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Exact receptance function of a tapered afg beam with nonlinearly varying ratios of beam properties carrying concentrated masses

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This paper presents a method for establishing the exact receptance function of a tapered axially functionally graded (AFG) beam with nonlinear ratios of properties using the Adomian method. In current papers, the Adomian method was applied for linearly tapered beams where the geometric series was used conveniently. | Vietnam Journal of Mechanics Vol. 45 No. 4 2023 pp. 296 317 DOI https doi.org 10.15625 0866-7136 19697 EXACT RECEPTANCE FUNCTION OF A TAPERED AFG BEAM WITH NONLINEARLY VARYING RATIOS OF BEAM PROPERTIES CARRYING CONCENTRATED MASSES Thao Thi Bich Dao1 2 Khoa Viet Nguyen1 2 3 Quang Van Nguyen1 1 Institute of Mechanics VAST Hanoi Vietnam 2 Graduate University of Science and Technology VAST Hanoi Vietnam 3 VNU University of Engineering and Technology Hanoi Vietnam E-mail nvkhoa@imech.vast.vn Received 15 October 2023 Revised 27 December 2023 Accepted 29 December 2023 Published online 31 December 2023 Abstract. This paper presents a method for establishing the exact receptance function of a tapered axially functionally graded AFG beam with nonlinear ratios of properties using the Adomian method. In current papers the Adomian method was applied for linearly tapered beams where the geometric series was used conveniently. However for nonuni- form AFG beams with nonlinearly varying ratios of properties the geometric series can- not be used thus the other type of power series needs to be established and applied. In this paper the derivation of the power series applied for obtaining the exact receptance function of a nonuniform AFG beam with nonlinearly varying ratios of properties is pre- sented. Numerical simulation results of the receptance function of a tapered AFG beam with nonlinearly varying ratios of beam properties carrying concentrated masses are con- ducted and provided. The influences of the concentrated masses and the varying ratios of properties of beam on the receptance matrix are also investigated and presented. Keywords receptance frequency response function concentrated mass functionally graded material beam. 1. INTRODUCTION Frequency response function is used in many problems such as finite element model updating vibration and noise control system identification structural damage detec- tion dynamic optimization numerous mechanical aerospace and civil .