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Applied Structural and Mechanical Vibrations 2009 Part 14

Tham khảo tài liệu 'applied structural and mechanical vibrations 2009 part 14', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | resistive elements that are cemented on a structure of which they measure the local deformation through the variation in resistance caused by elongation or contraction. Strain gauges function on a principle based on the expression R pL A which gives the resistance of a uniform conductor of resistivity p length L and cross-section area A. The fractional change in resistance is then given by AR AL _ _ Ap _ Ap p AL __ AL - - l 2i 1 2 l _ -R-- 14.1 R L p AL L L L where v is Poisson s ratio of the conductor material and ALỊL E is the strain. According to eq 14.1 strain gauges do not actually measure displacement but strain i.e. the average gauge elongation or contraction divided by the gauge length. The parameter K is called the gauge factor which accounts for the resistance variations due to dimensional changes represented by the term 1 2v and for those caused by the strain-induced resistivity variations Ap p l AL L . This latter effect is called the piezoresistive effect. Depending on the material of which the strain gauge is made the gauge factor assumes different values ranging from close to 2 for nickel-copper constantan and 2.1 nickel-chromium karma alloys to about 3.5 for isoelastic to above 100 for semiconductors. Metal alloy strain gauges are the most widely used and as shown in Fig. 14.2 they typically have the form of grid foils of various dimensions and geometry supported by an insulating backing carrier which allows them to be bonded to the body under test. The backing carrier performs the fundamental function of transferring the strain from the specimen to the gauge with maximum fidelity. The nominal values of resistance are normally 120 350 700 or 1000 Q with strain-induced variations that are usually quite small as low as few parts per million ppm and therefore require special care in their measurement. Moreover the temperature appreciably influences both the gauge resistance and the gauge factor producing the so-called thermal output which is due to the