内蒙古民族大学学报（自然科学版）
內矇古民族大學學報（自然科學版）
내몽고민족대학학보（자연과학판）
JOURNAL OF INNER MONGOLIA UNIVERSITY FOR NATIONALITIES(NATURAL SCIENCES)
2015年
1期
5-9
,共5页
试探函数方法%变截面杆%纵振动%固有频率
試探函數方法%變截麵桿%縱振動%固有頻率
시탐함수방법%변절면간%종진동%고유빈솔
Trial function method%Variable cross-section rod%Longitudinal vibration%Matural Frequency
用一种新的试探函数方法，研究了变截面杆的纵振动问题。首先用试探函数方法，研究一般变截面杆的纵振动控制方程，得到了一种新型变截面杆，并给出了此杆控制方程的贝塞尔函数形式的精确解析解。其次，求出了两端自由边界条件下的频率方程，计算出了无量纲固有频率，并绘制位移振幅变化曲线，分析了节点位置、放大系数和形状因数等性能参量。结果表明，新型变截面杆有较大的形状因数，放大系数也有一定的提高。结果对一种新型变截面杆的设计具有一定的理论参考价值。
用一種新的試探函數方法，研究瞭變截麵桿的縱振動問題。首先用試探函數方法，研究一般變截麵桿的縱振動控製方程，得到瞭一種新型變截麵桿，併給齣瞭此桿控製方程的貝塞爾函數形式的精確解析解。其次，求齣瞭兩耑自由邊界條件下的頻率方程，計算齣瞭無量綱固有頻率，併繪製位移振幅變化麯線，分析瞭節點位置、放大繫數和形狀因數等性能參量。結果錶明，新型變截麵桿有較大的形狀因數，放大繫數也有一定的提高。結果對一種新型變截麵桿的設計具有一定的理論參攷價值。
용일충신적시탐함수방법，연구료변절면간적종진동문제。수선용시탐함수방법，연구일반변절면간적종진동공제방정，득도료일충신형변절면간，병급출료차간공제방정적패새이함수형식적정학해석해。기차，구출료량단자유변계조건하적빈솔방정，계산출료무량강고유빈솔，병회제위이진폭변화곡선，분석료절점위치、방대계수화형상인수등성능삼량。결과표명，신형변절면간유교대적형상인수，방대계수야유일정적제고。결과대일충신형변절면간적설계구유일정적이론삼고개치。
In this thesis, the problem on longitudinal vibration of variable cross-section rod is studied by using a new kind of trial function method. First, the longitudinal vibration of variable cross-section rod’s general governing equa-tion is studied by using trial function method, and a new type of variable cross-section rod is obtained, and then exact analytical solution in Bessel function form to governing equation is given. Second, according to the both ends free boundary conditions, the frequency equation is established, and the dimensionless natural frequencies are calculated, and then the graphs of displacement amplitudes are plotted, the performance factors such as, displacement node, am-plitude amplification factor and form factor are analyzed. Results indicate that new type of variable cross-section rod’ s form factor is larger and it is better in amplitude amplification factor. The results will provide a valuable theoretical reference for the design of new type of variable cross-section rod.
