Material properties can be tailored through modification of their geometry or architecture. With this concept, a lot of smart materials, metamaterials, and smart structures have been developed. Auxetic materials and structures are a novel class of materials which exhibit an interesting property of negative Poisson's ratio. By virtue of the auxetic behavior, mechanical properties such as fracture toughness, indentation resistance, etc., can be improved. In order to exploit the interesting properties of auxetic materials, several potential applications of auxetic materials have been explored in medical, sports, automobile, defense, etc. Design and modeling of novel auxetic materials and structures is still on the way. Here, the article focuses upon the different aspects of auxetic materials and structures. A comprehensive updated review of auxetic materials, their types and properties, and applications has been presented. This paper also discusses the design and modeling approaches of auxetic structures.

Three Decades of Auxetics Research − Materials with Negative Poisson's Ratio: A Review

Mechanical design and multifunctional applications of chiral mechanical metamaterials: A review

Bending, buckling and free vibration of laminated composite and sandwich beams: A critical review of literature

Vibrations of straight and curved composite beams: A review

Finite element modelling and updating of a lively footbridge: The complete process

The dynamic bending–torsion coupled vibrations of elastic axially loaded slender thin-walled beams with monosymmetrical cross-sections are investigated by using normal mode method. The Bernoulli–Euler beam theory is employed and the effects of warping stiffness and axial force are included in the present formulations. The theoretical expressions for the displacement response of axially loaded slender thin-walled beams subjected to concentrated or distributed loads are presented. The method is illustrated by its application to two test examples to describe the effects of warping stiffness and axial force on the dynamic behavior of thin-walled beams. The numerical results for the dynamic bending displacements and torsional displacements are given. The proposed theory is fairly general and can be used for thin-walled beam assemblage of arbitrary boundary conditions subjected to various kinds of loads.

Dynamic response of axially loaded monosymmetrical thin-walled Bernoulli–Euler beams

An exact dynamic stiffness approach for vibration analysis of laminated composite beams with arbitrary ply orientation is introduced in this paper. The influences of Poisson effect, shear deformation and rotary inertia are accounted for in the formulation. The coupled equations of motion are derived first by using the Hamilton principle and the dynamic stiffness matrix is established based on the analytical solutions of the governing differential equations. The automated Muller root search algorithm is then applied to the developed dynamic stiffness matrix to calculate the natural frequencies and mode shapes of the particular composite beams. The influences due to Poisson effect, shear deformation, anisotropy, slenderness ratio and boundary condition on the natural frequencies of the composite beams are investigated. Numerical results of the present method are validated by comparison with those previously published in literature.

A Dynamic Stiffness Approach for Vibration Analysis of a Laminated Composite Beam

The dynamic stiffness method for studying the vibration characteristics of the laminated composite shallow circular arches is introduced in this article. The exact dynamic stiffness matrix is formulated from the analytical solutions of the governing differential equations of motion of the laminated circular arches, based on second-order shear deformation theory. The application of the present method is illustrated by miscellaneous numerical examples, in which the effects of material orthotropy, the lamination scheme, the curvature ratio, length-to-thickness ratio, and boundary condition upon the natural frequencies of the composite arches are investigated. Compared to those solutions available in the literature, the numerical results demonstrate the accuracy and effectiveness of the present method.

Free Vibration of Laminated Composite Circular Arches by Dynamic Stiffness Analysis

The finite element (FEM) and the boundary element method (BEM) are combined together to solve the underwater radiation noise of ships. First,a finite element model of entire ship including power plant in engine room is built by using 30 geometric parameters and five kinds of finite elements,such as SHELL63, BEAM4,SOLID95,COMBIN14 and MASS21.Finite element method is employed to analyze the vibration responses of ship to excitations in consideration of fluid-structure interaction.Then,the outer surface of finite element model is treated as the boundary element model and the vibration displacement responses of the ship surface are treated as the velocity boundary condition for calculation underwater radiation noise.Boundary element method is employed to calculate the underwater radiation noise.In this paper,the underwater radiation noise of ship to propulsion diesel engine,auxiliary diesel energy or gearbox excitations have been predicted respectively.And, total sound pressure levels of ship underwater radiation noise to all excitations have been calculated during design phase and show a good agreement with experimentally measured results.

Study on characteristics of ship underwater radiation noise

The spectral element matrix is derived for a straight and uniform beam element having an arbitrary cross-section. The general higher-order beam theory is used, which accurately accounts for the transverse shear deformation out of the cross-sectional plane and antielastic-type deformation within the cross-sectional plane. Two coupled equations of motion are derived by use of Hamilton's principle along with the full three-dimensional constitutive relations. The theoretical expressions of the spectral element matrix are formulated from the exact solutions of the coupled governing equations. The developed spectral element matrix is directly applied to calculate the exact natural frequencies and mode shapes of the illustrative examples. Numerical results of the thick isotropic beams with rectangular and elliptical cross-sections are presented for a wide variety of cross-section aspect ratios. Beam members are basic structural components widely used in many types of structures within the fields of mechanical, aeronautical, automobile and civil engineering. Because of the practical importance, a large number of investigators have made efforts to deal with the static and dynamic analyses of the beams. The analyses of slender beams have been performed mostly using the elementary Bernoulli-Euler theory. This theory assumes that the plane sections of the cross-section remain plane and particular to the beam axis. A more refined beam theory is Timoshenko beam theory which accounts for the shear deformation and rotary inertia that are neglected in the elementary theory. In Timoshenko beam theory the distribution of the transverse shear strain is constant through the beam thickness and therefore requires the shear correction factor to correct the strain energy of deformation. Timoshenko (1) first developed a theory which allowed one to study the vibrational behavior of the thick beams by approximately accounting for transverse shear deformation and rotary inertia, where the cross-section remained undistorted and the in-plane stresses were zero. Mindlin and Deresiewicz (2) calculated the shear correction factor for a variety of cross-sections of the beams. The dynamic shear strain distribution may differ significantly from the parabolic form of the static shear strain distribution. Cowper (3) presented a method to determine the shear correction factor based on the static three-dimensional elasticity theory along with Saint- Venant's static flexure warping function. Hutchinson (4) investigated the behavior of the shear coefficient for a rectangular Timoshenko beam by comparison of the Timoshenko beam solution with a three-dimensional solution for a simply-supported beam. It was found that a shear coefficient would have to be a function of the wave length as well as the aspect ratio.

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Hua Hongxing

Papers

Dynamic response of axially loaded monosymmetrical thin-walled Bernoulli–Euler beams

A Dynamic Stiffness Approach for Vibration Analysis of a Laminated Composite Beam

Free Vibration of Laminated Composite Circular Arches by Dynamic Stiffness Analysis

Study on characteristics of ship underwater radiation noise

A spectral finite element model for vibration analysis of a beam based on general higher-order theory