噪声与振动控制
譟聲與振動控製
조성여진동공제
NOISE AND VIBRATION CONTROL
2014年
3期
6-10,14
,共6页
振动与波%变截面%旋转梁%有限差分%固有频率%状态空间
振動與波%變截麵%鏇轉樑%有限差分%固有頻率%狀態空間
진동여파%변절면%선전량%유한차분%고유빈솔%상태공간
vibration and wave%taper%rotating beams%finite difference%natural frequency%state space
根据哈密尔顿原理建立旋转梁的弯曲振动方程，运用有限差分方法对旋转梁的动力方程进行离散处理，得到旋转梁的质量和刚度矩阵。借助MATLAB振动工具箱对系统的弯曲振动进行模态分析，得到圆形、矩形和叶片类型三种变截面旋转梁的固有频率，并与相关文献进行比较。在差分离散矩阵的基础上，建立旋转梁的线性定常状态空间方程。运用MATLAB振动工具箱对旋转梁的自治系统和非自治系统进行仿真，分别求得旋转梁的时间位移曲线和相轨迹。最后对非自治系统的旋转梁进行频域分析，得到幅频特性和相频特性曲线。
根據哈密爾頓原理建立鏇轉樑的彎麯振動方程，運用有限差分方法對鏇轉樑的動力方程進行離散處理，得到鏇轉樑的質量和剛度矩陣。藉助MATLAB振動工具箱對繫統的彎麯振動進行模態分析，得到圓形、矩形和葉片類型三種變截麵鏇轉樑的固有頻率，併與相關文獻進行比較。在差分離散矩陣的基礎上，建立鏇轉樑的線性定常狀態空間方程。運用MATLAB振動工具箱對鏇轉樑的自治繫統和非自治繫統進行倣真，分彆求得鏇轉樑的時間位移麯線和相軌跡。最後對非自治繫統的鏇轉樑進行頻域分析，得到幅頻特性和相頻特性麯線。
근거합밀이돈원리건립선전량적만곡진동방정，운용유한차분방법대선전량적동력방정진행리산처리，득도선전량적질량화강도구진。차조MATLAB진동공구상대계통적만곡진동진행모태분석，득도원형、구형화협편류형삼충변절면선전량적고유빈솔，병여상관문헌진행비교。재차분리산구진적기출상，건립선전량적선성정상상태공간방정。운용MATLAB진동공구상대선전량적자치계통화비자치계통진행방진，분별구득선전량적시간위이곡선화상궤적。최후대비자치계통적선전량진행빈역분석，득도폭빈특성화상빈특성곡선。
The bending vibration equations of rotating tapered beams are established based on Hamilton’s principle. The equations are then discretized by using finite difference method and the mass and stiffness matrices are gotten. The natural frequencies for circular, rectangular and blade cross-section beams are obtained by using MATLAB vibration toolbox. The results of computation are analyzed and compared with those in relevant references. The linearized stationary state spaces of autonomous and non- autonomous systems are built based on the mass and stiffness matrices. Then the displacement curves and phase tracks of the rotating tapered beams are drawn with MATLAB vibration toolbox. Finally the amplitude-frequency and phase-frequency characteristic curves for the non-autonomous rotating tapered beams are plotted based on the frequency-domain analysis.
