A new thin beam element with cross-section distortion of the absolute nodal coordinate formulation

A novel modelling approach to beams with thin cross-sections is proposed in the absolute nodal coordinate formulation (ANCF), where the Lagrange interpolating and curve fitting techniques of numerical analysis are utilized for construction of the thin beam cross-section contour. Although the slope vector with respect to the coordinate line on cross-section contour is not considered in nodal coordinates, the cross-section distortion could be adequately captured through selecting an appropriate degree of polynomial. The main advantages of the present ANCF thin beam element are that the computational costs are more inexpensive than the ANCF shell element due to less generalized coordinates, there is very small amount of input data because slope vectors of the cross-section are eliminated, and the cross-sectional stress distribution may always be continuous on account of the fact that the cross-section is not discretized into a set of finite elements. Moreover, the formulations of elastic forces and Jacobian of thin laminated composite beam are also derived based on the continuum mechanics. Finally, several examples including both static and dynamic problems are performed to verify the new element and meanwhile demonstrate its general characteristics.

INVESTIGATION OF RESIDUAL STRESSES AND DEFORMATIONS OF A PULTRUDED THIN BEAM PROFILE

In the present study, a coupled 3D transient thermo-chemical analysis together with 2D plane strain mechanical analysis is carried out for the pultrusion process. For the mechanical analysis, a cure hardening instantaneous linear elastic (CHILE) approach is used of a thin beam profile made of glass fibre and epoxy resin. The applied approach is efficient and fast to investigate the residual stresses and deformations together with the distributions of temperature and degree of cure obtained from the thermo-chemical analysis.

Elastic Metasurfaces for Low-Frequency Flexural Wavefront Control

Controlling elastic/acoustic wave-front via compact designs has attracted increasing research interest in past decades. The emerging of metasurface concept provides an unconventional and attractive approach in this filed. A metasurface generally consists of a single array of subwavelength-scaled patterns in the host medium, introducing an abrupt phase shift in the wave propagation path. In this paper, we explored an elastic metasurface concept to control the propagation of low-frequency flexural Lamb waves. The phase modulation based on the Snell’s law was achieved by tailoring the thickness of thin beam resonators connecting two elastic host medium. Depending on the design of the phase-modulated structure (a.k.a. metasurface), elastic waves could be steered or focused which was verified through analytical and numerical models.

General Homogenised Formulation for Thick Viscoelastic Layered Structures for Finite Element Applications

Viscoelastic layered surface treatments are widely used for passive control of vibration and noise, especially in passenger vehicles and buildings. When the viscoelastic layer is thick, the structural models must account for shear effects. In this work, a homogenised formulation for thick N-layered viscoelastic structures for finite element applications is presented, which allows for avoiding computationally expensive models based on solids. This is achieved by substituting the flexural stiffness in the governing thin beam or plate equation by a frequency dependent equivalent flexural stiffness that takes shear and the properties of the different layers into account. The formulation is applied to Free Layer Damping (FLD) and Constrained Layer Damping (CLD) beams and plates and its ability to accurately compute the eigenpairs and dynamic response is tested by implementing it in a finite element model and comparing the obtained results to those given by the standard for the application—Oberst for the FLD case and RKU for the CLD one—and to a solid model, which is used as reference. For the cases studied, the homogenised formulation is nearly as precise as the model based on solids, but requires less computational effort, and provides better results than the standard model.

Theoretical and experimental investigation of a 1:3 internal resonance in a beam with piezoelectric patches

Experimental and theoretical results on the nonlinear dynamics of a homogeneous thin beam equipped with piezoelectric patches, presenting internal resonances, are provided. Two configurations are considered: a unimorph configuration composed of a beam with a single piezoelectric patch and a bimorph configuration with two collocated piezoelectric patches symmetrically glued on the two faces of the beam. The natural frequencies and mode shapes are measured and compared with those obtained by theoretical developments. Ratios of frequencies highlight the realization of 1:2 and 1:3 internal resonances, for both configurations, depending on the position of the piezoelectric patches on the length of the beam. Focusing on the 1:3 internal resonance, the governing equations are solved via a numerical harmonic balance method to find the periodic solutions of the system under harmonic forcing. A homodyne detection method is used experimentally to extract the harmonics of the measured vibration signals, on both configurations, and exchanges of energy between the modes in the 1:3 internal resonance are observed. A qualitative agreement is obtained with the model.

Ultra-Thin Metamaterial Beam Splitters

Here, we present blueprints for three types of ultra-thin beam splitters based on versatile fishnet metamaterial structures at the 1.55 μ m optical communication wavelength. The thicknesses of the designed polarizing beam splitter and partially polarizing beam splitter are 1/26 of the free-space wavelength, while the thickness of the non-polarizing beam splitter is 1/13 of the free-space wavelength. Numerical simulations show that, compared to other miniaturization approaches including popular dielectric metasurfaces, metal-based metamaterial approach can provide much thinner beam splitters with reasonable performance. Such beam splitters can enable miniaturization of conventional and advanced quantum photonic systems towards higher density, scalability, and functionality.