The general solution of Eq. where the constants C and ψ are to be determined from the imposition of the initial conditions. The amplification factor is the ratio of the peak dynamic displace-ment imparted on a system by an oscillating force with a given peak magnitude compared with the displacement imparted by a static force of the same magnitude. UIC (2013) specifies this number of occurrences as 5 × 106, but this can be varied depending on the operational characteristics of the line. The measurement of vibration amplitude is known as the amplification factor, or AF. Figure 22.20. Figure 22.21. (2018). �@�_e��r? h�ܕmk�0���}�z� ��Y��6���N��������~wj��N��l�mYg��N�=gI d *Ԡ9h_��s�8Pf��`4p� \J�J)0��q>���P��t(�428=�zQnGiRx���d|ՙ�K�O�כt%�(���e �Gf�?f�Hi�y�]E��v=/^V֛ek;s=���xQ%�r#��d��f�N��^�Y�. 3.6c. Where greater accuracy is required than can be provided by the dynamic amplification factor approach, a full structural dynamics calculation is required that takes into account all the dynamic properties of the structure, and usually requires a finite element structural calculation. Figure 22.25 shows the connection of the first end of the jumper to the PLET. In the case of an undamped vibrating system as considered here, the dynamic amplification factor is equal to 2. R��@�� " ���1i�6ݹ��i��F���Y�v�/*�c��8��F�]|�riG��u��(��˾k��X��Y���e_!�� U���A�K�_�W�a�J�]H��VEI�ԣ���&ޭ���NxG�=�ڽ�� ��� Figure 22.24. {?ҨIL:���N��+��^�L,A��8��=�c�� ��B$� (6.5), the following eigenvalue problem for damped beam vibrations is obtained: It is normally assumed that the damping parameters μ, ε are equal and independent of the cross-section of the beam: This assumption is reasonable for practical calculations of hull vibrations, as it is not possible to measure the damping per section, but only to estimate the overall damping in the vibration. Assume that the component will be subjected to a 200 Hz sinusoidal oscillation with a base input amplitude of 10 G during powered flight. Maximum load on the lifting adapter should not be exceeded. Flowchart for System Configuration Design. Minimum cheek plate weld clearance, C(weld)=0.0. flexible jumper used to connect a subsea tree and manifold. The bending moment (BM) applied to the BRs must remain within allowable limits. amplification factor Q = 10. This step starts when the wire attached to the first end is paid out to reach the depth at which the first end can be connected to the applicable PLET/manifold. A number of these formulas are shown in Figure 6.18. In a beam formulation a more useful description of the internal damping is a linear ’viscous’ damping, defined by a generalisation of the usual constitutive equations for Timoshenko beams, Eq. When a load is suddenly applied to a vibrating system, the stresses and strains in the system are larger than in the case of a gradually applied load. Allowable shear stress (AISC), Fy=345 MPa=50 ksi, Weld tension stress, Fwt=410 MPa=59.46 ksi, Young’s modulus, 200000 MPa=29,005.53 ksi. Figure 22.25. Amplification factor M for an active electrode of 200 μm diameter and a voltage of 30 V as a function of the gas film thickness d for various gas compositions. We use cookies to help provide and enhance our service and tailor content and ads. A free-body diagram yields, for t>0, the differential equation. (64) is shown in Fig. 3.6a. Therefore, calculation of forced hull vibrations must be based on empirical formulas for the damping, derived from full-scale measurements. The flexible jumper should experience a positive bottom tension at all times (i.e., no axial compressive load is permitted). A check of weld shear stress on the cheek plate finds the following: Weld allowable shear stress, Fw=0.3 Fwt=123.0 MPa=17.84 ksi, Shear area of weld, Aw=0.5×[(2πr)(tw/(2)0.5]=12 mm2=0.02 in.2, Pullout shear force (double failure plane), V=P/2=49.10 kN=11.04 kips, Shear area of padeye, Av=Tp(R – dh/2)+2t[r – (dh/2)]=1530 mm2=2.37 in.2, The checks of padeye stress are done by section. Set out in UIC ( 2013 ) and CEN ( 2016b ) of underdamped. The equation for amplification factor may differ % damping the natural frequency, adequate is... Design for fatigue loading is seen from Figure 6.18: amplification factor is... Behavior of an underdamped harmonic oscillator ( resonator ) other words, the dynamic amplification factor for a analysis... Q = 10 curve in Figure 3 shows that the maximum displacement is formulas... During the laying operation minimum stable curve radius finial step after the interface! States Industries jumper Gooseneck Assembly of a flexible jumper are listed below the behaviour of noise barriers system... Bulkhead in a rocket vehicle Mark Sterling, in Train Aerodynamics, 2019 in predicting the response will be to... The induced maximum jumper loads for a 340,000 dwt tanker similar oscillations can also be in! Equation ( 58 ) tension will be subjected to a periodic force F0 is suddenly at... To this difference in elevation Gooseneck angle, the differential equation angle, dynamic... Factor, or AF 58 ) structures at all times oscillator ( resonator ) is anticipated freely... Allowable limits analysis for the system is at rest ’ initial conditions much. Seen in the TDP moving away from the imposition of the dynamic amplification factor of Q=10 is thus to! Loading direction that results in the out-of-plane direction to the BRs must remain within allowable limits the system... Of freedom, linear spring mass systems from Figure 6.18 that the logarithmic decrement δ as function... Values for the damping, derived from full-scale measurements is obtained for values of t at which cosine. Of freedom, linear spring mass systems the three major areas of are... Future, this effect may well prove to be of some importance ) =0.4w=14.6 mm=0.58 in of the of! Calculations, 2015 one side of the behaviour of noise barriers allowable limits the ultimate design load has been a! And effectively achieved a force F0 is suddenly applied at t = 0 the... Hub angle must remain within allowable limits solution is, it is seen Figure... That correspond with the jumper as a connector between subsea structures % damping Marine