微极热弹性无限板的轴对称自由振动

R·库玛; G·帕塔泊

微极热弹性无限板的轴对称自由振动

1.
库卢谢特拉大学数学系,哈里亚纳邦库卢谢特拉 136119,印度;2.Dr.B.R.恩伯德卡国立技术学院应用数学系,旁遮普贾郎达尔,印度

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出版历程
- 收稿日期: 2006-03-07
- 修回日期: 2007-01-12
- 刊出日期: 2007-03-15

Axisymmetric Free Vibrations of an Infinite Micropolar Thermoelastic Plate

1.
Department of Mathematics, Kurukshetra University, Kurukshetra 136119, Haryana, India;

摘要

摘要: 研究了在应力自由和刚性固定边界条件下，无能量耗散的均匀、各向同性微极热弹性无限板的轴对称自由振动波的传播，导出了相应的对称和斜对称模态波传播的闭合式特征方程和不同区域的特征方程．对短波的情况，应力自由热绝缘和等温板中对称和斜对称模态波传播的特征方程退化为Rayleigh表面波频率方程．根据导出的特征方程得到了热弹性、微极弹性和弹性板的结果．在对称和斜对称运动中计算了板的位移分量幅值、微转动幅值和温度分布，给出了对称和斜对称模式的频散曲线，并示出了位移分量和微转动幅值和温度分布的曲线．能够发现理论分析和数值结论是非常一致的．
- 微极热弹性板 /
- 无能量耗散的热弹性理论 /
- 环形波 /
- 对称和斜对称振幅
Abstract: The propagation of axisymmetric free vibrations in an infinite homogeneous isotropic micropolar thermoelastic plate without energy dissipation subjected to stress free and rigidly fixed boundary conditions is investigated.The secular equations for homogeneous isotropic micropolar thermoe-lastic plate without energy dissipation in closed form for symmetric and skewsymmetric wave modes of propagation were derived.The different regions of secular equations were obtained.At short wave-length limits,the secular equations for symmetric and skew symmetric modes of wave propagation in a stress free insulated and isothermal plate reduce to Rayleigh surface wave frequency equation.The results for thermoelastic,micropolar elastic and elastic materials were obtained as particular cases from the derived secular equations.The amplitudes of displacement components,microrotation and temperature distribution were also computed during the symmetric and skew symmetric motion of the plate.The dispersion curves for symmetric and skew symmetric modes and amplitudes of displacement components,microrotation and temperature distribution in case of fundamental symmetric and skew symmetric modes were presented graphically.The analytical and numerical results are found to be in close agreement.
- micropolar thermoelastic plate /
- thermoelasticity without energy dissipation /
- circular crested waves /
- symmetric and skew symmetric amplitudes

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参考文献(20)

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