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Behavior of bifurcation and chaos in a forced oscillator
$$\bar x_1 + \bar \delta \dot x_1 + \omega _0^2 x_1 - \bar \beta x_1^2 = \bar f\cos \omega \tau$$
containing a square nonlinear term is investigated by using Mel'nikov method and digital computer simulations.
In this paper, the generalized variational principle of dynamic analysis for the blast-resistant underground structures is established, and the corresponding generalized functionals of elastoplastic analysis for underground structures is derived, and the generalized variational principle of...
This paper discusses the generalized variational principles founded by the technique of Lagrangian multipliers in structural mechanics and analyzes the nonlinear statically indeterminate structures. It is assumed that the stress-strain relationship of the materials of structures has the form...
The results in Ref.  are not suitable for the cases of α≥2. For this reason, we use the method in Ref.  to derive the general expressions of the anisotropic plastic stress fields at a stationary plane-stress crack-tip for both of the cases of α=2 and α>2. As an example, we give the...
The solution of the cylindrical detonation wave generated by the linear explosion was obtained by numerical method in ref. .
A new stress function is found in this paper and then the problems of cosine pressures on a hollow cylinder are solved with the new stress function, which provides the basis for the solution of the problems of space symmetrical deformation of a hollow cylinder. When the pressures do not vary in...
The explosion process is usually used for satellite releasing during fairing separation. Explosion products are not allowed to be leaked from the detonating tube connecting two parts of the fairing during the fairing separation process. This paper predicts the contamination of the explosion...
The singular behaviour in the vicinity of intersection between the body and free surface is presented. It is shown that in the linear regime the singularity of velocity potential for transient problem is in d2⪙nd. The singular behaviour for harmonic problem is the same as the result for the...
In this paper, some explicit criteria of absolute stability for the trivial solution of the real second canonical form of non-linear control system are given, which include and improve the criteria in paper . By applying these criteria to the well-known equation of the longitudinal motion of...
In this paper, we give some sufficient conditions of the instability for the fourth order linear differential equation with varied coefficient, at least one of the characteristic roots of which has positive real part, by means of Liapunov's second method.
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