Linear and nonlinear vibrations of inhomogeneous Euler-Bernoulli beam

Dynamic problems arising from the Euler-Bernoulli beam model with inhomogeneous elastic properties are considered. The method of Green\'s function and perturbation theory are employed to find the deflection in the beam correct to the first-order. Eigenvalue problems appearing from transverse vibrations of inhomogeneous beams in linear and nonlinear cases are also discussed.