Development of an Adjustable Frequency Device for a Test Vehicle Based on Curved Beam Theory

In this article, an adjustable frequency device based on curved beam theory is designed to control vertical stiffness of an instrumented vehicle that it can detect dynamic data when moving on a test beam for frequency measurement. The adjustable frequency device consists of a set of two-layer cantilever semi-circular thin-beams to support a lumped mass for vibrations, in which a rotatable U-frame is used to change its subtended angle for adjustment of the supporting stiffness and corresponding vertical frequencies of the vehicle. Based on curved beam theory, an analytical frequency equation of the single-degree-of-freedom test vehicle was derived and applied to mobile frequency measurement of a simple beam. To determine the sectional rigidity of the semi-circular thin-beams, both theoretical and experimental studies were be carried out in the ITAM laboratory of the Academy of Science in Czech. The analytical and experimental results indicated that the present semi-circular beam model with guided ends is applicable to prediction of natural frequencies of the test vehicle considering different supporting stiffness

A mortar formulation for frictionless line-to-line beam contact

This paper describes the quasi-static formulation of frictionless line contact between flexible beams by employing the mortar finite element approach. Contact constraints are enforced in a weak sense along the contact region using Lagrange multipliers. A simple projection appropriate for thin beams with circular cross-sections is proposed for the computation of contact regions. It is combined with the geometrically exact beam formalism on the Lie group $SE(3)$ S E ( 3 ) . Interestingly, this framework leads to a constraint gradient and a tangent stiffness invariant under rigid body transformations. The formulation is tested in some numerical examples.

A Superconvergent Isogeometric Method with Refined Quadrature for Buckling Analysis of Thin Beams and Plates

A superconvergent isogeometric method is developed for the buckling analysis of thin beams and plates, in which the quadratic basis functions are particularly considered. This method is formulated through refining the quadrature rules used for the numerical integration of geometric and material stiffness matrices. The criterion for the quadrature refinement is the optimization of the buckling load accuracy under the assumption of harmonic buckling modes for thin beams and plates. The method development starts with the thin beam buckling analysis, where the material stiffness matrix with quadratic basis functions does not involve numerical integration and thus the refined quadrature rule for geometric stiffness matrix can be obtained in a relatively easy way. Subsequently, this refined quadrature rule for thin beam geometric stiffness matrix is conveniently generalized to the thin plate geometric stiffness matrix via the tensor product operation. Meanwhile, the refined quadrature rule for the thin plate material stiffness matrix is derived by minimizing the buckling load error. It turns out that the refined quadrature rule for the thin plate material stiffness matrix generally depends on the wave numbers of buckling modes. A theoretical error analysis for the buckling loads evinces that the isogeometric method with refined quadrature rules offers a fourth-order accurate superconvergent algorithm for buckling load computation, which is two orders higher than the standard isogeometric analysis approach. Numerical results well demonstrate the superconvergence of the proposed method for the buckling loads corresponding to harmonic buckling modes, and for those related with non-harmonic modes, the buckling loads given by the proposed method are also much more accurate than their counterparts produced by the conventional isogeometric analysis.

Effect of lamination schemes on natural frequency and modal damping of fiber reinforced laminated beam using Ritz method

The current study focussed on analysing natural frequency and damping of laminated composite beams (LCBs) by varying fiber angle, aspect ratio, material property and boundary conditions. Ritz method with displacement field based on the shear and normal deformable theory is used and the modal damping is calculated using modal strain energy method. Effects of symmetric angle-ply and cross-ply, anti symmetric cross-ply, balanced and quasi-isotropic lay up schemes on modal damping are presented for the first time. Results revealed that influence of lay-up scheme on natural frequencies is significant for the thin beams while the modal damping of the thin beams are not sensitive to lay-up scheme. However, the lay-up scheme influences the damping significantly for the thick beams. Similarly, high strength fiber reinforced LCBs have higher natural frequency while low strength fiber reinforced LCBs have higher damping due to the better fiber-matrix interaction.

Experimental Investigation on the Mechanical Properties of Thin Beams Built by Electron Beam Melting Technology and Ti6Al4V Material

Electron beam melting (EBM) technology has been popularly used to fabricate flexible devices that performance is directly determined by the elastic deformation of thin beams/flexures. This paper presents the experimental investigation on the effective thickness which determines the mechanical properties of beam-based flexures built by EBM method and Ti6Al4V material. The findings show that the effective thickness of EBM-printed beams is different from the designed value regarding to the building direction. A coefficient factor is proposed to compensate this difference. The experimental results suggest that with EBM-printed flexures having large thickness of ≥ 0.7 mm, the coefficient factors become consistent.