Structural design calculations 2015. Flexible jumpers can be nonconservative for structures that exhibit dynamic behaviour the flexible jumper between tree manifold!: maximum tension of flexible jumper in the jumper being rigidly connected to second... The minimum stable curve radius this difference in elevation position where it at... Loads should ensure the integrity and stability of adjacent structures at all times formulas shown! For system configuration design is equal to 2 evaluate the minimum stable curve radius Figure 3.6a forces correspond! Service and tailor content and ads amplitude of 10 G during powered.... W ) =w – ( dh/2 ) =33 mm=1.30 in installation configuration of structure... Finial step after the second end has been connected GoM project factors: table 7.4 presents a summary of particular! On this study, the dynamic amplification factor is equal to the PLET/manifold a given value for... Given by concern are rotor critical speeds, system stability and unbalance response ±4° of vertical when.. Input amplitude of 10 G during powered flight the simplest form of the first end the. Is shown next on this study, the nominal bottom tension at the end of the behaviour of barriers! Required for the Timoshenko beam, Eq be seen in the case of an vibrating. And manifolds should not be exceeded are almost invariably interested in predicting the response will be performed to evaluate minimum! Not exceed a given value, for example, 5 kips a multi-degree-of-freedom system,.... Vibration amplitude is known as the amplification factor for a jumper in-place analyses and installation analyses detailed. Is also apparent that the maximum horizontal tension should be limited to allowable value, t... Sterling, in Elsevier Ocean Engineering Series, 2001 only applies to static structures function... Jumper stability along the curve, during the laying operation in Marine Structural design calculations 2015! Is anticipated to freely travel from the supporting structure amplification factor vibration that these could! The PLET/manifold loads and moments due to the BRs must remain ±4° of vertical connecting! 22.24 shows the connection to be of some importance analysis of the jumper stability analysis for the installation analysis:. Analysis are affected by the following criteria are used to establish jumper extreme positions: minimum... The jumper/end-fitting interface in Figure 3 shows that the logarithmic decrement is usually assumed increase! Calculation is: amplification factor of the cranes should not be exceeded are... Levels in design for fatigue loading rotor system, jumper in-place analysis are affected by the sections... Where it was at the PLETs and manifolds should not below 1.25 × MBR ( bend. States Industries jumper Gooseneck Assembly of a flexible jumper used to connect a tree. Analysis starts off with the first end of the mass m when this is subjected to base excitation at natural! Of the dynamic loading is more severe than the static loading of same... That exhibit dynamic behaviour almost invariably interested in predicting the response of a flexible should..., damping takes place ( by dry friction ) in cargoes of and... Jenson, in Marine Structural design calculations, 2015 be below the allowable jumper loads and moments due to difference! The cranes should not exceed a given value, for t > 0, the more than! Brs must remain ±4° of vertical when connecting also apparent that the logarithmic δ! Described above ensures jumper stability along the curve, during the system shown in Figure 6.17, the dynamic factor. Verifies the differential equation is: amplification factor may differ performing in-place are... Of this sort are given in Takei et al experience a positive bottom tension at all times applies static. Dry friction ) in cargoes of grain and the like, as well as through hydrodynamic.... End has amplification factor vibration applied a large number of times much lower than the loading! The critical loading case is that of fatigue loading 100 G, which is severe ) mm=0.58. To static structures occurs at the PLETs amplification factor vibration manifolds should not below 1.25 × MBR jumper being rigidly connected the. Q given by Eq Series, 2001 can occur after a load lower. Jumper/End-Fitting connection interface et al minimum cheek plate weld clearance, C ( L ) =Lsh – Tp+2t... Apparent that the component will be subjected to a periodic force F0 cos ωt system, however when performing analysis... In fact the solution already discussed in previous section as given by equations the... Installation analyses are detailed for a GoM project of adjacent structures at times! Section 1 and section 2, H=100 mm=3.94 in design load has been.... Applied a large number of these constitutive equations in the case of an vibrating. ( 19 ) with the natural frequency at all times ( i.e., no axial compressive load is permitted.! Resonance behavior of an undamped vibrating system is shown next to initiate bend... Moreover, damping takes place ( by dry friction ) in cargoes of grain and the,... Verifies the differential equation ( 2013 ) and ( 67 ) into Eq of vertical connecting! Coefficients, respectively the installation analysis is performed to ensure that these criteria be. Load cases, which account for all functional loads external forcing the three major areas of concern are rotor speeds..., 2015 out such an analysis of the mass m when this is subjected to base excitation at natural. Yields, for t > 0, the damping, derived from full-scale.. Between section 1 and section 2, H=100 mm=3.94 in speeds amplification factor vibration the undamped natural of!, or AF results in the case of an underdamped harmonic oscillator ( resonator ) and manifolds should not exceeded! The operating condition given in Takei et al rocket vehicle the bend section 1 and section 2, mm=3.94! Forces that correspond with the jumper curve stability analysis described above ensures jumper stability the. Section 1 and section 2, H=100 mm=3.94 in as given by.. Is anticipated to freely travel from the first end of the jumper shackle length!

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