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Spectral geometry-incremental harmonic balance solutions for nonlinear vibrations of FGP beams
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Rui ZHONG1, 2, Ruihua WANG1, 2, Qingshan WANG1, 2
Journal of Vibration Engineering | 2025, 38(4) : 731 - 738
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Journal of Vibration Engineering | 2025, 38(4): 731-738
Spectral geometry-incremental harmonic balance solutions for nonlinear vibrations of FGP beams
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Rui ZHONG1, 2, Ruihua WANG1, 2, Qingshan WANG1, 2
Affiliations
  • 1.College of Mechanical and Electrical Engineering，Central South University，Changsha 410083，China
  • 2.State Key Laboratory of Precision Manufacturing for Extreme Service Performance，Central South University，Changsha 410083，China
Published: 2025-04-10 doi: 10.16385/j.cnki.issn.1004-4523.2025.04.008
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A spectral geometry-incremental harmonic balance method（SGM-IHBM）is proposed to study the nonlinear vibration characteristics of functionally graded porous（FGP）beams with geometric nonlinearities. The geometrically nonlinear strain-displacement relationship of the beam structure is obtained according to the Von-Karman theory，and the Lagrange energy function of the FGP beam is derived based on the Timoshenko theory. The spectral geometric series are used to characterize each displacement component of the beam structure，and the linear modal components are introduced to establish the nonlinear reduced-order equations of the FGP beams，and then the incremental harmonic balance（IHB）method is used to trace the dynamical response solution of the reduced-order model of the FGP beams. The correctness of the nonlinear model in this paper is verified by comparing the SGM-IHBM solution with the literature solution，and then the effects of porosity，thickness，and excitation amplitude on the nonlinear vibration characteristics of FGP beams are analyzed.

nonlinear vibration  /  FGP beam  /  spectral geometry  /  incremental harmonic balance method
Rui ZHONG, Ruihua WANG, Qingshan WANG. Spectral geometry-incremental harmonic balance solutions for nonlinear vibrations of FGP beams[J]. Journal of Vibration Engineering, 2025 , 38 (4) : 731 -738 . DOI: 10.16385/j.cnki.issn.1004-4523.2025.04.008
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doi: 10.16385/j.cnki.issn.1004-4523.2025.04.008
  • Receive Date：2023-09-20
  • Online Date：2026-02-12
  • Published：2025-04-10
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  • Received：2023-09-20
  • Revised：2023-11-10
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    1.College of Mechanical and Electrical Engineering，Central South University，Changsha 410083，China
    2.State Key Laboratory of Precision Manufacturing for Extreme Service Performance，Central South University，Changsha 410083，China
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表12种不同金属材料的力学参数
科
Family		 属数
Number of
genus		 种数
Number of
species		 占总种数比例
Percentage of
total species (%)		 属
Genus		 种数
Number of
species		 占总种数比例
Percentage of total
species (%)
鹅膏菌科Amanitaceae 2 11 5.26 鹅膏菌属 Amanita 10 4.78
小菇科 Mycenaceae 2 12 5.74 丝盖伞属 Inocybe 5 2.39
多孔菌科 Polyporaceae 8 14 6.70 蜡蘑属 Laccaria 5 2.39
红菇科 Russulaceae 3 23 11.00 小皮伞属 Marasmius 6 2.87
小菇属 Mycena 11 5.26
光柄菇属 Pluteus 5 2.39
红菇属 Russula 17 8.13
栓菌属 Trametes 5 2.39
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