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The mode shapes are presented in graphs.
Natural frequencies and mode shapes are determined.
Vibration frequencies and mode shapes are computed.
The exact expressions for frequencies and mode shapes are obtained.
Free vibration frequencies and mode shapes are also found.
Natural frequencies, damping ratios, and pressure mode shapes are identified.
The mode shapes are visualized using computer graphics.
Exact expressions for natural frequencies and mode shapes are derived.
The mode shapes are expressed as infinite polynomial series.
Therefore, the higher thermal buckling mode shapes are formed.
The effects of temperature and mode shapes are examined.
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