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Answer: Negative added mass is a mathematical arrangement of terms in equation of motion. The inertia term, which arise from variable submergence effect shall result in added mass and placed in the RHS of equation of motion, for convenience. Further, positive and negative depends on whether the submergence is above or below, MSL respectively.
Answer: Few structures undergo serious damages even under transient state of loads (For example, Ringing response of offshore TLPs) Even though, the forced vibration may not sustain for a long period to reach a steady state, but still, the damage can be significant. Hence it is important to study the response under such conditions
Answer: After you understand the methods of writing equation of motion for variety of problems (both in single and multi-dof models), then you can try to use the software at https://nees.org/resources/nonlin This can give more insight of dynamic analysis, as a whole.
Answer: All compliant structures are designed to have explicit two sets of frequencies namely soft and stiff. It is the selection of FORM which enables this partition of frequency bands. Therefore, two translations namely surge, sway and 1 rotation namely yaw are soft degrees-of-freedom. Their periods are very high (in the order of 40 to 100 sec). Remaining heave, pitch and roll are stiff degrees-of-freedom by virtue of design. This concept is by and large true for three-lagged articulated towers also.
Answer: Dunkerley and stodla methods are used to compute only fundamental frequency due to its mathematical formulation in eigenvalue problem. Higher modes cannot be computed using stodla as it does not guarantee convergence of higher modes for the assumed mode shapes. Modified Rayleigh-Ritz procedure can be used to compute higher modes if the shape function is assumed appropriately. Further, it is very important to understand the necessity of emphasizing fundamental mode of vibration. structures will vibrate in their fundamental mode first as this is first zero crossing of the eigen vector. If the forcing frequency band is closer to this first mode frequency, then the structure will be subjected to high displacements (response). This will further add to self-induced vibration in the system, which can grow un-bounded. It is hence imperative to design the system for the forcing function frequency well away from the fundamental frequency. Therefore first mode and fundamental frequency are important in the design point of view.
Answer: While computing wave loads on offshore structures, most of the wave theories recommend estimation of wave forces upto MSL; modifications suggested by Chakrabarti, Wheeler and Hogen are improvements. In reality, for a considerably higher wave amplitudes, forces on members above the MSL (till the crest) or release of forces below MSL (upto trough) need to be considered or else, the force estimate becomes highly conservative. This effect is known as the variable submergence effect and is one of the main sources of non-linearity. Water particle movement above MSL or below MSl (+ or -), therefore will activate the acceleration force on he body, which need to be considered in he analysis. In case of compliant structures like TLP, this problem becomes more serious. Therefore added mass effect is an important variable that is considered in the design.