Functionally graded materials(FGMs)are a novel class of composite materials that have attracted significant attention in the field of engineering due to their unique mechanical properties.This study aims to explore th...Functionally graded materials(FGMs)are a novel class of composite materials that have attracted significant attention in the field of engineering due to their unique mechanical properties.This study aims to explore the dynamic behaviors of an FGM stepped beam with different boundary conditions based on an efficient solving method.Under the assumptions of the Euler-Bernoulli beam theory,the governing differential equations of an individual FGM beam are derived with Hamilton’s principle and decoupled via the separation-of-variable approach.Then,the free and forced vibrations of the FGM stepped beam are solved with the transfer matrix method(TMM).Two models,i.e.,a three-level FGM stepped beam and a five-level FGM stepped beam,are considered,and their natural frequencies and mode shapes are presented.To demonstrate the validity of the method in this paper,the simulation results by ABAQUS are also given.On this basis,the detailed parametric analyses on the frequencies and dynamic responses of the three-level FGM stepped beam are carried out.The results show the accuracy and efficiency of the TMM.展开更多
The nonlinear dynamic behaviors of a double cable-stayed shallow arch model are investigated under the one-to-one-to-one internal resonance among the lowest modes of cables and the shallow arch and external primary re...The nonlinear dynamic behaviors of a double cable-stayed shallow arch model are investigated under the one-to-one-to-one internal resonance among the lowest modes of cables and the shallow arch and external primary resonance of cables. The in-plane governing equations of the system are obtained when the harmonic excitation is applied to cables. The excitation mechanism due to the angle-variation of cable tension during motion is newly introduced. Galerkin’s method and the multi-scale method are used to obtain ordinary differential equations (ODEs) of the system and their modulation equations, respectively. Frequency- and force-response curves are used to explore dynamic behaviors of the system when harmonic excitations are symmetrically and asymmetrically applied to cables. More importantly, comparisons of frequency-response curves of the system obtained by two types of trial functions, namely, a common sine function and an exact piecewise function, of the shallow arch in Galerkin’s integration are conducted. The analysis shows that the two results have a slight difference;however, they both have sufficient accuracy to solve the proposed dynamic system.展开更多
基金the National Natural Science Foundation of China(Nos.12302007,12372006,and 12202109)the Specific Research Project of Guangxi for Research Bases and Talents(No.AD23026051)。
文摘Functionally graded materials(FGMs)are a novel class of composite materials that have attracted significant attention in the field of engineering due to their unique mechanical properties.This study aims to explore the dynamic behaviors of an FGM stepped beam with different boundary conditions based on an efficient solving method.Under the assumptions of the Euler-Bernoulli beam theory,the governing differential equations of an individual FGM beam are derived with Hamilton’s principle and decoupled via the separation-of-variable approach.Then,the free and forced vibrations of the FGM stepped beam are solved with the transfer matrix method(TMM).Two models,i.e.,a three-level FGM stepped beam and a five-level FGM stepped beam,are considered,and their natural frequencies and mode shapes are presented.To demonstrate the validity of the method in this paper,the simulation results by ABAQUS are also given.On this basis,the detailed parametric analyses on the frequencies and dynamic responses of the three-level FGM stepped beam are carried out.The results show the accuracy and efficiency of the TMM.
基金Project supported by the National Natural Science Foundation of China(Nos.11572117,11502076,and 11872176)
文摘The nonlinear dynamic behaviors of a double cable-stayed shallow arch model are investigated under the one-to-one-to-one internal resonance among the lowest modes of cables and the shallow arch and external primary resonance of cables. The in-plane governing equations of the system are obtained when the harmonic excitation is applied to cables. The excitation mechanism due to the angle-variation of cable tension during motion is newly introduced. Galerkin’s method and the multi-scale method are used to obtain ordinary differential equations (ODEs) of the system and their modulation equations, respectively. Frequency- and force-response curves are used to explore dynamic behaviors of the system when harmonic excitations are symmetrically and asymmetrically applied to cables. More importantly, comparisons of frequency-response curves of the system obtained by two types of trial functions, namely, a common sine function and an exact piecewise function, of the shallow arch in Galerkin’s integration are conducted. The analysis shows that the two results have a slight difference;however, they both have sufficient accuracy to solve the proposed dynamic system.
