Hybrid Frequency Time Domain Method Research Articles

Time-Domain Implementation and Analyses of Multi-Motion Modes of Floating Structures

The study of wave-structure interactions involving nonlinear forces would often make use of the popular hybrid frequency–time domain method. In the hybrid method, the frequency-domain analysis could firstly provide the reliable and accurate dynamic parameters and responses; then these parameters and responses are transformed to the parameters to establishing the basic time-domain equation. Additionally, with the addition of the required linear and nonlinear forces, the time-domain analysis can be used to solve for the practical problems. However, the transformation from the frequency domain to the time domain is not straightforward, and the implementation of the time-domain equation could become increasingly complicated when different modes of motion are coupled. This research presents a systematic introduction on how to implement the time-domain analysis for floating structures, including the parameter transformations from the frequency domain to the time domain, and the methods for calculating and approximating the impulse functions and the fluid-memory effects, with special attention being paid to the coupling terms among the different motion modes, and the correctness of the time-domain-equation implementation. The main purpose of this article is to provide relevant information for those who wish to build their own time-domain analyses with the open-source hydrodynamic analysis packages, although commercial packages are available for time-domain analyses.

Evaluation of long-term power capture performance of a bistable point absorber wave energy converter in South China Sea

Nowadays, extensive research has been conducted to generate electricity from ocean waves, but there are not too many studies on the capture of wave energy in a specific ocean area. As the largest sea area in China's offshore waters, the South China Sea contains a large amount of wave energy and is regarded as a natural wave energy power plant. A comparative study was conducted to investigate the effects of wave energy converter (WEC) parameters on the long-term power capture performance of a bistable point absorber WEC installed in the South China Sea in this paper. Combined with the joint probability distribution of significant wave height Hs and peak wave period Tp in South China Sea, a mathematical model was developed for the evaluation of long-term power performance of WECs. The governing equations of the point absorber WEC were established using the hybrid frequency-time domain method. The dynamic response and captured power can be obtained after numerically solving the equations of motion with the 4th order Runge-Kutta Method. The results show that the bistable mechanism has great advantages in the long-term captured power of WEC. In general, a circular truncated cone-shaped buoy WEC with a larger buoy size and smaller nonlinear parameter tend to result in better long-term power capture performance. The insights given in this study provide a motivation and foundation for developing a complete set of performance optimization methods of point absorber WECs installed in South China Sea.

A frequency-time domain method for ship fatigue damage assessment

Ships in ocean waves are suffered from cyclic wave loads which can cause fatigue damage to ship structures. Classification societies require owners to carry out fatigue assessment for ship structure for its potential great loss caused by fatigue failure. Currently there are many fatigue assessment methods including simplified method, deterministic method, spectral-based method and time domain method. But none of them predict fatigue life precisely and effectively. Based on linear superposition theory and the assumption that a linear relationship occurred between waves and ship structural response, some scholars proposed the hybrid frequency-time domain method. This method avoids the imprecise narrow band approximation in spectral-based method and adopts rainflow counting instead. However, the hybrid method is not applied extensively on ship fatigue assessment because relevant research is insufficient. In this paper, aiming to validate the hybrid method, a segmented ship model test is carried out, and the short-term fatigue damages of a 4600TEU container forecasted by hybrid method and traditional methods are compared. Results shows that the hybrid method forecasts the closest fatigue damage prediction to time domain analysis and owns enough efficiency. But in some area located at midship, hybrid method may predict lower fatigue damage than time domain method.

Fatigue analysis of water intake risers: Hydrodynamic damping effect and a hybrid frequency-time domain method

The fatigue performance is key to the design of water intake risers (WIRs), which is a novel concept used to convey cooling water for liquefaction of natural gas at sea. To estimate the fatigue life, it is crucial to accurately predict the response amplitude of the WIRs, which is dominated by hydrodynamic damping. In operational conditions, the motion amplitudes of WIRs are usually smaller than their diameter, and thus leading to a flow regime of KC < 5. It is found in this flow regime; the hydrodynamic damping largely depends on the motion magnitude of the risers. To consider this coupling effect, a hybrid frequency-time domain fatigue analysis method is proposed, where a nonlinear stress transfer function is adopted. The hybrid method accounts for the coupling effect between the hydrodynamic damping and the structural motion. Significantly reducing the computational cost, this method provides results as accurate as that from a time domain analysis based on the relative velocity model with a constant drag coefficient. Furthermore, recommendations for further simplification of the fatigue analysis recognizing the coupling effect are given.

