Solution of the Love problem with nonclassic boundary conditions (Q5950864)

An elastic half-space with density \(\rho_2\) and shear modulus \(\mu_2\) contacts with an elastic layer \( -a\leq x\leq 0 \) with density \(\rho_1\) and elasticity modulus \(\mu_1\). It is assumed that the shear wave velocities \( v_1\equiv\sqrt{\mu_1/\rho_1} \) and \( v_2\equiv \sqrt{\mu_2/\rho_2} \) satisfy the condition \( v_1<v_2\). The author studies the propagation along \(z\) axis of stationary harmonic waves \(u_y = f(x)\sin(\omega(\frac{z}{p} - t))\), \(u_x = u_z = 0\) where \(f(x)\) is amplitude function, \(\omega\) is angular frequency, and \(p\) is phase velocity.