# Investigation on Ship Hydroelastic Vibrational Responses in Waves
## 1 Introduction  
Structural evaluation of marine vessels during their design stage relies on accurate prediction of hydrodynamic loading and subsequent wave-structure interactions. For the cases where the elastic deformation of the structure plays a negligible role in determining the hydrodynamic forces, the structural analysis can be performed separately from the hydrodynamic analysis. However, large vessels with pronounced bow flare are susceptible to frequent and severe wave impact, subjecting them to subsequent significant transient hull vibrations, called _whipping_, which inevitably interferes with the surrounding fluid field and violates the basic assumption of the conventional decoupled method mentioned above. Hydroelasticity theory sufficiently considers the effects of structural vibrational responses on the hydrodynamic forces, and therefore, provides a framework in which structural and hydrodynamic analyses are fully coupled. Research on robust and efficient numerical methods for evaluation of ship wave loads and structural responses is still in progress. [PERSON] and [PERSON] [1] first introduced the methodology of hydroelasticity into ship engineering, paving the way for the following fruitful development. Early research efforts mainly focused on 2D theories in which 2D strip theories, linear or nonlinear, are adopted to analyze the hydrodynamics, while the elastic responses of the ship are represented by the modal superposition method [2; 3; 4]. With the advent and popularization of high-performance computers, 3D hydroelastic analysis gradually captured the attention of the marine community, especially for the cases where the assumptions of the strip method are not appropriately satisfied [5; 6]. The fluid flow is modeled by the 3D potential flow theory, and the ship structure is considered using a 1D or 3D finite element (FE) model [7; 8; 9]. Recently, Computational Fluid Dynamics (CFD) simulation of fluid flow has been incorporated into the methodology of hydroelasticity [10; 11], but the immense amount of time required at present hinders the development of this process, and makes it impractical for use in practical engineering applications. Together with the development of a theoretical approach is the experimental investigation. Small scale ship model tests in towing tanks have been widely conducted to study hydroelastic responses, such as vertical motions and bending moments, with the experimental conditions ranging from moderate seas to high seas [12; 13; 14]. Besides those small scale model tests, large scale model tests and even the full-scale ship tests have been conducted to further enhance the understanding of fluid-structure interaction mechanisms [15; 16; 17; 18]. A benchmark study on the performance of seventeen hydroelastic analysis codes applied to a target containership was carried out [19]. The hydroelastic model experiment of the target containership was conducted to further test each seakeeping code. Comprehensive comparisons showed that the participating codes gave scattered results for severe sea conditions, indicating the need for further theoretical research and subsequent verification by experiments. [PERSON] and [PERSON] [20] experimentally investigated the characteristics of vertical bending moments (\(M_{BV}\)) for different hulls in extreme seas. The analysis showed that large bow flares significantly affect the \(M_{BV}\)s.  
The understanding and simulation of nonlinearities associated with hydroelastic vibrational responses of large vessels in high seas are the central task for the ship engineering community. The fierce fluid structure interaction is characterized by strongly nonlinear slamming, wave breaking, large amplitude ship motion, etc., posing great technical difficulties on the theoretical prediction of ship responses. More often than not, severe seas have highly-irregular wave conditions which make the characteristics of ship hydroelasticity very different from those in regular waves.