科研之友
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摘要
This paper presents analytical approximate solutions for the initial postbuckling deformation of sandwich beams including transverse shear. The approximate procedure is based on the nonlinear beam equation (with transverse shear included) by coupling the well-known Maclaurin series expansion and orthogonal Chebyshev polynomials; the governing differential equation with sinusoidal nonlinearity can be reduced to form a cubic-nonlinear equation. Analytical approximations to the resulting boundary condition problem are established by combining the methods of Newton linearization and harmonic balance. Unlike the classical method of harmonic balance, the linearization is performed prior to proceeding with harmonic balancing thus resulting in a set of linear algebraic equations instead of one of nonlinear algebraic equations, thereby establishing analytical approximate solutions. Illustrative examples are presented for a few typical sandwich construction configurations, and it is shown that the proposed approximate solutions are in excellent agreement with the numerical solution obtained via the shooting method for both small and large angles of rotation.
