Harmonic analysis of a Simply-Supported-Fixed-Beam of uniform cross-section with a concentrated mass and concentrated harmonic force at mid-span using Numerical Simulation

Abstract

Vibration measurements and analysis on beam is important for the safe design, construction, and operation of variety of machines and structures. This is because one of the key components of failure of beams is associated with vibration and the phenomenon of resonance. The behavior showcased by a structure at resonance is a key aspect of structural dynamics. Therefore, when a beam is subjected to cyclic loads it is important to study how the beam behaves at various frequencies, especially those that are close to its natural frequencies. This is done with the help of modal and harmonic analysis. These analyses help to verify whether an engineering design that includes a structural member like beam will successfully overcome resonance, fatigue and other harmful effects of forced vibration. The paper presents the modal analysis of a uniform simply-supported-fixed beam of 0.5 m length, 0.005 m width, and 0.005 m height in the absence and in the presence of concentrated mass of 0.07 kg at its mid-span in ANSYS 'Modal' analysis system. The simulation results are validated through comparison with results from well-established theories of vibration, namely the Eigenvalue Method and the Rayleigh Method. The harmonic analysis is then performed with the addition of harmonic force of 5 N at the mid-span of the beam through ANSYS `Harmonic Response' analysis system. From the harmonic analysis, it is observed that the beam undergoes a maximum transverse directional deformation of 13.995 mm and experiences a maximum von-Mises stress of 624.520 MPa when it is vibrating at the frequency of 45.007 Hz.