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For the analyze of forced and free vibrations of composites with periodically varying interfaces, we develop an energetic boundary function method. Three types of beams under different homogeneous boundary conditions and a sequence of boundary functions for each type beam are given, which automatically satisfy the homogeneous boundary conditions. Then we derive an energy equation and construct the energetic boundary functions by further satisfying the energy equation. The solution of forced vibration is expressed in terms of energetic boundary functions as the numerical bases, and then we can derive the linear system to decide the expansion coefficients by a simple collocation technique. To find out the natural frequencies of composite beams we iteratively solve the varying linear systems which include the unknown natural frequencies, and at each iteration we employ the Rayleigh quotient to calculate the natural frequencies until convergence. Through numerical tests we find that the energetic boundary function methods are highly efficient and very accurate for solving the proposed vibration problems of composite beams. [ABSTRACT FROM AUTHOR]

The Variational Asymptotic Method (VAM) that is a powerful method for solving thin-walled beam problems is used for nonlinear static and stability analysis of composite beams. The finite difference and the finite elements methods are used for calculating elastic deformation of beams with clamped-free boundary conditions. The case of simply supported beams is also solved using linear and nonlinear formulations and the results are compared with each other. Next, the shooting method is used for performing nonlinear elasto-static analysis of cantilever beams. Finally by applying perturbations on the equilibrium equations and using an eigenvalue analysis, elastic stability of clamped-free composite beams is analyzed. The obtained results are compared with the available data in the literature that have been obtained using deformation analysis. [ABSTRACT FROM AUTHOR]

In this stud y, we attempt to analyse free nonlinear vibrations of buckling in laminated composite beams. Two new methods are applied to obtain the analytical solution of the nonlinear governing equation of the problem. The effects of different parameters on the ratio of nonlinear to linear natural frequencies of the beams are studied. These methods give us an agreement with numerical results for the whole range of the oscillation amplitude. [ABSTRACT FROM AUTHOR]

A Multiresolution finite wavelet domain meshless approach is presented for the simulation of guided waves in composite beams. The Daubechies wavelet and scaling functions are both employed as basis functions and their remarkable properties for the hierarchical spatial approximation of state variables are explored. The first level of the multiresolution approximation provides the coarse solution, while finer resolution components are sequentially calculated and superimposed on the coarse solution, until the desired level of accuracy is achieved. The development of the multiresolution wavelet-based beam element that encompasses first-order shear deformation theory kinematic assumptions is described, and the multiresolution equations of motion including stiffness and mass matrices are formulated. Numerical results for the simulation of guided wave propagation in aluminum and laminated composite beams are presented, demonstrating substantial reduction in computational effort compared to single resolution approaches and traditional finite elements. Convergence studies using various Daubechies wavelet interpolation functions, are evincing extraordinary convergence rates with very low requirements of grid points per wavelength. Furthermore, additional benefits of the proposed method are encompassed in the analysis of multiple guided wave modes, attributed to the low-pass filter behavior of the scaling functions and the band-pass filter behavior of the wavelet functions that can result in isolation of different wave modes by the individual resolution components of the total solution. • Novel hierarchical refinement type that employs the non-converged solutions to achieve convergence. • Diagonal mass matrices yield uncoupled multiresolution equations of motion using explicit integration. • Rapid simulations of guided wave propagation in aluminum and composite beams. • Remarkable convergence rates compared to single-resolution approaches and finite elements. • Unique capabilities of different wave mode isolation by the individual resolution components of the total solution. [ABSTRACT FROM AUTHOR]

Abstract: This paper discusses three recent updates to the variational asymptotic beam sectional analysis (VABS). The first update is a change to the warping constraints in terms of three-dimensional variables, so that one-dimensional beam variables are treated with more rigor. The second update, although its formulation has only been analytically derived but has not been implemented yet, is the incorporation of the effects due to applied loads. The third update is a more accurate energy transformation to generalized Timoshenko form, which is a crucial aspect in finding the stiffness constants to the generalized Timoshenko beam theory. Examples are presented to demonstrate that the updated energy transformation may yield significantly different stiffness predictions from previous versions of VABS and to show that the updated version is indeed more accurate. In addition to the updates, this paper includes a comprehensive derivation of the geometrically-exact nonlinear one-dimensional beam theory and the asymptotically-correct cross-sectional analysis that together form the basis of VABS. [Copyright &y& Elsevier]