Stability Analysis of Multispan Pipeline Embedded in Temperature-Dependent Matrix

Table 2

The key point data of Figures 3 and 4.

Temperature variation	Natural frequency U = 0, (Hz)	Critical velocity (m/s)	Critical pressure (N/m^2)
ΔT = 0	1st order 55	1st order 252	1st order 5.1 × 10^7
	2nd order 81	2nd order 344	2nd order 9.3 × 10^7
	3rd order 201
ΔT = 10 K	1st order 48	1st order 220	1st order 3.85 × 10^7
	2nd order 76	2nd order 320	2nd order 8.15 × 10^7
	3rd order 195
ΔT = 20 K	1st order 30	1st order 180	1st order 2.6 × 10^7
	2nd order 70	2nd order 296	2nd order 6.95 × 10^7
	3rd order 190