In this paper,we consider two Cauchy systems of coupled two wave equations in the whole line R under one or two frictional dampings,where the coupling terms are either of order one with respect to the time variable or...In this paper,we consider two Cauchy systems of coupled two wave equations in the whole line R under one or two frictional dampings,where the coupling terms are either of order one with respect to the time variable or of order two with respect to the space variable.We prove some L^(2)(R)-norm decay estimates of solutions and their higher-order derivatives with respect to the space variable,where the decay rates depend on the number of the present frictional dampings,the regularity of the initial data,and some connections between the speeds of wave propagation of the two wave equations.Both our systems are considered under weaker conditions on the coefficients than the ones considered in the literature and they include the case where only one frictional damping is present,so they generate new difficulties and represent new situations that have not been studied earlier.展开更多
针对海上浮式风机复杂的受荷环境,特别是持续、周期性的海浪作用带来的疲劳损伤隐患,对其在波浪耦合作用下的疲劳性能展开了研究,给出了一种浮式风机长期视角下的疲劳损伤评估方法。以Spar型海上浮式风机为对象,基于拉格朗日方程建立了...针对海上浮式风机复杂的受荷环境,特别是持续、周期性的海浪作用带来的疲劳损伤隐患,对其在波浪耦合作用下的疲劳性能展开了研究,给出了一种浮式风机长期视角下的疲劳损伤评估方法。以Spar型海上浮式风机为对象,基于拉格朗日方程建立了其8-DOF(dgree of freedom)的波浪耦合作用非线性模型,并验证了所建模型的准确性,随后在所建模型基础上根据所提方法对其疲劳性能进行了探讨。结果表明,浮式风机的疲劳损伤与波浪载荷特性关系很大,不同工况下表现出不同的损伤性能,由于海况条件的随机性,仅按传统方法对风机进行疲劳估计不足以准确了解其疲劳性能,还需进行长期视角下的疲劳分析。而且风机塔架根部疲劳损伤的峰值出现在塔架自振周期附近,而长期疲劳损伤的峰值则出现在海域高概率海况周期范围,因此应尽量使风机的自振周期避开其峰值周期,从而避免风机损伤的高位叠加,减小疲劳损伤。分析还表明了所提基于蒙特卡洛法的浮式风机长期疲劳计算方法的有效性,精度高且耗时少,提出的改进算法能使输出结果波动变小、稳定性增强,结果也更为精确。展开更多
文摘In this paper,we consider two Cauchy systems of coupled two wave equations in the whole line R under one or two frictional dampings,where the coupling terms are either of order one with respect to the time variable or of order two with respect to the space variable.We prove some L^(2)(R)-norm decay estimates of solutions and their higher-order derivatives with respect to the space variable,where the decay rates depend on the number of the present frictional dampings,the regularity of the initial data,and some connections between the speeds of wave propagation of the two wave equations.Both our systems are considered under weaker conditions on the coefficients than the ones considered in the literature and they include the case where only one frictional damping is present,so they generate new difficulties and represent new situations that have not been studied earlier.
文摘针对海上浮式风机复杂的受荷环境,特别是持续、周期性的海浪作用带来的疲劳损伤隐患,对其在波浪耦合作用下的疲劳性能展开了研究,给出了一种浮式风机长期视角下的疲劳损伤评估方法。以Spar型海上浮式风机为对象,基于拉格朗日方程建立了其8-DOF(dgree of freedom)的波浪耦合作用非线性模型,并验证了所建模型的准确性,随后在所建模型基础上根据所提方法对其疲劳性能进行了探讨。结果表明,浮式风机的疲劳损伤与波浪载荷特性关系很大,不同工况下表现出不同的损伤性能,由于海况条件的随机性,仅按传统方法对风机进行疲劳估计不足以准确了解其疲劳性能,还需进行长期视角下的疲劳分析。而且风机塔架根部疲劳损伤的峰值出现在塔架自振周期附近,而长期疲劳损伤的峰值则出现在海域高概率海况周期范围,因此应尽量使风机的自振周期避开其峰值周期,从而避免风机损伤的高位叠加,减小疲劳损伤。分析还表明了所提基于蒙特卡洛法的浮式风机长期疲劳计算方法的有效性,精度高且耗时少,提出的改进算法能使输出结果波动变小、稳定性增强,结果也更为精确。
