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completely unfavourable dynamic behaviour, but some improvement of the dynamic
properties could be achieved changing the supporting system design, performed by
modification of boundary conditions of the steam line structure.
The selected main mode shapes and the values of the natural frequencies of the
pipeline structure in a compression station, obtained in reanalysis are shown in Fig. 7.
The based excitation frequency produced by rotation of the compressor shaft is at the
level of 7.2 Hz. It is to take care of derived excitations which obtained by an integer
multiplier from the basic eigenvalue.
Figure 7: Sixth, seventh, sixteenth and seventeenth mode shapes of the intake structure of the
piping in compressor station and corresponding diagrams of increment difference distribution of
potential and kinetic energies (
ΔE
p
-
ΔE
k
)
5. CONCLUSIONS
Critical structures regarding dynamic behaviour in service should be reanalysed in
order to find out the best approach for properties improving. Studying the dynamic
behaviour of structures the responses introduced by changes in its shape, size or selected
elements materials can be predicted. The main goal of dynamic optimization is to
increase natural frequencies and to enlarge the difference between them. Especially, the
lowest frequencies are the most interesting and with the values close to frequency
excitation force in the system.
Presented approach is applicable for:
I
The elements with kinetics and potential energy, which values are negligible
comparing to other elements.
II
Elements with the kinetics energy greater than the potential energy.
III
Elements with the potential energy greater than kinetics.
IV
Elements with kinetics and potential energy, which values are not negligible
comparing to other elements.
Presented examples revealed the possibility to modify the system and improve its
behaviour after detailed structural reanalysis, considering the graphs of potential and
kinetic energy increment difference distribution and obtained modes shape, what could be
significant help in dynamic structures service.
REFERENCES
1.
Inamura, T., Eigenvalue Reanalysis by Improved Perturbations, International Journal of
Numerical Methods in Engineering, Vol. 26, No. 1, 1988, pp. 167-181
2.
Ki, I.K., Nonlinear Inverse Perturbation Method in Dynamic Redesign, PhD, Thesis, Michigan
University, USA, 1983.
3. Wang, B.P., and Pilkey, W.D., Eigenvalue Reanalysis of Locally Modified structures Using a
Generalized Rayleight’s Method, AIAA Journal, Vol. 24, No. 6, 1986, pp. 983-990