scholarly journals Dynamics of a Pipeline Span on an Elastic Seabed

2021 ◽  
Author(s):  
Ralf Peek ◽  
Matt Witz ◽  
Knut Vedeld
Keyword(s):  
Axial Force ◽  
Exact Analytical Solution ◽  
Damping Ratio ◽  
Approximate Solutions ◽  
Mode Shapes ◽  
Element Analysis ◽  
Modal Damping Ratio ◽  
Modal Damping ◽  
Vortex Induced Vibrations ◽  
Arch Action

Natural frequencies, mode shapes and modal damping ratios must be estimated to assess subsea pipeline spans for vortex-induced vibrations (VIV) and response to direct wave loading. Several approximate solutions exist for a linearly elastic pipe under constant axial force supported by linearly elastic springs beyond the span’s shoulders. An exact analytical solution has only recently been published. That solution is used here in a Rayleigh-Ritz approximation to account for arch action arising from combined effects of sag under gravity loads and axial restraint at the shoulders. The method allows survey data to be used directly to quantify arch action. Its accuracy is confirmed by finite element analysis. Further, the modal damping ratio is estimated based on the fractions of the potential energy in bending, the axial force, and the soil springs, all of which are determined analytically. Thus, it is found that the effective modal damping ratio increases without a bound as the axial load approaches the buckling load in compression.

Nonlinear Span Assessment by Amplitude-Dependent Linearization

2020 ◽  
Vol 142 (5) ◽  
Author(s):  
Ralf Peek
Keyword(s):  
Eigenvalue Problem ◽  
Current Practice ◽  
Nonlinear Eigenvalue Problem ◽  
Damping Ratio ◽  
Mode Shapes ◽  
Inelastic Behavior ◽  
Modal Damping Ratio ◽  
Linear Behavior ◽  
Modal Damping ◽  
Vortex Induced Vibrations

Abstract Although it has long been recognized that vortex-induced vibrations of subsea pipeline spans involve nonlinear and inelastic behavior, the current practice to assess such spans for fatigue and ultimate loading conditions is based on the modal analysis assuming linear behavior. Nevertheless, nonlinearity can be captured approximately by making the linearization amplitude dependent. The eigenvalue problem to be solved for the natural frequencies and mode shapes then involves a stiffness matrix that depends on the mode shape and amplitude of vibration. An important part of the nonlinearity comes from the soil, which is generally represented by springs. This paper presents a simple and particularly effective algorithm to solve this nonlinear eigenvalue problem by using the same algorithm that serves to track the bifurcated solution branches in quasi-static structural stability (buckling) analyses. This method is applied to an example in which the nonlinearity comes from the soil springs. The results demonstrate the importance of the nonlinearity, even at relatively low vortex-induced vibrations (VIV) amplitudes typical of the pure inline response. The inelasticity of the soil springs is also used to calculate the associated contribution to the modal damping ratio.

ANALYTICAL RANDOM VIBRATION ANALYSIS OF BOUNDARY-EXCITED THIN RECTANGULAR PLATES

2013 ◽  
Vol 13 (03) ◽  
pp. 1250062 ◽  
Author(s):  
ASHKAN HAJI HOSSEINLOO ◽  
FOOK FAH YAP ◽  
NADER VAHDATI
Keyword(s):  
Random Vibration ◽  
Printed Circuit Boards ◽  
Damping Ratio ◽  
Excitation Frequency ◽  
Jet Impingement ◽  
Mode Shapes ◽  
Rectangular Plates ◽  
Frequency Range ◽  
Modal Damping Ratio ◽  
Modal Damping

Fatigue life, stability and performance of majority of the structures and systems depend significantly on dynamic loadings applied on them. In many engineering cases, the dynamic loading is random vibration and the structure is a plate-like system. Examples could be printed circuit boards or jet impingement cooling systems subjected to random vibrations in harsh military environments. In this study, the response of thin rectangular plates to random boundary excitation is analytically formulated and analyzed. In the presented method, closed-form mode shapes are used and some of the assumptions in previous studies are eliminated; hence it is simpler and reduces the computational load. In addition, the effects of different boundary conditions, modal damping and excitation frequency range on dynamic random response of the system are studied. The results show that increasing both the modal damping ratio and the excitation frequency range will decrease the root mean square acceleration and the maximum deflection of the plate.

scholarly journals Dynamic behaviour of a gymnasium floor

1986 ◽  
Vol 13 (3) ◽  
pp. 270-277 ◽  
Author(s):  
J. H. Rainer ◽  
J. C. Swallow
Keyword(s):  
Concrete Slab ◽  
Damping Ratio ◽  
Mode Shapes ◽  
Resonant Frequencies ◽  
Modal Damping Ratio ◽  
Modal Damping ◽  
Load Factors ◽  
Resonance Frequencies ◽  
Floor Vibrations ◽  
Vibration Tests

Ten mode shapes, natural frequencies, and modal damping values have been measured for a steel-joist concrete-slab floor spanning 32.1 m. From ambient vibrations and steady-state shaker tests the frequency of the fundamental mode was determined to be 3.5 Hz, and the modal damping ratio to be approximately 1% of critical. A comparison of vibration criteria in Appendix G of CAN3-S16.1-M84 confirms satisfactory performance for walking, but for other rhythmic exercises disturbing vibrations developed. These occurred primarily at the forcing frequency of the exercises and not at floor resonance frequencies. Values of dynamic load factors, α, for rhythmic loadings of this floor were evaluated in accordance with the guidelines on floor vibrations in the Commentary to the National Building Code of Canada 1985. Key words: floors, gymnasiums, vibration tests, resonant frequencies, mode shapes, dynamic loads, dynamic response.

