Semi-Analytical Study of Fluid-Induced Nonlinear Vibrations in Viscoelastic Beams with Standard Linear Solid Model Using Multiple Time Scales Method

Document Type : Research Article

Authors

1 Assistant Professor, Department of Mechanical engineering, Guilan University, Rasht, Iran,

2 PhD candidate, Department of Mechanical engineering, Guilan University, Rasht, Iran

Abstract

In this research, the behavior of nonlinear vibrations of the viscoelastic Euler-Bernoulli beam under the influence of external fluid flow has been studied. The governing equations of motion are obtained by assuming Von-Karman nonlinear strain-displacement relations and considering the interaction between structure and fluid. To consider more realistic hypotheses, contrary to previous researches, the effect of viscoelastic behavior has been evaluated using a more complete and practical model called the Standard linear solid model. After non-dimensionalizing the motion equations, the governing nonlinear differential equations are discretized using the Galerkin method. Then, the system's analytical response is acquired through the method of multiple time scales. After verifying the results and confirming the semi-analytical method's accuracy with the numerical solution results, different parameters' effect on the system's dynamic behavior has been analyzed. The results indicate that the viscoelastic behavior and the nonlinear model significantly affect the lock-in area and the maximum amplitude of the viscoelastic beam vibrations. In most studies on viscoelastic beams' vibrations, the damping effect in nonlinear terms has been neglected. However, this study demonstrates that the effect of damping on terms related to the nonlinearity of strain fields is substantial.

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Main Subjects

References

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Amirkabir Journal of Mechanical Engineering
Volume 53, Issue 10
January 2022
Pages 5105-5122

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