| Nonlinear Vibrations of Timoshenko Beams with Various Boundary Conditions |
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| 作者姓名： | 郭强 刘曦 钟宏志 |
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| 作者单位： | DepartmentofCivilEngineering,TsinghuaUniversity,Beijing100084,China |
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| 基金项目： | Supported by Basic Research Foundation of Tsinghua University (No. JC2001003) |
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| 摘 要： | This paper is concerned with the effects of boundary conditions on the large-amplitude free vibrations of Timoshenko beams The effects of nonlinear terms on the frequency of Timoshenko beams with simply supported ends (supported-supported, SS), clamped ends (clamped-clamped, CC) and one end simply supported and the other end clamped (clamped-supported, CS) are discussed in detail Given a specific vibration amplitude, the change of nonlinear frequency according to the effects of boundary conditions is always in the following descending order: SS, CS, and CC It is found that the slenderness ratio has a significant influence on the nonlinear frequency For slender beams, the nonlinear effects of bending curvature and shear strain are negligible regardless of the boundary conditions For short beams and especially for those of large amplitude vibrations, however, the nonlinear effects of bending curvature and shear strain become noticeable in the following ascending order: SS, CS, and CC
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| 关 键 词： | 非线性振动 边界条件 振幅 微分正交法 Timoshenko梁 |
Nonlinear Vibrations of Timoshenko Beams with Various Boundary Conditions |
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| GUO Qiang,LIU Xi,ZHONG Hongzhi.Nonlinear Vibrations of Timoshenko Beams with Various Boundary Conditions[J].Tsinghua Science and Technology,2004,9(2):125-129. |
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| Authors: | GUO Qiang LIU Xi ZHONG Hongzhi |
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| Institution: | GUO Qiang,LIU Xi,ZHONG Hongzhi Department of Civil Engineering,Tsinghua University,Beijing 100084,China |
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| Abstract: | This paper is concerned with the effects of boundary conditions on the large-amplitude free vi-brations of Timoshenko beams. The effects of nonlinear terms on the frequency of Timoshenko beams with simply supported ends (supported-supported, SS), clamped ends (clamped-clamped, CC) and one end simply supported and the other end clamped (clamped-supported, CS) are discussed in detail. Given a spe-cific vibration amplitude, the change of nonlinear frequency according to the effects of boundary conditions is always in the following descending order: SS, CS, and CC. It is found that the slenderness ratio has a significant influence on the nonlinear frequency. For slender beams, the nonlinear effects of bending curva-ture and shear strain are negligible regardless of the boundary conditions. For short beams and especially for those of large amplitude vibrations, however, the nonlinear effects of bending curvature and shear strain become noticeable in the following ascending order: SS, CS, and CC. |
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| Keywords: | nonlinear vibration Timoshenko beam differential quadrature method |
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