平面刚架横向振动模态分析新方法探讨

研究的主要目的是探讨分析平面刚架在其平面内的弯曲振动模态新方法 ,并提出弹性支承梁法 还试图将其分析的结果同目前流行的一些近似方法 ,如集中质量法、矩阵位移法、模态综合法等进行比较 为此 ,首先推导了弹性支承梁横向自由振动模态的特征方程 ,其推导方法与一般著作上对刚性支承梁的模态分析方法类似 对于刚架的模态分析 ,笔者提出了弹性支承梁方法 ,即取刚架的一部分单元为弹性支承梁 ,而其动刚度系数是其他部分对它的影响 利用动刚度系数相等从而建立起刚架的特征方程 ,进而求出刚架的各阶模态 算例表明 :提出的弹性支承梁方法应用于平面刚架的弯曲振动模态分析取得了较好的结果 将文中提出的弹性支承梁法与准确的有限梁方法和上述几种近似方法作了对比分析 ,表明弹性支承梁法具有准确、简便和计算范围宽的优点

A Discussion on a New Method for the Analysis of Plane Rigid Frame's Lateral Vibrational Mode

The main purpose of the study is to discuss a new method for the analysis of plane rigid frame's winding vibration mode in its plane, and an elastic bearing beam method is presented. The results of the analysis are compared with some similar popular methods such as concentrate quality method, matrix displacement method and mode integration method. First, the characteristic equation of elastic bending beam's lateral free vibration mode is derived.The deriving process is analogical to rigid bending beam's mode analytic method in current literatures. The elastic bending beam method is presented to analyze rigid frame's mode, namely, part of rigid frame's elements are used as the elastic bending beam whose vibration rigid coefficient reveals the effect it receives from other parts. The rigid frame's characteristic equation is presented via the equivalency of vibration rigid coefficient, and every mode of the rigid frame can be acquired. The computed example shows that the elastic bending beam method is satisfactory when it is applied to the plane rigid frame's winding vibration mode analysis. The elastic bending beam method is compared with the precise finite beam method and the above-mentioned analogical methods.The comparison shows that the elastic bending beam method is precise,convenient and widely applicable.