Abstract
The present paper analyzes the vibration issue of thin‐walled beams under combined initial axial load and end moment in two cases with different boundary conditions, specifically the simply supported‐end and the laterally fixed‐end boundary conditions. The analytical expressions for the first natural frequencies of thin‐walled beams were derived by two methods that are a method based on the existence of the roots theorem of differential equation systems and the Rayleigh method. In particular, the stability boundary of a beam can be determined directly from its first natural frequency expression. The analytical results are in good agreement with those from the finite element analysis software ANSYS Mechanical APDL. The research results obtained here are useful for those creating tooth blade designs of innovative frame saw machines.
Highlights
Academic Editor: Itzhak Green e present paper analyzes the vibration issue of thin-walled beams under combined initial axial load and end moment in two cases with different boundary conditions, the supported-end and the laterally fixed-end boundary conditions
The stability boundary of a beam can be determined directly from its first natural frequency expression. e analytical results are in good agreement with those from the finite element analysis software ANSYS Mechanical APDL. e research results obtained here are useful for those creating tooth blade designs of innovative frame saw machines
Results of Validations and Discussion is section serves to validate the analytical expressions obtained from the two approaches. e results are compared with the numerical data obtained from the finite element methods (FEMs) software ANSYS Mechanical APDL
Summary
Flexural-Torsional Vibration of Thin-Walled Beams Subjected to Combined Initial Axial Load and End Bending Moment: Application to the Design of Saw Tooth Blades. E second approach, which is developed based on analytical tools, has drawn the interest of many researchers due to its ability to express the explicit relationships between the vibration properties and the structural parameters of thin-walled beams Using this approach, Bokaian [15] and Abramovich [16] studied the natural frequencies of beams under tensile and compressive axial loads, respectively. We focus on developing analytical expressions to determine the first natural frequency of a thin-walled beam subjected to an axial load and end moment.
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