Boundary reaction method for nonlinear analysis of soil–structure interaction under earthquake loads

This paper presents a boundary reaction method (BRM) for nonlinear time domain analysis of soil–structure interaction (SSI) under incident seismic waves. The BRM is a hybrid frequency–time domain method, but it removes global iterations between frequency and time domain analyses commonly required in the hybrid approach, so that it operates as a two-step uncoupled method. Specifically, the nonlinear SSI system is represented as a simple summation of two substructures as follows: (I) wave scattering substructure subjected to incident seismic waves to calculate boundary reaction forces on the fixed interface boundary between a finite nonlinear structure-soil body and an unbounded linear domain; and (II) wave radiation substructure subjected to the boundary reaction forces in which the nonlinearities can be considered. The nonlinear responses in the structure–soil body can be obtained by solving the radiation problem in the time domain using a general-purpose nonlinear finite element code that can simulate absorbing boundary conditions, while the boundary reaction forces can be easily calculated by solving the linear scattering problem by means of a standard frequency domain SSI code. The BRM is verified by comparing the numerical results obtained by the proposed BRM and the conventional frequency-domain SSI analysis for an equivalent linear SSI system. Finally, the BRM is applied to the nonlinear time-domain seismic analysis of a base-isolated nuclear power plant structure supported by a layered soil medium. The numerical results showed that the proposed method is very effective for nonlinear time-domain SSI analyses of nonlinear structure-soil system subjected to earthquake loadings.

Steady-State Response of a Piping System Under Harmonic Excitations Considering Pipe-Support Friction With Variable Normal Loads

Dynamic loads in piping systems are mainly caused by transient phenomena generated by operating conditions or installed equipment. In most cases, these dynamic loads may be modeled as harmonic excitations, e.g., pulsating flow. On the other hand, when designing piping systems under dynamic loads, it is a common practice to neglect strong nonlinearities such as shocks and friction between pipe and support surfaces, mainly because of the excessive cost in terms of computational time and the complexity associated with the integration of the nonlinear equations of motion. However, disregarding these nonlinearities for some systems may result in overestimated dynamic amplitudes leading to incorrect analysis and designs. This paper presents a numerical approach to calculate the steady-state response amplitudes of a piping system subjected to harmonic excitations and considering dry friction between the pipe and the support surfaces, without performing a numerical integration. The proposed approach permits the analysis of three dimensional piping systems, where the normal forces may vary in time and is based in the hybrid frequency–time domain method (HFT). Results of the proposed approach are compared and discussed with those of a full integration scheme, confirming that HFT is a valid and computationally feasible option.

A novel hybrid frequency-time domain method for the fatigue damage assessment of offshore structures

The cumulative fatigue damage analysis plays a key role during offshore structural design. Although many methods have been developed, there is not yet a method that can predict fatigue life effectively and efficiently. A hybrid frequency-time domain method, which can be considered to be a hybrid of the spectral method and the time-domain analysis method, is proposed in this paper. In the newly developed method, the spectral density function of structural stress is first obtained in the frequency domain and then converted into a stress time history by using an improved signal conversion approach. With this methodology, the fatigue damage of structures can be assessed easily with the rain-flow counting method and Palmgren–Miner rule. In contrast with the traditional fatigue damage assessment methods, the Rayleigh distribution assumption of the stress range, which is associated with narrow band random process and is commonly used in the spectral method, is not required for the hybrid frequency-time domain method. At the same time, the newly developed damage assessment method can avoid the complicated coupled dynamic analysis used in the time domain method, greatly reducing computation time. To verify the effectiveness of the present method, a case study for a monopile platform was conducted. Numerical results illustrate that the fatigue life assessed by the new method is more accurate than that by the spectral method, and the new method takes much less computational time than the time-domain method.