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. | Vietnam Journal of Mechanics Vol. 46 No. 1 2024 pp. 15 30 DOI https 0866-7136 20575 FREQUENCY RESPONSE FUNCTION OF CRACKED TIMOSHENKO BEAM MEASURED BY A DISTRIBUTED PIEZOELECTRIC SENSOR 1 Nguyen Tien Khiem Tran Thanh Hai1 Nguyen Thi Lan1 Ho Quang Quyet1 Ha Thanh Ngoc2 Pham Van Kha3 1 Institute of Mechanics VAST Hanoi Vietnam 2 Institute of Mechanics and Environmental Engineering VUSTA Hanoi Vietnam 3 HCMC Occupational Safety amp Health Inspection amp Training JSC Ho Chi Minh City Vietnam E-mail ntkhiem@ Received 20 January 2024 Revised 14 March 2024 Accepted 25 March 2024 Published online 31 March 2024 Abstract. 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 re- sponse 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. Keywords frequency response function cracked Timoshenko beam piezoelectric layer sensitivity analysis. 1. INTRODUCTION The vibration-based method VBM has been proven to be the most productive tech- nique in health monitoring of engineering structures and the important results obtained recently in this field were reviewed in 1 3 . As is well known the core problem in struc-
