Bending cantilever beam measurement

The stress measurement technique employed in our laboratory is based on the principle of a bending cantilever beam. 

Microcantilever deflection changes as a function of adsorbate coverage when adsorption is confined to a single side of a cantilever (or when there is differential adsorption on opposite sides of the cantilever). Since we do not know the absolute value of the initial surface stress, we can only measure its variation. A relation can be derived between cantilever bending and changes in surface stress from Stoney s formula and equations that describe cantilever bending [15]. Specifically, a relation can be derived between the radius of curvature of the cantilever beam and the differential surface stress ... 

In most cases the variation in surface stress has been determined indirectly by measuring the potential dependence of the strain (i.e., electrode deformation) and then obtaining the variation in stress from the appropriate form of Hookes law (-> bending beam or cantilever beam method, bending plate methods e.g., the measurement of the deformation of the electrode with the help of a —r Kosters laser interferometer). 

BENDING OF A BEAM. The complex dynamic Young s modulus can be determined from the forced, non-resonant oscillations of a single or double cantilever beam. The apparatus considered in this paper is the Dynamic Mechanical Thermal Analyzer (DMTA) (6), manufactured by Polymer Laboratories, Inc. Figure 3 shows the experimental setup for the single cantilever measurement. A thin sample is clamped at both ends. One end is attached to a calibrated shaker through a drive shaft. 

S.D. Senturia, Characterization of the mechanisms producing bending moments in polysilicon micro-cantilever beams by interferometric deflection measurements. 

Several methods have been described for measuring the bending modulus of hbers. The balanced hber method of Scott and Robbins [73,74] appears to be the easiest to handle experimentally (except for very curly hair) and provides less scatter than the other methods [74], The vibrating-reed method (oscillating hber cantilever) has also been used with human hair [10], The cantilever beam method [75], the loop deformation method [76], and the center load beam method [76] have been described for textile hbers. 

Instrumentation. A cantilever with a sharp tip interacting with the surface under investigation is used. The actual bending of the cantilever is measured with a laser beam deflected from a mirror-like surface spot on the back of the cantilever towards a position-sensitive photodetector. The measured signal is used to control the piezo actuators. A constant force mode in which the cantilever-surface distance is kept at a preset interaction force and a constant height mode of scanning operation are possible. The principle of operation is schematically outlined in Fig. 7.9. 

In the previous methods, the use of a continuous membrane for measuring cell forces has the disadvantage that the traction forces are convoluted by the observed bead displacements. Because the calculation is not direct, constraints or assumptions are required to solve the inverse problem. A technique to transduce individual traction forces comes from the use of microfabricated cantilevers. The first demonstration of these sensors was a horizontal silicon cantilever that was made with microfabrication techniques (Figure 22.6a). As a cell migrates across the surface, it bends the cantilever under the load of the traction force. Because the sensor is mechanically decoupled from the substrate, the deflection of the cantilever directly reports only the local force. The simple spring equation relates the deflection of the cantilever beam 8 to the cellular traction force ... 

Biosensors Using Lasers, Fig. 7 Scheme of the optical readout method for a microcantilever bending evaluation. The displacement of the free end of the cantilever is measured by monitoring the optical deflection of an incident laser beam on a position-sensitive detector... 

Cantilever-beam stiffness n. A method of determining stiffness of plastics by measuring the force and angle of bend of a cantilever beam made of the specimen material. The ASTM test is D747. 

This test method can be used to measure the relative susceptibility of materials by "Determining the Threshold Stress Intensity Factor for Environment-Assisted Cracking EAC of Metallic Materials. Constant load specimens, both the fatigue precracked single edge beam SE(B) and precracked compact specimens are tested in bending. The SE(B) was originally referred to as the Cantilever Beam Test. 

This bending can be measured with the light lever technique, as done in AFM, where a laser beam is pointed at the free end of the cantilever (iii) the measured signal is not the actual bending , but the inclination dz/dv at the free end of the cantilever. 

The tensile strength and stress of the IPMC are measured in the same manner as those of the IP. The bending stiffness of a fully hydrated IPMC sample is estimated using the free oscillation attenuation method. By bending the sample to the appropriate initial displacement, the free vibration response can be recorded. The natural frequency of the cantilever, is obtained from the fast Fourier transform of the free vibration response curve. The stiffness of the IPMC, Egg, is determined using Eq. 4, which is based on the thin cantilever beam theory of material mechanics ... 

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