^3$, mass $m\propto t$. Especially when using materials with a high volumetric stiffness (e.g., steel), the resulting structure becomes so thin that the plates have unpractically low eigenmodes. The same goes for buckling under flight loads.

Instead, the aircraft designer must resort to a poorer volumetric efficiency to get sufficient out-of-plane strength and stiffness. Basically, increase that $t$ without increasing $m$ too much by choosing perhaps less stiff but much lighter materials (welcome composites and perhaps aluminium). However, that still leaves (too) much to be desired, so you add stiffeners, stringers, ribs... (all increasing the effective $t$) until a sufficient performance is obtained. Most efficient is to make a so-called sandwich construction: two stiff layers with a light (e.g., foam) core in-between, which has a stiffness of $D\propto t\cdot h^2$ (with $h$ the foam core thickness and $t$ the skin thickness). See e.g., here.

This is all to say that there is no optimal rib/stringer spacing unless you know how the 'skin' is constructed. Remember, eigenmodes are all about stiffness and mass ($f\propto\dfrac{k}{m}$), so low eigenmodes are indicative of mass not contributing to stiffness of that particular mode.

  • $\begingroup$ A very interesting and informative answer. Thanks! $\endgroup$
    – xxavier
    Aug 24 '21 at 23:09
  • $\begingroup$ Seems like adequate strength can be had with thicker skin, and the foam core acts to damp unwanted oscillations (but is very light). $\endgroup$ Aug 25 '21 at 5:01
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    $\begingroup$ @Robert No the main effect here is stiffness (force due to displacement), not damping (force due to velocity). Although of course the damping is a welcome side effect, and the modes are especially easy to damp now we raised their frequency. Of course, this won't show up in a SOL103 analysis which only looks at real eigenvalues. $\endgroup$
    – Sanchises
    Aug 25 '21 at 5:53

to obtain the expected normal modes of a wing

One might turn to nature to get a better feel for this issue. One may build strong and stiff, but it will be heavy. And even skyscrapers have harmonic modes.

The natural solution is a combination of strength and shock absorbing ability. The bone and tendon arrangement, seen in the horse, allows 1000 lbs of weight to be dropped on one foot over and over again without breaking the bone.

The tendon aborbs the impact over a longer period of time, reducing strength requirement. What is worrisome about adding internal structure (such as ribs) and thinner skin is that it will create a levered bending point (at the rib). So one part is too stiff, the other not stiff enough (thin skin), so to reduce fatigue at that point, more ribs must be added.

It seems a flexible, shock absorbing approach serves to not only reduce peak strength requirement (from a gust or manuvering),saving weight, but also will reduce or eliminate unwanted harmonics.

So now we may look at another design, avian wing bone. Even without the attached feathers, muscles, ligaments, and tendons, we see a round, thick walled structure with a hollow interior. Strong, flexible, and light.


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