Non-stationary vibrations of an orthotropic cylindrical shell with flowed liquid, which is located in a rigid cylinder, at harmonious finite perturbation of speed of the stream
Keywords:
an orthotropic cylindrical shell, ideal incompressible liquid, speed of a stream, amplitude, frequency and duration of perturbationsAbstract
Results of numerical and analytical studies of the transient oscillatory processes in an orthotropic cylindrical shell with ideal incompressible liquid flowing throw it in the longitudinal direction are presented. The shell is coaxially oriented inside the rigid cylinder. The space between the shell and the cylinder is filled with ideal incompressible liquid flowing with constant longitudinal speed U1 . Shell radial flexural oscillations are induced by speed perturbations of the internal liquid flow U (t). The perturbations, which represent deviations of speed value from a steady-state value U0 , have impact during the finite time period [t1, t2], when the speed value is described by equation U(t)=U0 + u Sin [l(t - t1). Duration of the perturbation period, the values U1 , U0 , and magnitudes of the amplitude u and harmonic perturbation frequency l are considered as known. Basing on equations of the classical theory of shells the technique which numerically defines evolutions of bending around maxima and minima of the radial flexures in any shell point under the transient process and determines a point, where flexures are maximum at the end of perturbing time, was developed and implemented. Proposed technique determines an absolute value of dimensionless Max |W| /h maximum flexures for the whole period of non-stationary oscillations as well. The functional dependences of magnitudes Max |W| /h on arguments u , l and duration of perturbations t2- t1are examined for the various fixed values of the parameters of internal and external flows. It was shown that the magnitudes of maximum flexures in the transient process can significantly exceed the values which observed during the steady oscillations under the certain values U1 , U0 , u , l and t 2-t 1. Such flexures can exceed constructive restrictions which are imposed in design of various pipelinesReferences
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