Dynamical Behavior of Viscoelastic Cylindrical Shells Under Axial Pressures

The hypotheses of the Kármán-Donnell theory of thin shells with large deflections and the Boltzmann laws for isotropic linear, viscoelastic materials, the constitutive equations of shallow shells ae first derived. Then the governing equations for the deflection and stress function are formulated by using the procedure similar to establishing the Kármán equations of elastic thin plates. Introducing proper assumptions, an approximate theory for viscoelastic cylindrical shells under axial pressures can be obtained. Finally, the dynamical behavior is studied in detail by using several numerical methods. Dynamical properties, such as, hyperchaos, chaos, strange attractor, limit cycle etc., are discovered. Paper from CHENG Chang-jun, Member of Editorial Committee, AMM Foundation item: the National Natural Science Foundation of China (19772027); the Development Foundation of Shanghai Municipal Commission of Education (99A01); the Science Foundation of Shanghai Municipal Commission of Science and Technology (98JC14032); the Postdoctoral Science Foundation of Shanghai (1999 year) Biography: CHENG Chang-jun (1937-), Professor, Doctor Director