Chapter 3 Flashcards
Receptance or dynamic stiffness?
Most often receptance form is the most practical:
1) In practice much easier, to realize unloaded free conditions than fixed rigid conditions at boundaries.
2) elements of the receptance matrix are invariant with respect to adding or removing degrees of freedom. a dof is removed by deleting the corresponding row and column of the receptance matrix, this is not true of dynamic stiffness matrix
Receptance function measurement (process and things to consider)
1) excite in point 1 with force and known time history
2) measure time history o the motion caused by the exciting force at the response point 2.
3) use the measured force and motion signals to estimate the receptance h12
- difficult to measure the excited DOFs
- BCs may be difficult to realize
- the excitation necessary may be difficult
- environmental factors, measurement and signal analysis equipment add noise and errors to the measured signals
Measurement setup
consists of 4 parts:
a. the measurment object
b. the excitation setup…measures time history of excit. force
c. the response set up…measures time history of the response
d. the signal processing and presentation setup…processes measured signals to the required receptance function and display results
How to support the structure
Support must be chosen so that no external exciting forces other the one required by the BCs act on the structure. Therefore the structure should, as far as possible be vibrationally isolated from the environment.
Another problem is due to reaction forces…reaction forces fromMight the supports should be avoided, since these are external they contribute to the response measured at the response point, but the reaction forces are not measured so their contribution to the vibration velocity can not be compensated for. thus the structure should be supported in a way that makes this ocntribution negligable.
1) suspend the structure from the ceiling with elastic strings
2) place the structure on a very weak elastic foundation or elastic slab
Rule of thumb: the contribution to the responding motion from the support is negl if the eigen freqs of all rigid body modes are located well below the lowest eigen frequency of the investigated elastic modes of the structure. (Might be hard when the elastic mode eigen-freqs are low..). They should be lower than 30% or 1/3 of the lower freq limit of the investigated freq range.
Excitation (basic)
1) shall supply a sufficient amount of vibration energy to the test structure at all freqs of interest
2) should deliver an accurate force signal to the signal processing unit
3) vibration large enough to produce measureable response at all observation points (if not, they will be disrupted by noise)
setup consists of:
- an excitation supply unit
- an excitation measuremernt unit w force transducers and signal conditioners
Signal types (basic)
Stochastic - white noise random signal
Deterministic signals - pure sinusoidal signal
Transient signals - impact hammer
Combined signals
Stochastic signals + and -
+ FRF estimation yields the optimum linear approximation to a nonlinear relation b/w the excitation and the response
+ provides excitation energy to all freqs
+ data acquisition is rel fast even if the number of avgs is high
+ freq characteristics can be controlled and optimised for the specific measurement situation
- true random signals are not periodic in the time window, may cause considerable leakage errors
- since rand signals yields the optimum linear model b/w an input and an output it is not useful for investigating the nonlinear properties of a structure
- take time to prepare excit equip
- in freq regions where the test structure is difficult to excite, ie the receptance is low, the FRF suffers from low signal to noise ratio (often look at structures that are easy to excite though, so not really a problem)
summary: pure random signal is often one of the first excit signals that is tried in a measurement situation
Deterministic signals (stepped sine) + and -
+ no problem w/ leakage errors
+ very high signal to noise ratio since the excit energy is concentrated to one single freq
+ best choice when nonlinear properties properties are investigated
+ once stationary conditions is reached it is straight froward task to calculate the FRF from the amplitude and phase properties at a single freq component
- extremely slow when a range of freqs has to be covered
…better alternative yet is to sweep the freq through the desired freq range
summary: swept sine is the most frequently used deterreminsitic signal. Accurate but slow, so really only use when very accurate results required. Stepped sine signal may be an alternative if accurate results required in a narrow freq range
Transient signals + and -
Starts and ends at 0. in theory contains energy at all freqs. Rise and fall times determine the harmonics…short rise and fall times leads to high energy at the harmonics and vice versa
STEEL TIP: short pulse gives higher upper freq limit
PLASTIC TIP: longer pulse gives shorter lower upper frequency limit
+ like stochastic signals, it gives excit energy in a WIDE FREQ BAND
+ the transient excit methods used in practice are SIMPLE and FAST
- in practice it is not possible to perform a large number of averages
- low CONTROL over the excitation spectrum
summary: useful for quick investigations of a wide freq range. ipact excitation using a hammer is usually the first method tried in a measurement. next choice is usually a shaker.
Combined signals
periodic random signal: both excitation and response signals are periodic in the time window and leakage errors avoided (positive aspects of periodic and random signals)
burst random signal: properties of random and transient signals.
Exciters (types and side notes)
supply the test object with excit energy.
IMPACT HAMMER: has a force transducer that converts impact force to electric signal. Stiffer tip-narrow force pulse and force spectrum w/ energy at higher freqs. Its MASS is also important, a heavy test structure requires a hammer w/ high mass and vice versa.
+ FAST measurements
+ LOADING of the object is LIMITED to a minimum
SHAKER: Electrodynamic…. moving coil placed in a permanent magnetic field, a time varying electrtic current introduced will produce a force w/ the same time variation
- force time history is LIMITED by the mechanical PROPERTIES(stiffness, mass) of shaker table.
Electrohydraulic…. hydraulic power by a pump driven by an electric motor
+ can generate very HIGH FORCES
+ no lower freq limit
+ generate high displacements
- LOW UPPER FREQ limit at about 100 Hz
controlled by internal signal sources: + can be directly controlled and optimised by the FFT analyser to give best possible results
or elctrohydraulic.
Force transducers
sensors which give an electric output signal proportional to the force loading its terminals
1) Piezoelectric force transducers
2) load cells based on strain gauges (resistance changes in proportion to strain)
- any transducer based on piezoelectricity must be operated together with a charge amplifier
- strain gauges can measure w/ high sensitivity for low freqs down to DC ie 0 Hz. Piezoel. transducers cannot measure at DC and suffer from decreasing sensitivity at low freqs.
- strain gauge based transducers are easier to design for a wider range of applications (torque, bending, shear)
- the integrated strain gauge transducers are larger in size and more expensive than piezoelectric transducers
Force signal conditioning
(systems consist of preamplifiers and various filters)
- force transducer output should be amplified so that it covers as large a part as possible of the analyser input range(if only a small part is used, the signal to noise ratio may become too low)
- Make sure to sample the signal w/ as high sampliong rate as possible w/o getting data storage problems(can always downsample after to a smaple rate suitable for your purpose) a high sampling rate will incerase dynamic range
- good to filter the signal to remove parts of the signal not needed(requires that the filter has negl. influence on the significant parts of the signal)
Excitation measurement in practice
inaccurate excit maybe one of the most important error sources in receptance measurements..
- force transducer mounted as close and rigidly as possible to the excit point(use threaded stud or threaded washer)
- contributions from undesired DOFs very difficult…if force not applied to center of gravity we receive combined rotation and translation, like bending moment. impossible to avoid but we can make them negligable through for example push rods.
- push rod is the coupling element b/w the transducer and the shaker
- shaker should be vibrationally isolated from the environment to reduce flanking transmission
-
Response measurement
(similar to excit measurement)
Response is NOT CONTROLLED and could be small and hidden in noise.
Accurate response measurement results require proper signal processing to enhance the response signal:
- averaging
- windowing
- filtering
