| Budget Amount *help |
¥2,100,000 (Direct Cost: ¥2,100,000)
Fiscal Year 1987: ¥700,000 (Direct Cost: ¥700,000)
Fiscal Year 1986: ¥1,400,000 (Direct Cost: ¥1,400,000)
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| Research Abstract |
The purpose of out studies is to inverstigate the dynamic stability problems of nonlinear elastic systems under quasi-static nonconservative external forces from new points of view, such as sttrange attractor, poincare map or Lyapunov exponents. 1.The stability problem of ziegler-Herrmann model has been examined as the lineraized eigenvbalue problem up to the present. In Ref.1, nonlinear Ziegler-Herrmann model is studied as simple idealized model in dynamics, and it is shown that both limit cycle and chaotic vibrations may occur in the flutter region of the linearized analysis by the study of phase plane trajectories, Poinacare maps, Lyapunov exponents and power spectrun. 2.The existence of limit cycly vibrations arround nontrivial equilibrium points of nonlinear Reut model is shown in Refs.2 and 3. 3.An example of chaos in autonomous mechanical systems is known as socalled panel flutter of Dowell's elastic plate. Chaotic vibrations of Dowell's plate may occur only in the case with both compressive load and a fluid flow. In contrast with Dowell's plate, it is shown in Ref.3 that chaotic vibrations may occur in slightly curved plates, namely shallow circuler shell segments, for no compressive load, but with a fluid flow of sufficiently large velocity. 4.A consistent theory for the stability analysis of thin elastic shells is proposed in Ref.4, and some applications of the nonlinear shell theory are shown in Refs.5 and 6. For example, the nonlinear shell theory is applied to the nonconservative stability problem of spherical shells with movable adges and to circular cylindrical shells subjected to tangential forrlower forces, and it is shown that loss of stability can take place in the form of dynamic instability.
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