振动与冲击
振動與遲擊
진동여충격
Journal of Vibration and Shock
2015年
19期
98-102
,共5页
矩形板%点支承%基频%Rayleigh-Ritz 方法%Lagrange 乘子
矩形闆%點支承%基頻%Rayleigh-Ritz 方法%Lagrange 乘子
구형판%점지승%기빈%Rayleigh-Ritz 방법%Lagrange 승자
rectangular plates%point supports%fundamental frequency%Rayleigh-Ritz method%Lagrangian multiplier
四角点固定支承矩形板横向振动固有特性的研究对其实际应用及故障诊断具有重要意义。基于能量守恒原理并结合固定支承点处的约束条件建立四角点固定支承矩形板横向振动的拉格朗日方程。采用幂级数多项式来描述其振型函数，根据 Rayleigh-Ritz 理论推导出四角点固定支承矩形板的横向振动频率方程；由频率方程给出了不同长／宽比矩形板基频的理论计算结果，并应用该方法获得了四角点简支矩形板的频率方程。对典型算例的理论计算结果和有限元分析结果进行比较和分析，给出便于工程应用求解其基频的近似计算式；通过试验研究表明理论计算结果与有限元分析结果和试验结果具有较好的一致性。
四角點固定支承矩形闆橫嚮振動固有特性的研究對其實際應用及故障診斷具有重要意義。基于能量守恆原理併結閤固定支承點處的約束條件建立四角點固定支承矩形闆橫嚮振動的拉格朗日方程。採用冪級數多項式來描述其振型函數，根據 Rayleigh-Ritz 理論推導齣四角點固定支承矩形闆的橫嚮振動頻率方程；由頻率方程給齣瞭不同長／寬比矩形闆基頻的理論計算結果，併應用該方法穫得瞭四角點簡支矩形闆的頻率方程。對典型算例的理論計算結果和有限元分析結果進行比較和分析，給齣便于工程應用求解其基頻的近似計算式；通過試驗研究錶明理論計算結果與有限元分析結果和試驗結果具有較好的一緻性。
사각점고정지승구형판횡향진동고유특성적연구대기실제응용급고장진단구유중요의의。기우능량수항원리병결합고정지승점처적약속조건건립사각점고정지승구형판횡향진동적랍격랑일방정。채용멱급수다항식래묘술기진형함수，근거 Rayleigh-Ritz 이론추도출사각점고정지승구형판적횡향진동빈솔방정；유빈솔방정급출료불동장／관비구형판기빈적이론계산결과，병응용해방법획득료사각점간지구형판적빈솔방정。대전형산례적이론계산결과화유한원분석결과진행비교화분석，급출편우공정응용구해기기빈적근사계산식；통과시험연구표명이론계산결과여유한원분석결과화시험결과구유교호적일치성。
The natural characteristics of a rectangular plate clamped at 4 corner points are of importance in its application and fault diagnosis.Firstly,its Lagrange equation of transverse vibration based on the principle of energy conservation under constraint conditions of support locations was established to analyze its free vibration problem. Secondly,the frequency equation of the rectangular plate was obtained using Rayleigh-Ritz method with simple polynomials as its modal functions.Finally,the fundamental frequencies were gained for different side ratios according to the theoretical results of the rectangular plates,they were compared with those obtained using the finite element method. In order to get the fundamental frequencies conveniently,approximate expressions were deduced for a typical plate with certain geometrical parameters and material constants in practical engineering.It was shown that the theoretical results agree well with those obtained using the finite element method and the test data.
