Fig. 1

Three porosity types and two temperature profiles of metal foam beams (UTD is for the uniform temperature distribution, and LTD is for the linear temperature distribution)[38]"

Table 1

TD coefficients for stainless-steel material (SUS304)[42, 46-47]"

Fig. 2

Young's moduli and mass densities of SUS304 beams (e0=0.4) with various porosity distribution (color online)"

Fig. 3

Geometry of metal foam beams"

Table 2

Approximate functions of metal foam beams[38]"

Table 3

Convergence studies for the UPD beams (UTD, L/h=20, and e0=0.4"

Table 4

Convergence of different approximate functions"

Table 5

Dimensionless fundamental frequency for the TID solution of beams (L/h=10) under the UTD type"

Table 6

Dimensionless fundamental frequency for the TD solution of Al2O3/SUS304 FG beams (L/h=20) under the UTD type"

Table 7

Critical buckling temperature (ΔTcr) for the TID solution of simply-supported porous Si3N4/SUS304 FG beams (L/h=20) under the LTD type"

Table 8

Dimensionless critical buckling temperature for the TD solution of Si3N4/SUS304 FG beams (L/h=20) under the UTD type"

Table 9

Dimensionless critical buckling temperature of beams (e0=0.4)"

Fig. 4

Dimensionless critical buckling temperatures for the TD and TID solutions of HH, CH, and CC beams (UTD, SPD, and e0=0.4) (color online)"

Fig. 5

Dimensionless critical buckling temperatures (λ1=400α300ΔTcr) for the TD and TID solutions of HH, CH, and CC beams (UTD, SPD, and e0=0.4) (color online)"

Fig. 6

Dimensionless critical buckling temperatures for the TD solution of HH beam (ASP and e0=0.4) under UTD and LTD types (color online)"

Fig. 7

Dimensionless critical buckling temperatures for the TD solution of UPD, SPD, and APD beams (CH, LTD, and L/h=10) with respect to porosity ratio (color online)"

Fig. 8

Dimensionless fundamental frequencies for the TD solution of HH, CH, and CC beams (SPD, LTD, L/h=10, and e0=0.4) with respect to temperature (color online)"

Table 10

Dimensionless fundamental frequency of metal foam beams (e0=0.4, L/h=10) under the UTD and LTD types"

Fig. 9

Dimensionless fundamental frequencies for the TD solution of CC beams (SPD, UTD, e0=0.4) with various slenderness ratios with respect to temperature (color online)"

Fig. 10

Dimensionless fundamental frequencies for the TD solution of HH beams (UPD, L/h=10, e0=0.4) under the UTD and LTD types with respect to temperature (color online)"

Table 11

Dimensionless fundamental frequency for the TD solution of beams (L/h=10)"

Fig. 11

Dimensionless fundamental frequencies for the TD solution of UPD, SPD, and APD beams (HH, LTD, and L/h=10) with respect to porosity ratio (color online)"