摘要
根据边界条件对变截面梁横向振动四阶变系数微分方程降阶,形成关于挠度和弯矩的二阶非显式递推变系数微分方程组;利用有限差分法,研究了变截面简支梁横向振动固有频率的数值计算方法及其精度.理论分析和正交计算的算例表明:数值计算算法简单,计算精度取决于计算步长的数目和梁横截面竖向渐变率,与梁宽和梁长无关;对于给定的计算步长或数目,可以估算数值计算的精度;对于给定的精度要求,可以确定合理的计算步长或数目.
Based on the boundary conditions of transverse vibration of non-uniform beams, second order inexplicit-recursive differential equations with variable coefficients about deflection and bending moment are obtained from the fourth order differential vibration equation with variable coefficients by the method of order reduction. By the method of finite difference, the numerical calculation method and its precision for the natural frequency of the transverse vibration of the simply supported non-uniform beams are studied. Examples of theoretical analysis and orthogonal calculation show that the numerical calculation algorithm is very simple, and its precision depends on the number of calculation steps and the vertical variation rates of the gradually changed cross-section and is independent of width and length of beams; the precision of the numerical calculation can be estimated according to a given length or the number of calculation steps and the reasonable length or the number of calculation steps can be determined by a given precision requirement.
出处
《力学与实践》
CSCD
北大核心
2011年第6期45-49,共5页
Mechanics in Engineering
关键词
变截面梁
横向振动
固有频率
数值计算
精度
Non-uniform beam, transverse vibration, natural frequency, numerical calculation, precision
