CAJ | 학술논문

以空间曲梁理论为基础,对一般横截面形状自然弯扭梁的振动特性进行了研究,包括横向剪切变形、转动惯量以及和扭转有关的翘曲的影响.应用差分法对空间坐标进行离散,把控制方程化为关于时间的常微分方程组,通过求解得到该梁的固有频率.在分析简谐激励作用下结构的动力响应时,对精细时程积分法中的向量积分采用Newton-Cotes公式,避免了矩阵求逆的困难.两端固支曲梁的固有频率以及强迫振动时的位移时程曲线的计算结果表明,数值解和有限元结果非常接近;两端固支圆截面螺旋弹簧固有频率的计算结果同样表明,数值解和相关文献的结果吻合得很好.
이공간곡량이론위기출,대일반횡절면형상자연만뉴량적진동특성진행료연구,포괄횡향전절변형、전동관량이급화뉴전유관적교곡적영향.응용차분법대공간좌표진행리산,파공제방정화위관우시간적상미분방정조,통과구해득도해량적고유빈솔.재분석간해격려작용하결구적동력향응시,대정세시정적분법중적향량적분채용Newton-Cotes공식,피면료구진구역적곤난.량단고지곡량적고유빈솔이급강박진동시적위이시정곡선적계산결과표명,수치해화유한원결과비상접근;량단고지원절면라선탄황고유빈솔적계산결과동양표명,수치해화상관문헌적결과문합득흔호.
Based on spatial curved beam theory, vibrational behavior for naturally curved and twisted beams with general cross-sectional shapes is theoretically investigated. The effects of transverse shear deformations, rotary inertia and torsion-related warping are included in the present formulations. The governing equations can be transformed to a set of ordinary differential equations with respect to time by utilizing a finite difference discretization in the spatial domain. Natural frequencies of the beams can be determined by solving these equations. In analyzing the dynamic response of the structures under harmonic excitation, Newton-Cotes formula, which avoids the trouble of the inverse matrix calculation, is used to evaluate vector integration in precise time-integration method. The present analysis will be used to solve the natural frequencies and the response curve of displacement of forced vibration of the beams fixed at both ends. Calculations show that the numerical results obtained are very close to the FE-results. Another example is related to the natural frequencies of cylindrical helical springs of circular cross-sections with both ends fixed. Results are in good agreement with other published data.