A Review of Advanced Modeling Methods for Thin-Walled Beams: From Deductive Methods to Data-Driven Approaches

This paper studies flexural-torsional doubly coupled vibration through periodic thin-walled open cross-section beams composed of two kinds of materials. Based on the doubly coupled vibration equation, plane wave expansion method for the thin-walled beams is provided. If the filling fraction keeps constant, the lattice is one of the factors that affect the normalized gap width. If the lattice and filling fraction keeps constant, the Young modulus contrast plays a fundamental role for the band gap width, but not density contrast. Finally, the frequency response of a finite periodic binary beam is simulated by finite element method, which provides an attenuation of about 40dB in the frequency range of the band gaps. The findings will be significant in the application of phononic crystals.

Based on the theory of plates and shells a method of modeling thin-walled beams is proposed. Using the tenets of the theory of plates and shells Papkovich–Neuber solution as well as the Saint Venant semiinverse method partial analytical solution of a system of nonlinear partial differential equations is applied to calculate inertial stress action on the deflected mode of lateral plates of thin-walled straight parts of waveguides with a rectangular cross-section. The novelty of this article is in the fact that the conducted research proved the cause of the behavior of a waveguide with rectangular cross-section. To achieve the desired results calculation methods were used based on the works of Vlasov Bychkov and Rzhanitsyn. The obtained results showed the correctness of this technique and revealed the necessity to specify the Zhuravsky formula when calculating shear stresses in thin-walled beams by Euler–Bernoulli beam theory.

A new method for the vibration of thin-walled beams

Triply coupled vibration through periodic thin-walled open cross section nonsymmetrical beams composed of two kinds of material is studied in this paper. Based on the triply coupled vibration equation, plane wave expansion method for the thin-walled beams is provided. If the filling fraction keeps constant, the lattice is one of the factors that affect the normalized gap width. If the lattice and filling fraction keep constant, the Young’s modulus contrast plays a fundamental role for the band gap width, but not density contrast. Finally, the frequency response of a finite periodic binary beam is simulated with finite element method, which provides an attenuation of over 20dB in the frequency range of the band gaps. The findings will be significant in the application of phononic crystals.

A lightweight method of thin-walled beams based on cross-sectional characteristic

Higher-order modeling of a thin-walled beam with a welded multicell cross-section and its application to welding line optimization

This paper addresses the construction of a dynamical model for a thin-walled beam with circular cross-section in the framework of one-dimensional higher-order beam theory. And a method for pattern recognition of circular thin-walled structures is proposed based on principal component analysis. Initially, a set of equal length linear segments are defined to discretize the mid-line of a circular section. Preliminary deformation modes of thin-walled structures, defined over the cross-section through kinematic concept, are parametrically derived through changing the discretization degree of the section. Next, the generalized eigenvectors are derived from the governing equations, and the characteristic deformation modes of circular sections with different discretization degrees are solved based on principal component analysis. In addition, a reduced higher-order model can be obtained by updating the initial governing equations with a selective set of cross-section deformation modes. The features include further reducing the number of degree of freedoms (DOFs) and significantly improving computational efficiency while ensuring accuracy. For illustrative purposes, the versatility of the procedure is validated through both numerical examples and comparisons with other theories.

Based on the differential equation for torsional vibration, which includes the effect of cross-sectional warping, the shape functions are determined and, in turn, the frequency-dependent mass and stiffness matrices are derived. The results show that this method gives more accurate results in the high-frequency range than those obtained by the static finite-element method

Stiffness method of thin-walled beams with closed cross-section

Multicell Thin-walled Method for Solid Multimaterial Beams

A data-driven procedure for one-dimensional dynamic analysis of thin-walled beams with arbitrary cross-sections

Data-driven approach for a one-dimensional thin-walled beam analysis

Influence of spatially varying material properties on the bimoment normal and shear stresses by warping torsion of FGM beams

A theory of coupled beams for strength assessment of passenger ships

Equivalent beam analysis of thin-walled beam structures