International Scholarly Research Notices

Research Article

Thermal Buckling of Piezoelectric Composite Beam

Table 3

Boundary conditions and minimum value of 𝜇 for various edge supports. ( 𝐶 indicates clamped, 𝑆 shows simply supported, and 𝑅 is used for roller edge).
B.C. B.Cs at 𝑥 = 0 B.Cs at 𝑥 = 𝐿 𝜇 𝑚 𝑖 𝑛 × 𝐿
𝑆 - 𝑆 𝑢 1 = 𝑤 1 = 𝑀 𝑥 1 = 0 𝑢 1 = 𝑤 1 = 𝑀 𝑥 1 = 0 𝜋
𝐶 - 𝐶 𝑢 1 = 𝑤 1 = 𝜙 1 = 0 𝑢 1 = 𝑤 1 = 𝜙 1 = 0 2 𝜋
𝐶 - 𝑆 𝑢 1 = 𝑤 1 = 𝜙 1 = 0 𝑢 1 = 𝑤 1 = 𝑀 𝑥 1 = 0 4.49341
𝐶 - 𝑅 𝑢 1 = 𝑤 1 = 𝜙 1 = 0 𝑢 1 = 𝑑 𝑤 1 = 𝑑 𝑥 𝑑 𝑀 𝑥 1 𝑑 𝑥 + 𝑁 𝑥 0 𝑑 𝑤 1 𝑑 𝑥 = 0 𝜋
𝑆 - 𝑅 𝑢 1 = 𝑤 1 = 𝑀 𝑥 1 = 0 𝑢 1 = 𝑑 𝑤 1 = 𝑑 𝑥 𝑑 𝑀 𝑥 1 𝑑 𝑥 + 𝑁 𝑥 0 𝑑 𝑤 1 𝑑 𝑥 = 0 𝜋 2