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中文摘要：
采用有限差分法研究在自由端固连刚性质量的非均匀立柱的横向自由振动响应.其中考虑端部集中质量的惯性力以及集中质量和梁的自重产生的轴向压力对系统振动的影响.采用有限差分法求解自由振动对应的变系数常微分方程两点边值问题,推导出递推求解数值计算过程,获得变截面立柱的自由振动响应,给出固有频率数值解.分析截面变化参数以及由重力产生的轴向压力对系统横向振动固有频率的影响.结果表明,随着截面非均匀参数值的增加频率增加,随着轴向压力的增加频率减小.
英文摘要：
Finite difference method was employed to study the transverse free vibration of the non-uniform column with a fixed rigid mass at its free end.The effects of the inertial force of the mass as well as the axial pressure caused by the mass and weight of the column,on the system free vibration were taken into account.Using finite difference method,the solution of two-point boundary problem of fourth-order ordinary differential equation was performed.The numerically recursive process and free vibration characteristics of column with variable cross-section was set up and obtained,respectively.Then,the numerical solution of natural frequency was given.The influence of the varying cross-section and the axial gravitational pressure on the natural frequency was analyzed.The results showed that the frequency would increase with the increase of the cross-sectional parameters and decrease with the axial pressure.
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Three-dimensional analysis for transient coupled thermoelastic response of a functionally graded rec
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