Naslov
Estimation of glass plate boundary conditions using laser Doppler vibrometer

Autori
Kožar, Ivica ; Plovanić, Marina ; Sulovsky, Tea

Vrsta, podvrsta i kategorija rada
Sažeci sa skupova, sažetak, znanstveni

Izvornik
10th International Congress of Croatian Society of Mechanics, Book of Abstracts / - : Hrvatsko društvo za mehaniku (HDM), 2022, 165-166

Skup
10th International Congress of Croatian Society of Mechanic (ICCSM 2022)

Mjesto i datum
Pula, Hrvatska, 28.09.2022. - 30.09.2022

Vrsta sudjelovanja
Predavanje

Vrsta recenzije
Nije recenziran

Ključne riječi
Parameter estimation ; boundary conditions ; laser Doppler vibrometer ; glass plate

Sažetak
Many sensors and data acquisition devices provide us with a large amount of data, and estimating properties and parameters from measurements is becoming increasingly important. Some material properties can be measured directly, but most can only be estimated indirectly. Structural parameters can almost always only be estimated indirectly. Due to the mounting technique with an elastic resin, the boundary conditions of a glass plate are between simply supported and clamped. However, comparing the results of computer models and experiments requires a fairly accurate knowledge of the extent to which the supports are clamped. In this paper, we present a method for estimating the boundary conditions of glass plates based on measurements of the vibration velocity at some points on the plate. The mathematical model is based on the theory of thin plates discretized with spectral elements [1]. Among other possibilities, Chebyshev polynomials are chosen for spatial interpolation of the domain of the differential equation. The application of the spectral method is to solve the strong formulation of a structural problem. The method can be formulated using matrix differentiation operators 𝒑𝑥=𝑫𝑁∙𝒑. (1) where p is a vector of discrete data of size N, px is its derivative, and DN is a matrix differential operator, a square matrix of size [NxN]. The boundary conditions must be included in DN. The plate is modelled with the Kirchhoff equation for thin plates discretized with N and M points in each direction. After discretization, the thin plate equation has the form ∆∆𝒘= (𝑰𝑀⊕𝑫𝑁^4)+2(𝑫𝑀^2⊕𝑰𝑁)(𝑰𝑀⊕𝑫𝑁^2)+ (𝑫𝑀^4⊕𝑰𝑁). (2). Here ⊕ is the Kronecker product and DN and DM are the derivative matrices for the respective directions. The corresponding boundary conditions are substituted into equation (2) with Lagrange multipliers. The load must be discretized in a form compatible with equation (2). Our experimental setup consists of a laser Doppler vibrometer, an excitation device with frequency generator, and accelerometers with loggers. The glass plate is excited and the vibration velocities are measured with the laser Doppler and the accelerations with the accelerometers. The spectrum of the excitation is as close as possible to the white noise spectrum. Fig.1 shows some of the experimental equipment and some measurement results. The recorded data are then compared with the vibration results from the numerical model. Unknown boundary conditions are parameterized with the parameter 'k', which describes the extent of the constraint on the supports and has a value in the interval (0..1). The parameter 'k' is visible only after the boundary conditions are introduced using Lagrange multipliers. The procedure is similar to [1], [2] and [3], but at this stage of development only experimental and calculated vibration results are compared. We propose to estimate the constraint on thin plates using experimental measurements and numerical simulations. The unknown extent of the constraint on the supports is determined from different types of data sets, such as displacements, velocities, and accelerations at different sampling frequencies. The extraction of the unknown parameter 'k' is done using inverse analysis techniques.

Izvorni jezik
Engleski

Znanstvena područja
Građevinarstvo, Temeljne tehničke znanosti

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