**1. Introduction**

New energy development and utilization have become the main focus of all human beings with the consumption of traditional energy. As one kind of renewable and clean energy, wind energy is developing rapidly. With abundant energy reserves and the farmland-free characteristic, offshore wind energy source has better development prospect rather than onshore wind energy. Offshore wind turbine (OWT) developed rapidly in China. From 2014–2018, the installed offshore wind turbine in China increased average of 60.5% per year.

OWTs are mainly under wind load and wave load [1], sometimes even earthquake load [2]. The structure of OWT can be divided into two parts, the tower above the seawater and the foundation partially submerged in the seawater, and partially embedded in the soil. The tower is under wind load, whereas the foundation is under wave load and soil reaction [3]. OWT is a slender structure, which means its dynamic response will be significantly influenced by the load frequency. In OWT design, it is needed to calculate the OWT structure natural frequency to prevent it falls within the frequency ranges of main loads [4]. As shown in Figure 1, the peak frequency of the wind load is usually within 0.01 Hz. The peak frequency of the wave load is 0.08 Hz~0.2 Hz. Definitions of 1P frequency and 3P frequency are presented below:


**Citation:** Shi, Y.; Yao, W.; Yu, G. Dynamic Analysis on Pile Group Supported Offshore Wind Turbine under Wind and Wave Load. *J. Mar. Sci. Eng.* **2022**, *10*, 1024. https:// doi.org/10.3390/jmse10081024

Academic Editors: Eugen Rusu, Kostas Belibassakis and George Lavidas

Received: 6 July 2022 Accepted: 23 July 2022 Published: 26 July 2022

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**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

load. Most OWTs are three-blade structures, and the model used in this paper is the same, so it is a 3P frequency.

**Figure 1.** Frequency spectrum of the dynamic loads [4].

As shown in Figure 1, in OWT design, three different design methods are considered, which are "soft-soft", "soft-stiff", and "stiff-stiff" methods. Most installed OWTs adopted "soft-stiff" design method. Therefore, it is needed to analyze the dynamic response of OWT under different frequencies.

Previous research mainly focused on the study of monopile-supported OWTs. The numerical method is used to analyze the overall dynamic structure response, including the finite element method [8] (FEM) and boundary element method (BEM). Kjørlaug [9] used SAP2000 to analyze the acceleration and structure natural frequency of OWT under lateral and vertical earthquake loads. Corciulo [10] used the OpenSees simulation platform to investigate the dynamic response of OWT under wind and wave load. Zuo [11] used ABAQUS to establish the model of OWT including blades and analyzed the dynamic response of OWT under operating and steady conditions. Galvin [12] used the FEM-BEM method and analyzed the dynamic response of OWT under earthquake load.

Another analysis method is the analytical method. The OWT structure can be divided into the superstructure and the foundation to investigate its dynamic response [13]. As for the foundation, the P-y curve method is used in early research [14,15]. This method is still widely used [6,16]. Andersen [17] simplified the pile–soil interaction as the equivalent coupled spring model and obtained the structure natural frequency. Adhikari and Bhattacharya [18,19] established the foundation model with elastic supports based on the Euler–Bernoulli beam, used horizontal and rotation springs to simulate the foundation reaction, and validated the result with the experimental result [20].

The foundation of OWT is partially embedded in the soil, and the dynamic equation of different pile parts is different. By using the transfer matrix method [21–23], the dynamic response of different pile parts can be connected. Wang [24] analyzed the onshore wind turbine structure natural frequency using the transfer matrix method. Huang [25] analyzed the dynamic response of the pile group supported OWT using the transfer matrix method.

This paper used the Morison equation to calculate the wave load applied to the pile, and calculates the pile–soil interaction using an improved Tajimi soil model [26,27]. By using the transfer matrix method, the dynamic response of the pile group embedded in the soil and submerged in the seawater are connected, and the overall pile group impedance is obtained. The stable forced vibration equation of the multiple-degree-offreedom OWT system is established by discretizing the tower into multiple segments. By substituting the pile group impedance into the equation, the dynamic response of OWT under different load frequencies is obtained. For the pile group, the pile–pile interaction factor is calculated, which considers the influence of the passive pile on the active pile. The calculated result is compared with the FEM result to validate the correctness of the proposed calculation method.
