AEROELASTICITY ESTIMATION IN THE CONSTRUCTION OF CURTAIN WALL SYSTEMS (English version)
Chief technical officer
of the design and construction company “EPSILON”
The article was published in the journal TallBuildings February/March 2013
As an independent branch aeroelasticity appeared in the 30’s of the previous century and it was closely connected with the developing aviation. M. Keldysh’s projects of the late 30’s laid the mathematical basis for the theory of aeroelasticity and made it possible to simulate the phenomenon in aerodynamic tunnels. The following researches contributed a lot to the study of practical issues of aeroelastic interactions: E. P. Grossman, Y.M.Parkhomovskiy, L. S.Popov, etc. N. M.Bronstein was the first to implement dynamic calculations in the field of engineering structures.
Dynamic interactions of buildings and structures were also studied by S. P. Timoshenko, I.M.Rabinovich, B.G.Korenev, etc. We can name V.Bierbaum, T.Carman, E.Simiu, A.Fershing, R.Mase among the foreign scientists who developed analytical, numerical and experimental methods of aerodynamics.
When the wind flows around the building there occurs the socalled instability of the aerodynamic parameters of the environment; a dramatic change of pressure takes place when the flow gets away from the construction. Vortex formation is triggered. As a result the appearing aerodynamic forces lead to the additional load of the building itself as well as its certain parts; and it is essential that this secondary stress is considered when strength prediction of CWS is estimated.
Most aeroelastic processes are of self-vibrating nature; it is caused by the energy exchange between the flow and the body in stream. The main aeroelastic phenomena are flutter (stalling flutter) and buffeting. When considering aeroelasticity in terms of its impact on the structure, it is necessary to mention such things vortex excitation, galloping across the air flow, divergence and half-integral resonance. From the point of view of the stability theory (founded by A. A. Lipunov) aerodynamic interactions can also be considered as processes of aeroelastic stability.
Flutter is the undamped elastic vibration of the structure (or its parts) when the air flows in it at a certain (critical) velocity. Flutter is a kind of self-induced vibrations with the energy source being the wind current and the feedback realized by the elastic building structure (or its part). At certain angles of interaction the current can stall (the so-called stalling flutter). Needless to say that
stalling flutter usually occurs when the velocity of flow is low.
Besides that there exists such a poorly studied phenomenon as panel flutter, i.e. undamped vibration of the panels (wainscot) that stems from the air flow that streams along them at a high velocity. Buffeting is forced vibration of the whole structure or its parts under the inluuence of unsteady aerodynamic forces when the air flow is stalled from the surface of the elastic object at
large angles of interaction (as a rule, these are bluff bodies). In other words in buffeting the stalling flow of one part of the construction influences the other (Fig. 1).
If flutter can be studied by means of locally focusing on a certain significantly elastic” part of the structure, buffeting requires that the entire building, even its “relatively non-elastic” (“rigid”) elements are regarded. One can refer to the phenomenon of flows interfering from the neighboring
buildings, which is closely related to buffeting.
The ways vortex excitation and flutter (stalling flutter) form are similar. This is due to the fact  that when the air flows in, the bluff body drops off vortices that alternate with frequency in a staggered order, which depends on the flow rate, the size and the shape of the body in stream (Fig. 2).
As a rule, galloping across the air flow occurs in flexible structures with certain cross-sectional shapes such as power lines, cable or curtain wall structures. It is a self-induced vibration
of an object that happens almost perpendicularly to the direction of the incoming flow. It is an issue of non-linear aerodynamic stability (the so-called stability under the influence of the “following” forces). Galloping in the wake flow is a kind of galloping across the air flow (due to the limited scope of the article, its description is to be omitted).
Divergence is first of all related to the twist of a body with a small cross width in the air flow that goes along the cross-section axis of the building.  The phenomenon is characterized by the increasing in time tortional self-induced vibrations of the structure (that cause increasing fore-drag of the profile) that lead to its destruction. Divergence is an issue of aerostability; it usually manifests itself in bridge bays and sculptural installations of flat cross-section.
Half-integral resonance is characterized by the complex nature of the interaction between the structure and the incoming flow; and in general with time it leads to the change of the
dynamic parameters, which results in the increase of vibration amplitude. As a rule, it is the structural frequency ω or the damping coefficient β that are subject to change. As an example one
can refer to the change of the tension load of stay roosts of a suspended bridge; this results in the increasing vibrations of the span. Similar problems are described by means of differential equations with periodic coefficients (for instance, the Mathieu-Hill equation):
Technically in most cases the study of aerointeraction of buildings and structures cannot separate one of the above mentioned phenomena from the other.
Recently there has appeared a type of engineering structures such as curtain wall systems (CWS) (Fig. 3) that has set new calculation tasks for engineers and designers to deal with.
Due to the use of light (thin-walled) metal panels the dynamic effect of wind has a significant impact on them.
In general CWS are decorative protective panels made of steel, aluminum or composite sheets that are mounted to the so-called subsystem. The system is a set of longitudinal and cross-sectional linear elements that transfer the force from the lining panel to the bearing construction of the building itself (Fig. 4). The force transmission is carried out via mounting points – brackets.
If required there is a heat insulating layer installed beneath the panels. CWS subsystems may consist of solely vertical or horizontal elements as well as cross-sectional parts.
