Effect of Structural Parameters on the Nonlinear Vibration of L-Shaped Beams

Date

2024-01-01

Author

Ekici, Yigitcan
Ciğeroğlu, Ender
Yazıcıoğlu, Yiğit

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In this chapter, nonlinear vibration analysis of L-shaped beams is performed for different structural parameters, and the effects of these parameters are observed. The L-shaped beam is composed of two beams joined end to end and perpendicular to each other; therefore, the system is considered as two separate beams with the same boundary conditions at their mutual ends. In addition to this, concentrated masses are attached to each beam on the L-shaped beam. The dynamic model is obtained by using Euler-Bernoulli Beam Theory and Hamilton’s principle. These equations are further simplified by disregarding the axial motions of the beams and only the transverse motions are considered in calculations. Galerkin’s method is utilized to discretize the obtained nonlinear partial differential equations into a set of nonlinear ordinary differential equations. These nonlinear ordinary differential equations are converted into a set of nonlinear algebraic equations by using Harmonic Balance Method (HBM), which are then solved numerically by using Newton’s method with arc-length continuation. In order to observe the effect of the nonlinearity, a linear solution is also obtained and compared with the nonlinear solution. Several case studies are performed in order to observe the effect of system parameters on the nonlinear steady-state response of the L-shaped beam.

Subject Keywords

Euler-Bernoulli beam theory, Nonlinear beams, Nonlinear L-shaped beams, Structural dynamics

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https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85176010818&origin=inward
https://hdl.handle.net/11511/108084

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Department of Mechanical Engineering, Conference / Seminar