Analytical solutions for the coupled thermoelastic vibrations of the cracked Euler-Bernoulli beams by means of Green's functions

The temperature coupling effects W1d (X; X0, Z0) and displacement coupling effects T1d(X, Z; X0, Z0) of the cracked simply supported Euler-Bernoulli beams for different excitation frequencies Ω=0.9 Ω0 (a), Ω=3.6 Ω0 (b) and Ω=7.2 Ω0 (c). Date are for β=0.1, ζ=0, (hr, Lc)=(0.4,0.4) and (X0, Z0)=(0.5,0.5).221