Thermoelastically Coupled Axisymmetric Nonlinear Vibration of Shallow Spherical and Conical Shells
-
摘要: 假设温度场与应变场相互耦合，研究了旋转扁薄球壳和锥壳的轴对称非线性热弹振动问题．基于von Krmn理论和热弹性理论，导出了本问题的全部控制方程及其简化形式．应用Galerkin技术进行时空变量分离后，得到了一个关于时间的非线性常微分方程组．根据方程的特点，分别用多尺度法和正则摄动法求得了壳体振动的频率与振幅间特征关系和振幅衰减规律的一次近似解析解，并讨论了壳体几何参数、热弹耦合参数以及边界条件等因素对其非线性热弹耦合振动特性的影响．Abstract: The problem of axisymmetric nonlinear vibration for shallow thin spherical and conical shells when temperature and strain fields are coupled is studied Based on the la be deflection theories of von-kûrnûn and the theory of thermoelasticity,the whole governing equations and their simplified type are derived The time-spatial variables xe separated by Galerlari's technique,thus reducing the governing equations to a system of time-dependent nonlinear ordinary differential equation.By means of regular perturbation method and multiple-scales method,the first order approximate analytical solution for chxacterislic relation of frequency vs amplitude pararreters along with the decay rate of ampfitude are obtained,and the effects of different geomdric parameters and coupling factors as well as boundary conditions on thermoelaslically coupled nonlinear vibration behaviors are discussed.
-
[1] Varadan T K, Pandalai K A V. Nonlinear flexural oscillation of orthotropic shallow spherical shells[J].Computers and Structures,1978,9(5):417—425. doi: 10.1016/0045-7949(78)90128-1 [2] 王永岗，王新志，宋慧芳.静载荷作用下正交各向异性旋转扁壳的非线性自由振动[J].应用数学和力学，1997,18(6):545—550. [3] Boley B A, Barber A D. Dynamic response of beams and plates to rapid heating[J].Journal of Applied Mechanics,1957,24(5):413—425. [4] Nowacki W.Dynamic Problems of Thermoelasticity[M].Leyden, The Netherlands: Sijthoff & Noordhoff International Publishers,1975，123—262. [5] Chang W P, Wan S M. Thermomechanically coupled nonlinear vibration of plates[J].International Journal of Nonlinear Mechanics,1986,21(5):375—389. doi: 10.1016/0020-7462(86)90021-1 [6] Trajkovski D, Bitola T F, Lola I R,et al.A coupled problem of thermoelastic vibrations of a circular plate with exact boundary conditions[J].Mechanics Research Communications,1999,26(2):217—224. doi: 10.1016/S0093-6413(99)00016-6 [7] Praveen G N, Reddy J N. Nonlinear transient thermoelastic analysis functionally graded ceramic-metal plates[J].International Journal of Solids and Structures,1998,35(33):4457—4476. doi: 10.1016/S0020-7683(97)00253-9 [8] Tauchert T R. Thermally induced flexure, buckling and vibration of plates[J].Applied Mechanics Reviews,1991,48(8):347—359. [9] Khdier A A, Ragab M D, Reddy J N. Thermal effects on the response of cross-ply laminated shallow shells[J].International Journal of Solids and Structures,1992,29(5):653—667. doi: 10.1016/0020-7683(92)90059-3 [10] 钱伟长.变分法及有限元[M].北京：科学出版社,1980,535—565. -
计量
- 文章访问数: 2883
- HTML全文浏览量: 146
- PDF下载量: 586
- 被引次数: 0
下载:
渝公网安备50010802005915号