Galerkin法求解弹性边界条件下圆板的流-固耦合振动特性
|
摘要
用干圆板振型作为基函数将圆板位移展开为级数形式,采用速度势函数描述流体运动,研究了弹性边界条件下圆板的流-固耦合振动特性。根据圆板的平衡微分方程和流-固耦合界面的速度连续条件,结合Galerkin法和Fourier-Bessel级数展开法,建立了系统的控制方程。求解了流体中圆板的固有振动特性,并将计算结果与数值仿真结果进行对比,验证了方法的正确性。通过改变弹簧刚度,分析了几种常见边界条件下圆板的振动特性,结果表明,自由和导向边界圆板的振型受流体的影响较小。研究了流体深度对圆板振动特性的影响,结果表明,当深度大于1.5倍圆板半径时,流体深度的改变对于圆板自由振动的影响可以忽略。
The fluid-structure coupled vibration of a circular plate under elastic boundary conditions was studied. The deflection of the plate was expanded into a series with its dry modal shapes taken as base functions and the motion of fluid was described with a velocity potential function. According to the equilibrium differential equation of the plate and the velocity continuous conditions on the fluid-structure coupled interface, Galerkin method and Fourier-Bessel series expansion one were used to establish the governing dynamic equation of the system. The natural vibration characteristics of the circular plate in contact with fluid were solved. The calculation results were compared with those of numerical simulation to verify the correctness of the proposed methods. Through changing spring stiffness, the vibration characteristics of the circular plates under several common boundary conditions were analyzed. The results showed that fluid has little influences on modal shapes of the circular plate under free and guided boundary conditions. The influences of fluid depth on the vibration characteristics of the circular plate were also studied. The results showed that when fluid depth is larger than 1.5 times of the plate's radius, influences of fluid depth on free vibration of the circular plate can be ignored.
The fluid-structure coupled vibration of a circular plate under elastic boundary conditions was studied. The deflection of the plate was expanded into a series with its dry modal shapes taken as base functions and the motion of fluid was described with a velocity potential function. According to the equilibrium differential equation of the plate and the velocity continuous conditions on the fluid-structure coupled interface, Galerkin method and Fourier-Bessel series expansion one were used to establish the governing dynamic equation of the system. The natural vibration characteristics of the circular plate in contact with fluid were solved. The calculation results were compared with those of numerical simulation to verify the correctness of the proposed methods. Through changing spring stiffness, the vibration characteristics of the circular plates under several common boundary conditions were analyzed. The results showed that fluid has little influences on modal shapes of the circular plate under free and guided boundary conditions. The influences of fluid depth on the vibration characteristics of the circular plate were also studied. The results showed that when fluid depth is larger than 1.5 times of the plate's radius, influences of fluid depth on free vibration of the circular plate can be ignored.
引文
[1]KWAK M K.Vibration of circular plates in contact with water[J].Journal of Applied Mechanics,1991,58(2):480-483.
[2]KWAK M K.Hydroelastic vibration of circular plates[J].Journal of Sound and Vibration,1997,201(3):293-303.
[3]KWAK M K,HAN S B.Effect of fluid depth on the hydroelastic vibration of free-edge circular plate[J].Journal of Sound and Vibration,2000,230(1):171-185.
[4]AMABILI M,KWAK M K.Free vibrations of circular plates coupled with fluids:revising the lamb problem[J].Journal of Fluids and Structures,1996,10(7):743-761.
[5]BAUER H F.Coupled frequencies of a fluid in a circular cylindrical container with elastic fluid surface cover[J].Journal of Sound and Vibration,1995,180(5):689-704.
[6]BAUER H F,CHIBA M.Hydroelastic viscous oscillations in a circular cylindrical container with an elastic cover[J].Journal of Fluids and Structures,2000,14(6):917-936.
[7]AMABILI M.Vibrations of circular plates resting on a sloshing fluid:solution of the fully coupled problem[J].Journal of sound and vibration,2001,245(2):261-283.
