[Turkmath:5656] Gebze Teknik Üniversitesi Matematik Bölümü Genel Seminerleri

[GTU Mathematics]

Sayın Liste Üyeleri,

3 Haziran Cuma günü saat 14:00'da *Doç Dr. Onur Baysal *(University of
Malta- Malta) *"*  *A Numerical Method for Source Identification
Problem Related to Dynamical Kirchoff Plate Equation* *”  *başlıklı bir
seminer verecektir. Seminerin detayları aşağıda olup tüm ilgilenenler
davetlidir.

Seminer için Microsoft Teams platformu kullanılacaktır. Seminere katılmak
için aşağıdaki linki kullanabilirsiniz:

https://teams.microsoft.com/l/meetup-join/19%3a0ae91f7b86a24e8fa1d818a6f74b22a1%40thread.tacv2/1653904979472?context=%7b%22Tid%22%3a%22066690f2-a8a6-4889-852e-124371dcbd6f%22%2c%22Oid%22%3a%22a343f6fd-86f8-4abe-95cf-3c7f4ad5f0ca%22%7d

Seminere bağlanırken aşağıdaki pencereyi görürseniz,


[image: image.png]


lütfen* Allow (İzin ver) *seçeneğine tıklayınız. Bu sizin toplantıya kamera
ve mikrofonunuzla bağlanabilmenizi sağlar.


Seminere giriş yaparken lütfen gerçek ve tam adınızı kullanınız.


Konuşmadığınız sürece lütfen mikrofonunuzu kapalı tutunuz.

Saygılarımızla.


Dear all,

*Assoc.Prof.Dr. Onur Baysal *from University of Malta (Malta) will give a
talk titled  *"*  *A Numerical Method for Source Identification
Problem Related to Dynamical Kirchoff Plate Equation* *” * on June 3rd at
14:00. All interested are invited.

Abstract: Kirchoff Plate model is an integral part of most engineering
fields including plate and shell structures [1]. In [2], some important
identification problems are stated and some properties are analyzed such as
stability and uniqueness. In this work we study the inverse problem of
identifying the unknown load distribution 𝑓(𝑥, 𝑦) in the rectangular
domain 𝛺: = (0, 𝑘) × (0, 𝑙) such that

  𝑢𝑡𝑡 + 𝐷𝛥2𝑢 = 𝑔(𝑡)𝑓(𝑥, 𝑦) in 𝛺𝑡: = 𝛺 × (0, 𝑇)

  𝑢(𝑥, 𝑦, 0) = 0, 𝑢𝑡(𝑥, 𝑦, 0) = 0, for (𝑥, 𝑦) ∈ 𝛺,

  𝑢 = 0, 𝜕𝑛 = 0, on 𝜕𝛺𝑖 × [0, 𝑇], for 𝑖 = 1,2,3,4,

  𝑢 = 0, −𝐷(𝜈𝑢𝑥𝑥 + 𝑢𝑦𝑦) = 0 on 𝜕𝛺1 × [0, 𝑇].


Here 𝑢(𝑥, 𝑦, 𝑡) or (𝑢(𝑥, 𝑦, 𝑡; 𝑓)) is the displacement at a point (𝑥,
𝑦) ∈ 𝛺 and a time 𝑡 ∈ [0, 𝑇], 𝜕𝑛𝑢 denotes the normal derivative of 𝑢
, 𝑔 ∈ 𝐿2(0, 𝑇) is the (known) temporal load, 𝐷: = 𝐸⁄(1 − 𝑣2) is the
bending


stiffness, 𝑣 ∈ (0,1)is the Poisson’s ratio, 𝐸 is the elasticity modulus
and 𝜕𝛺 = ∑ (i=1 to 4 ) 𝜕𝛺𝑖 where 𝜕𝛺1 = (0, 𝑘) × {0}, 𝜕𝛺2 = {𝑘} ×
(0, 𝑙), 𝜕𝛺3 = (0, 𝑘) × {𝑙}, 𝜕𝛺4 = {0} × (0, 𝑙). In determination of
𝑓we have the following


boundary observation on 𝜕𝛺1: 𝜃(𝑥, 𝑡): = 𝑢𝑦(𝑥, 0, 𝑡), for 𝑥 ∈ [0,
𝑙], 𝑡 ∈ [0, 𝑇]

The conjugate gradient algorithm (CGA) is designed for the numerical
solution of the identification problem. The proposed approach is based on
weak solution theory for PDEs, Tikhonov regularization combined with the
adjoint method. Computational results, obtained for noisy output data, are
illustrated to show an efficiency and accuracy of the proposed approach,
for typical classes of source functions.


References

1.  L. Fryba, Vibrations of the Solids and Structures under Moving Loads,
Thomas Telford Publishing House, 1999.
  2.  M. Yamamoto, Determination of forces in vibrations of beams and plates
by point wise and line observations, J. Inv. Ill-Posed Problems, Vol.4,
No.5, pp.437-457 1996.


Microsoft Teams platform will be used for the seminar. To join the seminar,
please use the following link:

https://teams.microsoft.com/l/meetup-join/19%3a0ae91f7b86a24e8fa1d818a6f74b22a1%40thread.tacv2/1653904979472?context=%7b%22Tid%22%3a%22066690f2-a8a6-4889-852e-124371dcbd6f%22%2c%22Oid%22%3a%22a343f6fd-86f8-4abe-95cf-3c7f4ad5f0ca%22%7d

If you see the following window when connecting to the seminar,
[image: image.png]



please select *Allow**. *Then you will be able to use your microphone and
camera during the seminar.


Please use your real and complete name when you enter the system.

Please switch your microphone off unless you are speaking.


Sincerely
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