正弦荷载作用下浮冰的稳态响应近似解析解
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摘要
为了解决浮冰在正弦荷载作用下的稳态响应问题,把浮冰视作黏弹性的浮板,利用汉克尔变换和拉普拉斯变换求解了浮冰在正弦荷载作用下的动力学方程,得到了其近似解析解以及数值计算结果.分析了正弦荷载频率对仿冰材料浮板稳态响应的影响,揭示了黏弹性浮冰的动力学现象.结果表明:当正弦荷载的频率为某一确定值时,浮冰的振动幅值会达到最大值,正弦荷载的频率对破冰效果影响较大.
The problem of the steady response of floating ice under sinusoidal loading was addressed.The dynamic equation of viscoelastic floating ice plate under sinusoidal loading was solved through the Hankel transformation and the Laplace transformation.Approximate analytical solutions and numerical calculation results of transient response of viscoelastic floating ice under sinusoidal loading were obtained.The influences of frequencies of sinusoidal loading on the displacement response of floating imitation-ice plate were discussed.Plenty of dynamic properties of viscoelastic floating ice plate were revealed.The results show that the frequency of sinusoidal loading is adjusted to a certain value,then the vibration amplitude of floating plate reaches the maximum value.The frequency of sinusoidal loading has greater effect on breaking ice.
The problem of the steady response of floating ice under sinusoidal loading was addressed.The dynamic equation of viscoelastic floating ice plate under sinusoidal loading was solved through the Hankel transformation and the Laplace transformation.Approximate analytical solutions and numerical calculation results of transient response of viscoelastic floating ice under sinusoidal loading were obtained.The influences of frequencies of sinusoidal loading on the displacement response of floating imitation-ice plate were discussed.Plenty of dynamic properties of viscoelastic floating ice plate were revealed.The results show that the frequency of sinusoidal loading is adjusted to a certain value,then the vibration amplitude of floating plate reaches the maximum value.The frequency of sinusoidal loading has greater effect on breaking ice.
引文
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[13]Pogorelova A V.Plane problem of the impact ofseveral shock pulses on a viscoelastic plate floatingon a fluid surface[J].Applied Mechanics and Tech-nical Physics,2010,51:155-163.
[14]Kozin V M,Chizhumov S D,Zemlyak V L.Influ-ence of ice conditions on the effectiveness of the res-onant method of breaking ice cover by submarines[J].Applied Mechanics and Technical Physics,2010,51:398-404.
[2]Lu D Q,Dai S Q.Flexural-and capillary-gravitywaves due to fundamental singularities in an inviscidfluid of finite depth[J].International Journal of Engi-neering Science,2008,46(3):1183-1193.
[3]陈克,姚俊,张辽远.动载状态下冰层振动分析及数值算法研究[J].沈阳理工大学学报,2010,29(2):1-3.
[4]蔡之瑞,孙柏涛,郭世荣,等.冰荷载的试验研究和计算方法[J].地震工程与工程振动,1997,17(4):49-56.
[5]史庆增,宋安.海冰荷载和冰激振动研究报告[R].天津:天津大学,2000.
[6]张丽敏,李志军,贾青,等.冰凌灾害研究的一个重要课题——冰荷载计算分析与研究[J].自然灾害学报,2009,18(2):191-194.
[7]Kozin V M,Milovanova A V.The wave resistance ofamphibian aircushion vehicles in broken ice[J].Applied Mechanics and Technical Physics,1996,37:634-637.
[8]Kozin V M,Pogorelova A V.Effect of broken ice onthe wave resistance of an amphibian air-cushion vehi-cle in nonstationary motion[J].Applied Mechanicsand Technical Physics,1999,40:1036-1041.
[9]Kozin V M,Pogorelova A V.Effect of a shock pulseon a floating ice sheet[J].Applied Mechanics andTechnical Physics,2004,45:794-798.
[10]Kozin V M,Pogorelova A V.Mathematical model-ing of shock loading of a solid ice cover[J].Interna-tional Journal of Offshore and Polar Engineering,2006(1):1-4.
[11]Zhestkaya V D,Kozin V M.Stress-deformed stateof a semi-infinite ice plate under the action of a mov-ing load[J].Applied Mechanics and Technical Phys-ics,1994,35:745-749.
[12]Zhestkaya V D,Kozin V M.Numerical solution ofthe problem of the effect of a shock pulse on an icesheet[J].Journal of Applied Mechanics and Techni-cal Physics,2008,49:285-290.
[13]Pogorelova A V.Plane problem of the impact ofseveral shock pulses on a viscoelastic plate floatingon a fluid surface[J].Applied Mechanics and Tech-nical Physics,2010,51:155-163.
[14]Kozin V M,Chizhumov S D,Zemlyak V L.Influ-ence of ice conditions on the effectiveness of the res-onant method of breaking ice cover by submarines[J].Applied Mechanics and Technical Physics,2010,51:398-404.
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