The eigenvalues and the first and second-order eigenvalue sensitivities of a uniform Euler–Bernoulli beam supported by the standard linear solid model for viscoelastic solids are studied in detail. A method is proposed that yields the approximate eigenvalues and allows the formulation of a frequency equation that can be used to obtain approximate eigenvalue sensitivities. The eigenvalue sensitivities are further exploited to solve for the perturbed eigenvalues due to system modifications, using both a first- and second-order Taylor series expansion. The proposed method is easy to formulate, systematic to apply, and simple to code. Numerical experiments consisting of various beams supported by a single or multiple viscoelastic solids validated the proposed scheme and showed that the approximate eigenvalues and their sensitivities closely track the exact results.
Eigenvalues and Eigenvalue Sensitivities of a Beam Supported by Viscoelastic Solids
Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received June 12, 2013; final manuscript received November 21, 2013; published online January 16, 2014. Assoc. Editor: Michael Leamy.
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Cha, P. D., Carbon, K. C., and Hsieh, R. (January 16, 2014). "Eigenvalues and Eigenvalue Sensitivities of a Beam Supported by Viscoelastic Solids." ASME. J. Vib. Acoust. April 2014; 136(2): 021017. https://doi.org/10.1115/1.4026175
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