A Fast Prediction Method for the Instability Range of Boundary Excited Slender Tension Beams
A technology of stable intervals and prediction methods, which is applied in the directions of instruments, geometric CAD, design optimization/simulation, etc., can solve problems such as not considering the time-varying tension prediction method, and achieve the effect of avoiding fatigue damage
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specific Embodiment approach 1
[0079] Specific implementation mode one: combine figure 1 , figure 2 , image 3 , Figure 4 with Figure 5 Describe this embodiment. In this embodiment, a complete vibration model 40 in which the boundary excitation and the standpipe structure are coupled to each other is established, and the vibration control equation is formed according to the vibration model 40. Based on the Galerkin method, the first four vibration modes are used for the vibration control equation. Discrete, combined with the Floquet theory to determine the unstable range of the variable tension flexible cylinder, by changing the damping performance of the variable tension flexible cylinder to form the minimum unstable region of the variable tension flexible cylinder, through the variable tension amplitude and frequency A process that is regulated to keep a variable tension flexible cylinder in a steady state.
specific Embodiment approach 2
[0080] Specific embodiment two: this embodiment is a further limitation of specific embodiment one, and the prediction method includes the following steps: the prediction method includes the following steps:
[0081] Step 1: Establish the vibration governing equation for the mutual coupling of boundary excitation and riser structure:
[0082] Take a flow transfer riser with a length L and a diameter D as a variable tension flexible cylinder, and use the variable tension flexible cylinder as a vibration model 40, and the two ends of the flow transfer riser are respectively hinged with the floating platform 30 to establish a right-hand Coordinate system, and then establish the vibration control equation as:
[0083]
[0084] In the above formula, m is the mass of the vibrating system per unit length; R is the structural damping R s and fluid damping R f The sum, the variable tension T(t)=T of the vibration model 40 given by the floating platform 30 0 -kasin(ω e t), T 0 i...
specific Embodiment approach 3
[0091] Specific embodiment three: the present embodiment is a further limitation of specific embodiment one or two, and the prediction method also includes step 2: based on the Floquet theory, the unstable interval of the coupling vibration control equation is judged, and the process of judging is:
[0092] The expressions for the first-order differential equations expressed in matrix form are:
[0093]
[0094] where Y=(y 1 ,y 2 ,...y2N ) T , Represents the first-order derivative with respect to time, A(t) is a 2N×2N periodic matrix, specifically expressed as Floquet theory is used to analyze the stability of expression (4), namely:
[0095] The expression for the basic solution U(t) of expression (4) is:
[0096] U(t)=P(t)exp(tF) (5)
[0097] In the above formula, U(t) is a 2N×2N periodic matrix with a period of 2π / ω; F is a 2N×2N periodic matrix, and the fundamental matrix solution U(t) of the periodic matrix grows with time when And only if at least one eigenva...
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