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Strain-Based Measurement Introduction:Applications Note 1-9:The Second-Order SystemAn accelerometer having an internal spring member that responded to accelerationinputs in two or more dimensions simultaneously would be of little use aswe would be unable to define a dimension that produced any given response.This is why an accelerometer spring member is designed to be flexible(responsive) in one dimension and stiff (unresponsive) in all other dimensions.Our goal would be to define the measurement axis precisely to produce a single-degree-of-freedomstructure. The single-degree-of-freedom spring-member-basedsensor class invariably show second-order responses.It should be noted that no mechanical system is able to perfectly imitatethe single-degree-of-freedom system and will simultaneously supportmotion, to some extent, in other dimensions. Even well-designed sensorstructures will show some degree of ÒtransverseÓ responsivity. Thesecond-order system is defined as a system where the transfer functionis the solution to a second-order differential equation. The second-orderresponse defines the response of any mechanical system possessingmass, where the restoring forces acting upon this mass are provided bya spring constant, and resistance to motion is provided by mechanicaldamping. The spring constant is quantified by the stiffness of the springmember. The damping forces acting upon the mass may result from theintrinsic structural damping of the material that comprises the springmember, or may derive from fluidic- or gas-damping provided in thesensor design. In the case of the piezoelectric element, the spring rateof the piezoelectric element is high and the internal structural dampingof the element is low yielding a close-to-zero-damped second-orderresponse. In the case of the seismometer, the spring restoring forces aregenerally provided by discrete spring elements of relatively low springrate, yielding fundamentally low resonance frequencies.CHAPTER 1-50 The Art of Practical and Precise Strain Based Measurement 2nd Edition © 1999
Applications Note 1-9:Seismic Instruments:The term ÒSeismic InstrumentsÓ is used to refer to the entire class of instruments,the dynamic behavior of which can be derived from the sum of theforces acting upon the internal seismic element, where the seismic elementis constrained to move primarily in one dimension (single-degree-of-freedomsystem). The seismic mass in low g range cantilever beam accelerometersmay consist of a concentrated mass at one end of the beam or can bethe distributed mass of the beam alone in very high range devices. In thecase of the pressure sensor diaphragm, the seismic mass is the distributedmass of the diaphragm, and the restoring spring force is provided by thespring constant of the diaphragm material. Load transducers are identical tothe diaphragm pressure sensor from the seismic viewpoint, with the springmember configured to produce bending in response to direct-force loading,as opposed, to the distributed-force loading that pressure environmentspresent to the diaphragm pressure sensor.NewtonÕs Law, F = MA, is the fundamental relationship which all seismicinstruments obey, in that, the net force exerted on a mass will result in theacceleration or deceleration of the mass with resulting displacement. Allseismic instruments show primarily second-order responses. It should alsobe noted that all sensor structures will show multiple higher-order resonancesas the various internal structures within the sensor possess differentmasses, geometries, and stiffness, and will support resonances at differentfrequencies. The objective of good sensor design is to ensure that theseinternal structures do not support resonant responses within the useful frequencyresponse range of the sensor.Referencing Figure 1-27, a seismic system is modeled showing the seismicmass and the spring as well as damping forces that will act upon this mass.This mechanical model is excited by the forcing function q i acting upon themass where the resulting displacement of the mass is defined as q o .The Art of Practical and Precise Strain Based Measurement 2nd Edition © 1999 CHAPTER 1-51
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The Art of Practical andPrecise Str
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Special Credits:Mrs. Helen Pierson,
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Table of ContentsBy James G. Pierso
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ContentsApplications Note 4-10:Lead
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ContentsCHAPTER 8Electrical Conside
Page 13 and 14: CHAPTER 1Strain-BasedMeasurementInt
Page 15 and 16: Applications Note 1-1: Introduction
Page 17 and 18: Applications Note 1-1: Introduction
Page 19 and 20: Applications Note 1-2:The Art of Ap
Page 21 and 22: Applications Note 1-31. The presenc
Page 23 and 24: Applications Note 1-3result in a pe
Page 25 and 26: Applications Note 1-4:The measureme
Page 27 and 28: Applications Note 1-4:uncertainty i
Page 29 and 30: Applications Note 1-5:All strain-ba
Page 31 and 32: Applications Note 1-6:Applications
Page 33 and 34: Applications Note 1-6:ical size of
Page 35 and 36: Applications Note 1-6:and where:j i
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