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University: Politecnico di Milano
Degree programme: Aerospace Engineering
Subject: WIND ENGINEERING
Material language: English
Academic year: 2025-2026
Classification: Notes · Other
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University study material for WIND ENGINEERING in the Aerospace Engineering degree programme at Politecnico di Milano. The document covers: Dipartimento di Scienze e Tecnologie Aerospaziali Politecnico di Milano Wind Engineering Wind Engineering Oral Questions Student: Tiano Riccardo Academic Year 2025-2026 Wind Engineering CONTENTS Contents 1 Wind climate, generation and turbulence 2 1.1 What is the wind? Why does

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Dipartimento di Scienze e Tecnologie Aerospaziali Politecnico di Milano Wind Engineering Wind Engineering Oral Questions Student: Tiano Riccardo Academic Year 2025-2026

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Wind Engineering 1 WIND CLIMATE, GENERATION AND TURBULENCE Wind Loading Chain” approach, where static effects and dynamic turbulent effects are calculated and then combined. 1.8 Cross correlation, how it works in time and space Cross-correlation is a statistical measure used to understand the relationship between wind fluctuations occurring at two different points, either in space or in time. It is a fundamental concept in wind engineering for modeling turbulence. In a turbulent wind field, gusts of wind (eddies) are not isolated point events; they have a physical dimension. If a large gust hits one point on a structure (Point P), it is highly likely that a nearby point (Point Q) will also experience a similar fluctuation shortly before, during, or after. Cross-correlation quantifies this ”similarity” or dependence between the wind speeds at P and Q. When we consider a single point in space (P = Q) and look at the wind speed at two different moments in time separated by a time lag τ , we are talking about autocovariance (or autocorrelation). It measures how much the wind fluctuation at time t, u(t), is related to the fluctuation at time t + τ , u(t + τ ). The formula is: Cu (τ ) = E[u(t) · u(t + τ )], where E is the expected value. If τ = 0, the autocovariance is simply the variance of the wind speed (the energy of the turbulence). As the time lag τ increases, the correlation generally decreases because the wind becomes less predictable compared to its past state. The integral of this function over time gives the Integral Time Scale (Tu ), which is a measure of the average duration of a wind gust. • Cross-correlation in space: When we consider two different points in space (Point P at coordinates y1 , z1 and Point Q at coordinates y2 , z2 ), we use the cross-covariance…

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Wind Engineering 3 CABLE DYNAMICS AND VORTEX SHEDDING where U is the wind velocity and D is the characteristic dimension (diameter) of the body. When this frequency fs approaches one of the structure’s natural frequencies, the periodic aerodynamic forces can excite the structure into resonance. Normally, the vortex shedding frequency fs increases linearly with wind speed U . However, when the structure begins to vibrate significantly, it imposes its own motion on the flow. In a certain range of wind speeds, the vortex shedding frequency ”locks onto” the natural frequency of the structure (fn ) and remains constant, even if the wind speed increases. This range is the Lock-in region (or synchronization region). Within this region, the structure undergoes large-amplitude resonant oscillations, which can be sustained over a wider wind speed range than predicted by linear theory. • Strouhal Number (St): As noted above, St = fsUD . It defines the geometry of the shedding process for a stationary body. Its value depends primarily on the shape of the cross-section (e.g., for a smooth cylinder, St ≈ 0.2). • Scruton Number (Sc): This is a non-dimensional parameter that incorporates the structure’s mass and damping. It is defined as: 2δm Sc = ρD2 where δ is the logarithmic decrement of structural damping, m is the mass per unit length, ρ is the fluid density, D is the characteristic diameter. The Scruton number essentially measures how ”hard” it is to move the structure. A low Scruton number means the structure is light and has low damping, making it highly susceptible to large- amplitude vortex-induced vibrations. Increasing the Scruton number (e.g., by adding structural damping or increasing mass) is the primary engineering strategy to suppress vortex-induced response. 3.3…

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Wind Engineering 4 BRIDGES 4 Bridges 4.1 1-DoF Instability, vertical dof The 1-DoF instability can be demonstrated by analyzing the homogeneous equation of motion for the bridge deck in a linearized aeroelastic system: ¨ + ([R ] + [R ])X [Ms ]X ˙ + ([K ] + [K ])X = 0 s A s A Instability occurs if the overall damping for a specific mode of vibration becomes negative. This happens when a diagonal term of the aerodynamic damping matrix [RA ] is negative and its absolute value is strictly greater than the corresponding structural damping term in the [Rs ] matrix. For the vertical degree of freedom (z), the structural damping is denoted as rz . The corresponding diagonal term for the vertical velocity ż in the aerodynamic damping matrix [RA ] is: 1 RA,zz = ρBLV (CD0 + KL ) 2 where ρ is the air density, B is the deck width, L is the reference length, V is the wind velocity, CD0 is the static drag coefficient evaluated at the equilibrium angle, KL is the slope of the lift coefficient ( ∂C ∂α ) evaluated at the equilibrium angle. For this aerodynamic damping term to become negative, L the sum (CD0 + KL ) must be negative. Since the static drag coefficient CD0 is always positive, this instability requires KL to be negative, and its absolute value must be greater than CD0 . hen this condition is met, the 1-DoF instability in the vertical mode is excited if the negative aerodynamic damping overcomes the structural damping rz : 1 ρBLV |CD0 + KL | ≥ rz 2 The wind velocity V at which this equality holds, marking the exact onset of the instability, is defined as the critical velocity Vc . When a bridge deck moves vertically with a certain velocity ż in a wind field of velocity V , the wind actually experienced by the deck is the relative velocity Vrel . This vertical motion alters…

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Wind Engineering 4 BRIDGES where [Ks ] is the structural stiffness matrix of the bridge, X0 is the vector defining the static deforma- tion (the static position of the bridge components, including the deck), and F A0 represents the static aerodynamic forces applied to all bridge members by the average wind. These forces are a function of the static aerodynamic coefficients (CD , CL , CM ) evaluated at the equilibrium angle of attack. Solving this equation is the first necessary step before linearizing the system to study dynamic responses like buffeting or flutter. 33

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