Author
Li Jun
Bio: Li Jun is an academic researcher from Shanghai Jiao Tong University. The author has contributed to research in topics: Timoshenko beam theory & Beam (structure). The author has an hindex of 12, co-authored 21 publications receiving 430 citations.
Papers
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TL;DR: In this paper, a dynamic finite element method for free vibration analysis of generally laminated composite beams is introduced on the basis of first-order shear deformation theory, where the influences of Poisson effect, couplings among extensional, bending and torsional deformations, shear deformations and rotary inertia are incorporated in the formulation.
72 citations
TL;DR: In this paper, the exact dynamic stiffness matrix of a uniform laminated composite beam based on trigonometric shear deformation theory is derived, and a refined laminated beam constitutive equation is derived that takes into account the breadth direction strains.
62 citations
TL;DR: In this article, the dynamic transfer matrix is formulated for a straight uniform and axially loaded thin-walled Bernoulli-Euler beam element whose elastic and inertia axes are not coincident by solving the governing differential equations of motion of the beam element.
41 citations
TL;DR: In this paper, a dynamic stiffness method is introduced to investigate the free vibration of laminated composite beams based on a third-order shear deformation theory which accounts for parabolic distribution of the transverse shear strain through the thickness of the beam.
Abstract: The dynamic stiffness method is introduced to investigate the free vibration of laminated composite beams based on a third-order shear deformation theory which accounts for parabolic distribution of the transverse shear strain through the thickness of the beam. The exact dynamic stiffness matrix is found directly from the analytical solutions of the basic governing differential equations of motion. The Poisson effect, shear deformation, rotary inertia, in-plane deformation are considered in the analysis. Application of the derived dynamic stiffness matrix to several particular laminated beams is discussed. The influences of Poisson effect, material anisotropy, slenderness and end condition on the natural frequencies of the beams are investigated. The numerical results are compared with the existing solutions in literature whenever possible to demonstrate and validate the present method.
40 citations
TL;DR: In this article, a dynamic transfer matrix method for determining natural frequencies and mode shapes of the bending-torsion coupled vibration of axially loaded thin-walled beams with monosymmetrical cross sections is developed by using a general solution of the governing differential equations of motion based on Bernoulli-Euler beam theory.
39 citations
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TL;DR: A critical review of literature on bending, buckling and free vibration analysis of shear deformable isotropic, laminated composite and sandwich beams based on equivalent single layer theories, layerwise theories, zig-zag theories and exact elasticity solution is presented in this paper.
327 citations
TL;DR: In this paper, the authors review most of the research done in recent years (1989-2012) on the vibration analysis of composite beams, with emphasis given to the theory being applied (thin, thick, layerwise), methods for solving equations (finite element analysis, differential transform and others) experimental methods, smart beams (piezoelectric or shape memory), complicating effects in both material and structure, and other areas that have been considered in research.
153 citations
TL;DR: In this paper, a number of refined beam theories were obtained by expanding the unknown displacement variables over the beam section axes by adopting Taylor's polynomials, trigonometric series, exponential, hyperbolic and zig-zag functions.
Abstract: A number of refined beam theories are discussed in this paper. These theories were obtained by expanding the unknown displacement variables over the beam section axes by adopting Taylor's polynomials, trigonometric series, exponential, hyperbolic and zig-zag functions. The Finite Element method is used to derive governing equations in weak form. By using the Unified Formulation introduced by the first author, these equations are written in terms of a small number of fundamental nuclei, whose forms do not depend on the expansions used. The results from the different models considered are compared in terms of displacements, stress and degrees of freedom (DOFs). Mechanical tests for thick laminated beams are presented in order to evaluate the capability of the finite elements. They show that the use of various different functions can improve the performance of the higher-order theories by yielding satisfactory results with a low computational cost.
115 citations
TL;DR: In this paper, a trigonometric higher-order plate theory is derived, which satisfies the free surface conditions, and the number of unknown functions involved in the present theory is only four as against six or more in case of other shear and normal deformation theories.
111 citations
TL;DR: In this article, an exact dynamic stiffness formulation using one-dimensional (1D) higher-order theories is presented and subsequently used to investigate the free vibration characteristics of solid and thin-walled structures.
107 citations