Effect of Damping on VIV Response in Umbilicals and Flexible Risers

2015 ◽  
Author(s):  
Kay Hansen-Zahl ◽  
Veronica Henøen ◽  
Rolf Baarholm ◽  
Farzan Parsinejad ◽  
Yiannis Constantinides
Keyword(s):  
Fatigue Life ◽  
Internal Pressure ◽  
Contact Force ◽  
Damping Ratio ◽  
Life Assessment ◽  
Stick Slip ◽  
Modal Damping Ratio ◽  
Modal Damping ◽  
Vortex Induced Vibrations ◽  
Flexible Risers

The fatigue life assessment of umbilicals and flexible risers due to vortex-induced vibrations (VIV) require special attention to the structural properties of the flexible bundle due to stick/slip behavior of helical elements in bending. The VIV response on umbilicals and flexible risers is complex, and it is controlled by several parameters. Structural damping is one of these parameters, but this is typically calculated based on the material damping of the structure. Similar to flexible risers and umbilicals, hysteresis damping due to the stick/slip behavior in the helical layers may be significant for cable structures. The purpose of this study is to evaluate the effect of the hysteresis damping on VIV response, and to demonstrate a procedure for consistent VIV fatigue analysis of flexible risers and umbilicals. The stick/slip hysteresis varies with varying contact force, and the contact force is dependent on internal pressure and effective tension. The effect of varying these parameters is included in the study. Furthermore, the study includes different riser system configurations and current profiles. In this paper, the stick/slip hysteresis has been established for two umbilicals and two flexible risers, with varying internal pressure and effective tension. Combined with five different configurations (both shallow and deep water) and 16 different current profiles, the VIV modes have been calculated and the corresponding stick/slip modal damping ratio has been established. Finally, using fatigue current profiles, fatigue life estimates have been made based on different damping ratios, including the estimated stick/slip damping ratio. The study presented in this paper has been carried out as part of the Norwegian Deepwater Programme (NDP).

Experimental Study the Vibro-Acoustic Performance of a Double Glazed Window

2012 ◽  
Vol 503-504 ◽  
pp. 1129-1132
Author(s):  
Qi Bo Mao
Keyword(s):  
Damping Ratio ◽  
Normal Wave ◽  
Sound Transmission ◽  
Least Square ◽  
Structural Vibration ◽  
Mode Shapes ◽  
Reverberation Chamber ◽  
Modal Damping Ratio ◽  
Modal Damping ◽  
Complex Exponential

This paper presents an experimental investigation of the sound transmission and structural vibration characteristics of the double glazed window. The laboratory experiments were performed placing the window between reverberation chamber and anechoic chamber. The window was subject to diffuse field, approximate normal wave and oblique wave acoustic excitations. The sound transmission performances at far-field were measured. Furthermore, experimental modal analysis has been performed. The Least square complex exponential algorithm is used to extract the modal parameters, i.e. mode shapes, natural frequencies and modal damping ratio of the structure. The results also show that the highest sound transmission of this experimental double glazed window appears around the mass-air-mass resonance frequency.

Modal damping ratio analysis of dynamical system with non-stationary responses

2016 ◽  
Vol 59 ◽  
pp. 138-146 ◽  
Author(s):  
Da Tang ◽  
Ran Ju ◽  
Qianjin Yue ◽  
Shisheng Wang
Keyword(s):  
Dynamical System ◽  
Damping Ratio ◽  
Ratio Analysis ◽  
Modal Damping Ratio ◽  
Modal Damping

scholarly journals Coupling of Flexural and Longitudinal Damped Vibration in a Two-Layered Beam

1998 ◽  
Vol 5 (5-6) ◽  
pp. 337-341
Author(s):  
F. Pourroy ◽  
S. Shakhesi ◽  
P. Trompette
Keyword(s):  
Damping Ratio ◽  
Modal Damping Ratio ◽  
Modal Damping ◽  
Resonance Frequencies ◽  
Layered Beam ◽  
Flexural Vibrations

In dynamics, the effect of varying the constitutive materials’ thickness of a two-layered beam is investigated. Resonance frequencies and damping variations are determined. It is shown that for specific thicknesses the coupling of longitudinal and flexural vibrations influences the global modal damping ratio significantly.

ODS Analysis on the Rack of Batching System Mixer

2013 ◽  
Vol 437 ◽  
pp. 257-260
Author(s):  
Li Zhang ◽  
Guang Yuan Nie
Keyword(s):  
Working Condition ◽  
Damping Ratio ◽  
Side Surface ◽  
Modal Parameters ◽  
Modal Shape ◽  
Modal Damping Ratio ◽  
Modal Damping ◽  
Before And After ◽  
Structure Vibration ◽  
Batching Machine

By using ODS (Operating Deflection Shapes) technology, the modal parameters of the rack of a batching system mixer under operating condition are identified and the modal shape and modal damping ratio of the rack in a few working frequencies are obtained. The results show that, the batching machine rack on working condition has a significant effect on some frequency and the work principal modes that appear as before and after exercise of two beams above the rack and swaying motion of the brackets of the two side surface. This paper provides a valuable reference for the structure vibration optimization of batching system mixer.

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