[8]YOUSEFZADEH S,JAFARI A A,MOHAMMADZADEH A.Effect of hydrostatic pressure on vibrating functionally graded circular plate coupled with bounded fluid[J].Applied Mathematical Modelling,2017,doi:10.1016/j.apm.2017.11.009
[9]CHEUNG Y K,ZHOU D.Hydroelastic vibration of a circular container bottom plate using the Galerkin method[J].Journal of Fluids and Structures,2002,16(4):561-580.
[10]JEONG K H,KIM K J.Hydroelastic vibration of a circular plate submerged in a bounded compressible fluid[J].Journal of Sound and Vibration,2005,283(1):153-172.
[11]ASKARI E,JEONG K H,AMABILI M.Hydroelastic vibration of circular plates immersed in a liquid-filled container with free surface[J].Journal of Sound and Vibration,2013,332(12):3064-3085.
[12]EFTEKHARI S A.Pressure-based and potential-based differential quadrature procedures for free vibration of circular plates in contact with fluid[J].Latin American Journal of Solids and Structures,2016,13(4):610-631.
[13]TARIVERDILO S,SHAHMARDANI M,MIRZAPOUR J,et al.Asymmetric free vibration of circular plate in contact with incompressible fluid[J].Applied Mathematical Modelling,2013,37(1):228-239.
[14]JEONG K H.Free vibration of two identical circular plates coupled with bounded fluid[J].Journal of Sound and Vibration,2003,260(4):653-670.
[15]曹志远.板壳振动理论[M].北京:中国铁道出版社,1989.
[16]张渭滨.数学物理方程[M].北京:清华大学出版社,2007.
[2]KWAK M K.Hydroelastic vibration of circular plates[J].Journal of Sound and Vibration,1997,201(3):293-303.
[3]KWAK M K,HAN S B.Effect of fluid depth on the hydroelastic vibration of free-edge circular plate[J].Journal of Sound and Vibration,2000,230(1):171-185.
[4]AMABILI M,KWAK M K.Free vibrations of circular plates coupled with fluids:revising the lamb problem[J].Journal of Fluids and Structures,1996,10(7):743-761.
[5]BAUER H F.Coupled frequencies of a fluid in a circular cylindrical container with elastic fluid surface cover[J].Journal of Sound and Vibration,1995,180(5):689-704.
[6]BAUER H F,CHIBA M.Hydroelastic viscous oscillations in a circular cylindrical container with an elastic cover[J].Journal of Fluids and Structures,2000,14(6):917-936.
[7]AMABILI M.Vibrations of circular plates resting on a sloshing fluid:solution of the fully coupled problem[J].Journal of sound and vibration,2001,245(2):261-283.
[8]YOUSEFZADEH S,JAFARI A A,MOHAMMADZADEH A.Effect of hydrostatic pressure on vibrating functionally graded circular plate coupled with bounded fluid[J].Applied Mathematical Modelling,2017,doi:10.1016/j.apm.2017.11.009
[9]CHEUNG Y K,ZHOU D.Hydroelastic vibration of a circular container bottom plate using the Galerkin method[J].Journal of Fluids and Structures,2002,16(4):561-580.
[10]JEONG K H,KIM K J.Hydroelastic vibration of a circular plate submerged in a bounded compressible fluid[J].Journal of Sound and Vibration,2005,283(1):153-172.
[11]ASKARI E,JEONG K H,AMABILI M.Hydroelastic vibration of circular plates immersed in a liquid-filled container with free surface[J].Journal of Sound and Vibration,2013,332(12):3064-3085.
[12]EFTEKHARI S A.Pressure-based and potential-based differential quadrature procedures for free vibration of circular plates in contact with fluid[J].Latin American Journal of Solids and Structures,2016,13(4):610-631.
[13]TARIVERDILO S,SHAHMARDANI M,MIRZAPOUR J,et al.Asymmetric free vibration of circular plate in contact with incompressible fluid[J].Applied Mathematical Modelling,2013,37(1):228-239.
[14]JEONG K H.Free vibration of two identical circular plates coupled with bounded fluid[J].Journal of Sound and Vibration,2003,260(4):653-670.
[15]曹志远.板壳振动理论[M].北京:中国铁道出版社,1989.
[16]张渭滨.数学物理方程[M].北京:清华大学出版社,2007.