The surface of CWS is exposed to horizontal or normal forces (usually wind) and vertical factors (weight, ice-load, etc). Temperature exposure is usually balanced out by the contraction joints and free-end bearings (anchorages). The article does not dwell on the impact of
The above mentioned influence triggers bending, cross-sectional and longitudinal load in CWS elements. By means of correct CWS construction designers try to stop any bi-moments
From the point of view of the structural layout of the CWS subsystem is a beam-and-column
construction (Fig. 5).
The lining panels transfer the force to the subsystem through either the springing line or through certain mounting points. Designers try not to take into account the shear rigidity of the panels due to the certain (friction) attach fitting of the subsystem.
The elements of a subsystem are mounted to one another by means of bolted-type connection, self-tapping screws or special mechanical joints. The mounting to the building
is carried out with self-hardening (self-anchoring) bolts, pre-defined embedded elements, and welding (very rarely) (Fig. 6).
The dynamic pattern “building-wainscot” can be considered as an elastic system with a set of mass that is fixed by elastic linkages (Fig. 7).
The design diagram of the CWS element is a single or multi-span beam that is pinned onto the supports (Fig. 8).
The free vibrations of a system like this are described by the famous equation:
where function y stands for the deviations of the core from the longitudinal axis within time t;
EI stands for the stiffness of the core;
m is the reduced mass per unit length of core;
l is the estimated length of the element.
One should mention that in CWS may range from a few to dozens of kilograms; l may range from 1 to 6 meters (no more than the floor height). The natural frequency is estimated by the formula:
If with most buildings M1> Σmi, at the same time the range of natural vibration of buildings and CWS elements is pretty close. If the first vibration period of buildings lasts for seconds, the vibration period of CWS elements lasts for decimal seconds. (When the CWS elements are covered with ice the vibration period increases). One should state that CWS are used in fairly large buildings that have high rigidity. With flexible buildings and most parts of structures other types of wainscot are used (the article does notdwell on these).
The aerodynamic impact and its role in the CWS work should be analyzed. As it is stated in point , “an architectural engineer pursues two aspects of vortex motion: the degree of turbulence of the natural air that flows into the building and local or “near-wall” turbulence, that is caused by the building itself.”
Due to the relatively high rigidity of buildings the flutter itself will not cause significant general dynamic effect (in comparison with the static impact). Stalling flutter, however, can cause significant damage to the wainscot of the building, especially in the corners. On top of that, as it was mentioned above panel flutter is the unexplored area of t he impact the wind has on the CWS, especially for buildings with extended facades.
Buffeting is a phenomenon which is difficult to reflect in the overall approach to designing CWS without considering certain layouts and arrangements of the building. No doubt this phenomenon very much a effects the work of CWS.
Just like stalling flutter, vortex excitation influences the CWS state in the corners and areas with elements that protrude from the fasade. Since there are no typical elements in CWS that depend on galloping across the air-flow and divergence designers do not have to take them into consideration. There may be an exception with various pendants, safe-guard hand rails and certainarchitecture elements but it can be solved by means of special construction activities.
Half-integral resonance is a mechanism, whose manifestations in the building structures are poorly studied. Given that the “building - wainscot” system is technically structurally non-linear, the elastic CWS parameters are different when the wind affects the building positively or negatively. For instance with half-integral resonance CWS destruction is very likely. Besides that one can consider the scheme (Fig. 9), in which the straight-line vertical core of the CWS subsystem will experience alternating longitudinal effect that can trigger cross-sectional vibrations. (This is possible with the alternate lopsidedness of the whole building caused by the overall impact of the wind.)
In the theory of aerodynamics  there is a formula that estimates the critical flutter velocity and similar effects:
g- is the acceleration of free fall;
ρ- is air density.
The correlation indicates that the critical velocity rises when the rigidity of the CWS bearing elements increases. Thus, we can draw two conclusions:
Firstly: when estimating CWS elements one has to introduce rigidity restrictions. In engineering practice there have been cases when the CWS elements would be chosen on
the basis of strength conditions, no possible destruction considered.
Secondly: when designing CWS it is necessary to implement structural elements that limit the velocity of the air flow along the surface of the faзade. For instance, the so-called green facade systems that are used in bio-positive construction can serve as a solution. 
With everything mentioned above, one can distinguish between three types of wind and aerodynamic influence on buildings in general and CWS in particular:
1. Direct wind exposure (static and dynamic) of the wind flow on the surface of the building (windward and downwind). It is fully reflected in point  (although there are a number of typographical mistakes).
When calculating the CWS one should consider the dynamic vibrations of the whole building as
2. General aeroelastic wind impact– when estimating certain CWS parts one should take into consideration the characteristics of the whole building. These refer to buffeting, half-integral
3. Local aeroelastic wind exposure – this locally a effects CWS and does not require all major characteristics of the building to be taken into consideration. It can refer to stalling flutter, panel flutter and partially vortex excitation. It is necessary to state that even if aerodynamics might not significantly a effect the whole building, its influence on the CWS can be critical.
Thus, the CWS are a separate type of building structures with a certain type of load to bear. As a result it is necessary to develop certain regulatory documents (a set of regulations) that govern design, construction, calculation and operation of these types of structures
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