二阶波浪力可写为：
其中，
? 波频运动求解所用方程为
M(s) 结构质量矩阵 M(a) = 流体力学附加质量矩 C 线性阻尼矩阵K(s)系统总刚度F 作用于系统的总外力（每单位幅值的力） X =结构响应（或者RAO） 其中：
ω为波浪力的频率
等式可化简为：其中，
RAO的计算公式：
其中
AQWA-Librium
? AQWA－LIBRIUM：可以综合考虑外部环境载荷（风，浪，流）及浮体间通过铰
接或停泊线连接的产生的相互作用力，确定浮体的的平衡位置。同时在计算浮体任意位置的浮力时，它也考虑水线面以上的单元的影响。这些载荷，再加上浮体自重，最终确定了浮体的六个自由度方向上的平衡位置。包括停泊线的静/动稳定性分析。定义平衡位置，为AQWA, FER, DRIFT, NAUT输出平衡位置，初步的停泊设计。 可以输出结构平衡位置已经回覆力(矩)倾覆力（矩),特征值模态以及动态平衡分析，分析时候考虑风浪流联合作用。静平衡分析，浮体系统动态分析的基础。 ? AQWA-LIBRIUM 用于确定平衡位置，静稳定性和动稳定性，结构是以很小的步骤
移动直到力平衡，从而找到平衡位置，然后，程序计算线性化刚度矩阵的特征值，得到静稳定性，通过阻抗矩阵的特征值得到动稳定性，AQWA-LIBRIUM可以同时定义多个波谱，程序会按照设定顺序逐一计算，最后以表格的形式的输出结果文件 ? AQWA-LIBRIUM 用于确定浮体系统的静态平衡位置，计算锚链线张力和确定其在
该位置的静动态稳定性，程序有三大功能：
? 找到静态平衡位置，计算锚链力，评估静态稳定性特征 ? 给出静态平衡位置，评估初动稳定特征
? 给出静平衡位置，计算锚链力，评估静动态稳定性
? 平衡位置，稳性和动稳性计算特点：
? 复杂船舶/近海结构系统
? 支持各种各样缆索，防护装置，滑轮（pulley），绞车（winch）各种约束条
件设置 ? 风浪流联合下的平衡位置计算
? Database approach for static catenary mooring line;
? 缆索动力学的有限元方法（非刚体AQWA唯一一处采用有限元方法）计算
张力和变形 ? 迭代方法确定平衡位置
? 通过计算特征值线性刚度矩阵求得浮体稳性（static stability) ? 给初特征值阻抗矩阵确定浮体的动稳性
? AQWA LIBRIUM有用的选项：
? STAT 只计算稳性（static stability）只用于静稳定性分析 ? DYNA 只计算动稳性（dynamic stability）只用于动力稳定性分析 ? LSTF 线性刚度，直接调用AQWA-LINE计算得到的水静力刚度
? PBIS 每两个积分步输出一次数据 (每个step输出所有数据) 打印迭代步
REST - RESTART Option This option is used when the program is being restarted at any stage greater than the first (see Section 5.2). A restart card must follow the options list when the restart option is used. This card indicates the
stage at which the program is to continue and the stage at which the program is to stop (see AQWA Reference Manual). DATA - DATA Option This option is used to check the data input to the program, and is equivalent to performing the first two stages of the program analysis (see Sections 6.1 and 6.2). If the data is correct, then the program would be restarted at Stage 3 of the AQWA-LIBRIUM analysis by using the RESTART option.
? PRST - PRINT GLOBAL STIFFNESS MATRIX This option causes the
global stiffness matrix, which is computed in the equilibrium analysis (Stage 5), to be output. PPEL - PRINT PROPERTIES of Each Element on Each Structure This option allows the user to output complete details of each element used in the body modelling. All important details of the body elements are output together with the resultant properties of the bodies. It should only be used when running AQWA-LIBRIUM as an independent program.
? ALDB - READ AQWA-LINE DATABASE Read the hydrodynamics database
from the hydrodynamics (.HYD) file created by a previous AQWA-LINE run. This option is used: (i)
if the user wishes to modify the hydrodynamic data calculated in a previous AQWA-LINE run, without having to re-run the AQWA-LINE radiation/ diffraction analysis.
(ii) if the user is setting up an analysis with several structures, and wishes to pick up the hydrodynamic data for one or more structures, calculated in a previous AQWA-LINE run
(ii)
? RDDB - READ DATABASE Read the hydrodynamics database from the
restart (.RES) file created by a previous AQWA-LINE run. This option is used if the user wishes to modify the hydrodynamic data calculated in a previous AQWA-LINE run, without having to re-run the AQWA-LINE radiation/ diffraction analysis. Note: Normally, this would be done using the option ALDB (see above). The RDDB option is only needed if the hydrodynamics file from the previous AQWA-LINE run has been accidentally deleted. Note that, as the model definition has to be read from the restart file before the hydrodynamics can be read, there is no possibility to change the model definition, when using this option (use ALDB instead). ? PRDL - PRINT DATA LIST FROM RESTART FILE This option causes the
program to read the data contained within the restart backing file and output it to the user. Typically all body modelling information is output, together with environmental wave loading details. ? LSTF - LINEAR STIFFNESS This option is used to instruct the program to
use the linear stiffness matrix calculated by AQWA-LINE, instead of calculating the hydrostatics by integrating over the wetted surface. ? RNDD - Reynolds No Drag/C for Morison Elements (switched by SC1/
CARD) This option causes drag coefficients to be set to zero, i.e. switches off