Three aluminium channel sections of US standard extruded dimension are mounted as cantilevers with x-axis symmetry. The flexural bending and shear that arise with applied axial torsion are each considered theoretically and numerically in terms of two longitudinal axes of loading not coincident with the shear centre. In particular, the warping displacements, stiffness and stress distributions are calculated for torsion applied to longitudinal axes passing through the section’s centroid and its web centre. The stress conversions derived from each action are superimposed to reveal a net sectional stress distribution. Therein, the influence of the axis position upon the net axial and shear stress distributions is established compared to previous results for each beam when loading is referred to a flexural axis through the shear centre. Within the net stress analysis is, it is shown how the constraint to free warping presented by the end fixing modifies the axial stress. The latter can be identified with the action of a ‘bimoment’ upon each thin-walled section.
Benefiting from the great advances of the femtosecond laser two-photon polymerization(TPP)technology,customized microcantilever probes can be accurately 3-dimensional(3D)manufactured at the nanoscale size and thus have exhibited considerable potentials in the fields of microforce,micro-vibration,and microforce sensors.In this work,a controllable microstructured cantilever probe on an optical fiber tip for microforce detection is demonstrated both theoretically and experimentally.The static performances of the probe are firstly investigated based on the finite element method(FEM),which provides the basis for the structural design.The proposed cantilever probe is then 3D printed by means of the TPP technology.The experimental results show that the elastic constant k of the proposed cantilever probe can be actively tuned from 2.46N/m to 62.35N/m.The force sensitivity is 2.5nm/μN,the Q-factor is 368.93,and the detection limit is 57.43nN.Moreover,the mechanical properties of the cantilever probe can be flexibly adjusted by the geometric configuration of the cantilever.Thus,it has an enormous potential for matching the mechanical properties of biological samples in the direct contact mode.
Famei WANGChangrui LIAOMengqiang ZOUDejun LIUHaoqiang HUANGChao LIUYiping WANG
This paper presents the design,fabrication,and characterization of cantilever-type resonators with a novel stacked structure.Aluminum nitride is adopted as the material for both the structural layer and the piezoelectric layer;this simplifies the fabrication process and improves the quality factor of the resonator.Both in-plane and out-of-planeflexural modes were investigated.The effect of the structural dimensions and electrode patterns on the resonator’s performance were also studied.Finite-element simulations and experiments examining anchor loss and thermoelastic damping,which are the main loss mechanisms affecting the quality factor of these resonators,were carried out.The optimal structural dimensions and electrode patterns of the cantilever-type resonators are presented.A quality factor of 7922 with a motional impedance of 88.52 kΩand a quality factor of 8851 with a motional impedance of 67.03 kΩwere achieved for the in-plane and out-of-planeflexural-mode resonators,respectively.The proposed resonator design will contribute to the development of high-performance devices such as accelerometers,gyroscopes,and pressure sensors.
Shuai ShiQingrui YangYi YuanHaolin LiPengfei NiuWenlan GuoChen SunWei Pang
The snap-through behaviors and nonlinear vibrations are investigated for a bistable composite laminated cantilever shell subjected to transversal foundation excitation based on experimental and theoretical approaches.An improved experimental specimen is designed in order to satisfy the cantilever support boundary condition,which is composed of an asymmetric region and a symmetric region.The symmetric region of the experimental specimen is entirely clamped,which is rigidly connected to an electromagnetic shaker,while the asymmetric region remains free of constraint.Different motion paths are realized for the bistable cantilever shell by changing the input signal levels of the electromagnetic shaker,and the displacement responses of the shell are collected by the laser displacement sensors.The numerical simulation is conducted based on the established theoretical model of the bistable composite laminated cantilever shell,and an off-axis three-dimensional dynamic snap-through domain is obtained.The numerical solutions are in good agreement with the experimental results.The nonlinear stiffness characteristics,dynamic snap-through domain,and chaos and bifurcation behaviors of the shell are quantitatively analyzed.Due to the asymmetry of the boundary condition and the shell,the upper stable-state of the shell exhibits an obvious soft spring stiffness characteristic,and the lower stable-state shows a linear stiffness characteristic of the shell.
The chaotic dynamic snap-through and complex nonlinear vibrations are investigated in a rectangular asymmetric cross-ply bistable composite laminated cantilever shell,in cases of 1:2 inter-well internal resonance and primary resonance.The transverse foundation excitation is applied to the fixed end of the structure,and the other end is in a free state.The first-order approximate multiple scales method is employed to perform the perturbation analysis on the dimensionless two-degree-of-freedom ordinary differential motion control equation.The four-dimensional averaged equations are derived in both polar and rectangular coordinate forms.Deriving from the obtained frequency-amplitude and force-amplitude response curves,a detailed analysis is conducted to examine the impacts of excitation amplitude,damping coefficient,and tuning parameter on the nonlinear internal resonance characteristics of the system.The nonlinear softening characteristic is exhibited in the upper stable-state,while the lower stable-state demonstrates the softening and linearity characteristics.Numerical simulation is carried out using the fourth-order Runge-Kutta method,and a series of nonlinear response curves are plotted.Increasing the excitation amplitude further elucidates the global bifurcation and chaotic dynamic snap-through characteristics of the bistable cantilever shell.