Large amplitude forced vibrations of Timoshenko beams using coupled displacement field method

Abstract

Forced vibration behaviour of a Timoshenko beam, with a concentrated mass at the centre, subjected to a concentrated harmonic force is investigated using the coupled displacement field method. The expressions for the transverse displacement were deduced from the assumed admissible function having a single term undetermined coefficient for a total rotation of the beam using the coupled displacement field method. The equation of motion for the forced vibration condition is derived using the principle of conservation of total energy. The Newmark method is employed to solve the equation of motion to obtain the dynamic response of the Timoshenko beam. The dynamic forced vibration response for the two boundary conditions, simply supported and clamped-clamped, is computed by applying the mode superposition technique for the obtained coupled displacement field equations. The authors also carried out the finite element analysis using ANSYS 21 software to validate the results obtained by the coupled displacement field method, and the results are also validated with the existing literature wherever possible. The obtained results are very closely matching with the FEM and other published results.

Keywords

• Coupled displacement field method
• Timoshenko beams
• Nonlinear forced vibration
• Newmark method
• Mode superposition technique