Appunti del Corso Advanced Measurement Techniques

Experimental set-up

Actuators

• Electrodynamic shaker -> f ↑, bandwidth ↑
• Hydraulic type actuator -> f ↓, bandwidth ↓
• Vibrodrive -> f ↑, bandwidth ↓
• Electrodynamic linear motor -> f = Mω²a ⟹ ↑↑ ↓ ↓ = f ↑ @ ω ↓
• Piezo actuator -> bandwidth at a node -> f ↑, bandwidth ↑

• Low axial effect for bending
• So it just links with the structure for bending
• Can be used as node
• Our piezo needed to have ΔV _i
• Resonance for benders
• Benders provide low energy
• More benders needed to excite
• See the model

• Impacted mass to produce "mapdobe"
• Impact hammer
  • Easy and fast
  • No axial effect
  • Input force not continuous

• Natural excitation -> you don't know the input force at nodes^at the excitation
• point, so you cannot measure the input, that means you won't
• know the force that is exciting
• the system and for this reason
• you can't know how to model the
• model parameters -> operational

Model condition

• Various measuring
• The response -> PS and CS -> rows and
• columns correlation eigenvalues
• Eigenvectors and model
• are estimated

You should you don't know the

model mass excited

to avoid aliasing f_s > 2f_p

to avoid leakage f_p = NA f_s σ = D T = N/f_p

which can be measured in terms of displacement, velocity, and acceleration

Transducers to measure the torque:

• displacement transducers => useful in iterative motion rotating arm
• velocity transducers => not used however the real angular transducers is very useful because its constant, but the price is huge and evaluates the data itself
• the working principle is that the rotating system changes each speed that is caught by the receiver
• piezoelectric accelerometers => it is the most diffused and it is the only able to compute absolute motion on the whole frequency range, that means also great frequency components

• good sensibility
• low weight
• broad dynamic range
• wide frequency range
• simple design
• higher environmental resistance
• low thermal sensitivity
• simple mounting methods

dynamics range = max measured amplitude / min measured amplitude

high free scale means higher dynamic range that allows detection noise S/N

mminüità => annouñ of the atmï of the traveller

Mass < ¹/₁₀ M̃ M̃

M̃ = "base" dynamic mass of the vibrating pot on which it is mounted

1.1 → K_hold medium K_soft

1.1 → K_vpt medium K_hold

SISO → added the method able to work with SDOF systems that mean we perform the modal extraction for any single mode. We can use it also with MDOF systems applying the method for each considered mode & applying it more times, however to do that resonances cannot be close.

SIMO/MIMO → give modal potential for more than one mode. They work on more than one mode at the same time. This mean they are applied to MDOF systems → usual commercial softwares work in this way.

GROUNDED"Prerm like characteristics"

FREE"non domination characteristics"

ex. plate

I mode

II mode

• 1-2 couple is not able to distinguish between the two
• 1-3 couple of modes is good

NEXT path - user's response - PS and CS - auto and user correlation

from mathematical model

mathematical parameters are related

with auto/union correlation, beta of

data and expected values. To reach

a correlation that doesn't depend

on the (unknown) input value.

This means we are able to eliminate

this unit and with algorithm in time

or frequency domain it is possible to

obtain the model parameters. However,

once already functional it is unknown the

model inputs having access.

Microphone performance depends on: environment of work (medium)

• Sensitivity - click or dB Pa
• Frequency range - where the transducer works properly (no peaks or zero responses)
• Maximum admissible acoustic pressure - before damage
• Directivity - sensitivity changes depending on direction
• Dynamic range - max amplitude and min amplitude range

It is interesting to analyze how the sensitivity changes depending on the orientation of the incoming sound pressure wave (incident angle).

• Free-field microphone - sensitivity constant in image & range
• Random incidence microphones - sensitivity constant in wide range
• Pressure microphones - used in high pressure environment

Remember to pay attention to the road effect given by the admission!, indeed an amplifier is always linked to the microphone: increasing the admission (i.e. with raycone) otherwise the loss of high range would be considered by scale. It happens when (T) becomes comparable to microphone admission, so go high frequencies values. To avoid that road effect moreover microphones are in both cases in this way the sensitivity values are converted because they presents low energies due to their lower risk, but the frequency range becomes much.

Moreover, ears are able to overlap and acdiphate the sensitivity depending on the frequency value, they act as a filter. To practically reproduce this effect weighting functions such as the A-weighting, are employed.

Identification of acoustic source represents an important problem in engineering fields so that many techniques exist that implies different approaches and instruments. We can use microphones, intensity probe or numerical methods, depending on the use.

The more simple technique pursued through an array of microphones, to measure the sound field of a source given by an emitting source in the incoming. The sound field is reconstructed at the receiving place thanks to microphones' shane resolution; the microphones array is made of a number of microphones placed in a linear of plane way; then measure the sound pressure at the same time and with the Beamforming algorithms it possible to find the noise source.

Next Demonstration:

m_iq̈_i + c_iq̇_i + k_iq_i = Φ_iF(t)

q_i(t) = ∫_−∞^∞ Φ_i ℓ _• g_i(t−τ)u(τ) dτ

x(t) = ∑_i=1^N Φ_i Φ_T ∫_−∞^t ℓ _• g_i(t−τ) ω dτ

= ∑_i=1^N ∑_k=1^N Φ_i Φ_k ∫_−∞^t+ f_k(ω) g_i(t−τ) ω dτ

= R_ijk(τ) = E [x_ik_(t+T) x_Jk(t)]

= E [ ∑_i=1^N ∑_s=1^N Φ_i Φ_k Φ_s Φ_k ∫_−∞^t+ f_k(ω) g_i(t−τ)g_s(t−τ) f_k(ω) ω dω]

Knowing the input is a random function and using expected value properties, we can bring the random function out of the expected value.

So also doing white noise kp, we know f_pk(τ−τ) = E [ _•(τ) β_c(υ)] = α_k δ(τ−τ) α_k = aωn

So using delta of dirac properties, an integral is eliminated R_ijk(τ) = ∑_i=1^N ∑_s=1^N Φ_i Φ_k Φ_s Φ_k α_k ∫_−∞^t g_i(t+T−τ) g_s(t−τ) dω

I can fit this mathematical model with the measured data. Here, there isn't the dependence on the input force anymore that is the unknown term.

We can find natural frequencies, non-dimensional damping ratios and the mode shapes, that are not needed because we don't know α_k, nor even impose it.