Frequency response function of cracked Timoshenko beam measured by a distributed piezoelectric sensor

Nguyen Tien Khiem, Tran Thanh Hai, Nguyen Thi Lan, Ho Quang Quyet, Ha Thanh Ngoc, Pham Van Kha
Author affiliations


  • Nguyen Tien Khiem \(^1\) Institute of Mechanics, VAST, Hanoi, Vietnam
  • Tran Thanh Hai \(^1\) Institute of Mechanics, VAST, Hanoi, Vietnam
  • Nguyen Thi Lan \(^1\) Institute of Mechanics, VAST, Hanoi, Vietnam
  • Ho Quang Quyet \(^1\) Institute of Mechanics, VAST, Hanoi, Vietnam
  • Ha Thanh Ngoc \(^2\) Institute of Mechanics and Environmental Engineering, VUSTA, Hanoi, Vietnam
  • Pham Van Kha \(^3\) HCMC Occupational Safety & Health Inspection & Training JSC, Ho Chi Minh City, Vietnam



frequency response function, cracked Timoshenko beam, piezoelectric layer, sensitivity analisis


In the present report, a novel concept of frequency response function (FRF) is introduced for piezoelectric beam. First, a model of Timoshenko beam bonded with a piezoelectric layer is established and used for deriving the conventional frequency response function acknowledged as mechanical frequency response function (MERF). Then, the output charge produced in the piezoelectric layer is calculated from the MFRF and therefore obtained frequency-dependent function is called electrical frequency response function (EFRF) for the integrated beam. This concept of FRF depends only on exciting position and can be explicitly expressed through crack parameters. So that it provides a novel instrument to modal analysis and structural health monitoring of electro-mechanical systems, especially for crack detection in beams using distributed piezoelectric sensor. The sensitivity of EFRF to crack has been examined and illustrated in numerical examples for cracked Timoshenko beam.


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