Green’s Function for Bending–Torsion Coupled Composite Beams

The main objective of the present paper is to solve the vibration problem of bending–torsion coupled composite cantilever beams. In order to find a solution for this problem, we determine the Green’s function of the relevant equilibrium problem. Knowing the Green’s function, the solution of the equilibrium problem can be written in a closed integral form, where the integrand is the product of the Green’s function and the load. If the load is the inertial force system, think of our vibration problem; a homogeneous Fredholm-type integral equation is obtained for determining the natural frequencies and the shape modes—the Green’s function is the kernel. By reducing the homogeneous Fredholm-type integral equation to an algebraic eigenvalue problem, it is possible to solve the eigenvalue problem numerically. Comparing the numerical results obtained with other numerical solutions reflects the efficiency of the method.