Finite Elements in Analysis and Design
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The finite element formulation and equivalent linearization technique used in the study of nonlinear vibrations of beams have been reexamined based on the earlier comments. Errors present in the equivalent linearization procedure, in the substitution of inplane boundary conditions at the element level instead of at the system level, and in the use of different connotation for the frequency, are discussed. A simply-supported beam with immovable ends is considered as an example to evaluate these errors. A formulation in terms of transverse displacement alone is also presented based on the assumption of average nonlinear stretching force.