This appendix summarises the aeroelastic systems used throughout this book.
A.1 Galloping Oscillator
Consider the 2D cross‐section of a square cylinder shown in Figure A.1. The square of height h can oscillate in the plunge direction, y, restrained by an extension spring of stiffness k and is exposed to uniform free stream flow with airspeed U and density ρ. The spring can be seen to represent the bending stiffness of the compete 3D structure. The equation of motion for the square cylinder can be written as (Paidoussis et al., 2011)
(A.1)
where m is the mass per unit length of the body, d the structural damping coefficient, k the spring stiffness and the aerodynamic force coefficient
where fy is the aerodynamic force in the plunge direction. A nonlinear galloping model can be obtained by choosing a polynomial form for (Parkinson and Smith, 1964), that is
Figure A.1 Two‐dimensional rectangular cylinder with a plunge degree of freedom
The nonlinearity ...
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the aerodynamic force coefficient
(Parkinson and Smith, 1964), that is