Novel method for analyzing the behavior of composite beams with non-smooth interfaces

Abstract

An almost exact solution is derived for the forced vibration of a composite beam with periodically varying non-smooth interface through a moderate weak-form formulation. The material property of a non-uniform beam is characterized by its flexural rigidity function R(x). In the novel method, R(x) is relaxed to be an integrable function rather than a \({\mathcal{C}}^2\) smooth function in the usual approach. The R(x)-orthogonal bases in the linear span of all boundary functions are derived such that the second-order derivatives of the bases elements are orthogonal with respect to the weight function R(x). When the deflection of the beam is expressed in terms of the bases, the expansion coefficients can be determined exactly in closed form owing to the R(x)-orthogonality of the bases. The solution obtained is almost exact, since its accuracy can be up to the order \(10^{-15}\) . This powerful method is used to analyze the forced vibration behavior of composite beams with three different periodic interfaces.

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