Coupled axial-bending dynamic stiffness matrix and its applications for a Timoshenko beam with mass and elastic axes eccentricity

The dynamic stiffness matrix of a coupled axial-bending Timoshenko beam is developed to investigate the free vibration behaviour such beams and their assemblies. Applying Hamilton's principle, governing differential equations motion in derived by considering coupling effect arising from mass axis eccentricity with elastic cross-section. are then solved an exact sense, giving expressions for axial bending displacements as well rotation. force, shear force moment formed using natural boundary conditions which resulted Hamiltonian formulation. Next, frequency-dependent relating amplitudes corresponding displacement, displacement resulting effectively applied making use Wittrick-Williams algorithm solution technique. results emphasis on effects importance deformation rotatory inertia frameworks discussed significant conclusions drawn.