Modified transfer matrix method for steady-state forced vibration: a system of beam elements*

Abstract

The EST (Elements by a System of Transfer equations) method offers exact solutions for various vibration problems of trusses, beams and frames. The method can be regarded as an improved or modified transfer matrix method where the roundoff errors generated by multiplying transfer arrays are avoided. It is assumed that in a steady state a beam will vibrate with the circular frequency of an excitation force. The universal equation of elastic displacement (4th order differential equation) is described as a system of first order differential equations in matrix form. For the differential equations, the compatibility conditions of a beam element displacements at joint serve as essential boundary conditions. As the natural boundary conditions at joints, the equilibrium equations of elastic forces of beam elements are considered. At the supports, restrictions to displacements (support conditions) have been applied. For steady-state forced vibration, the phenomena of dynamic vibration absorption near the saddle points are observed, and the response curves for displacement amplitude and elastic energy are calculated. * A sequel to "Modified transfer matrix method for steady-state forced vibration: a system of bar elements [1]

Keywords

• steady-state forced vibrations
• frequency response curves
• dynamic vibration absorption
• forcing functions
• transfer equations
• essential dynamic boundary conditions at joints
• natural boundary conditions at joints
• dynamic support conditions.