IN-PLANE VIBRATION OF CIRCULAR ARCHES WITH VARIABLE CROSS-SECTIONS
IN-PLANE VIBRATION OF CIRCULAR ARCHES WITH VARIABLE CROSS-SECTIONS
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DOI：
10.1006/jsvi.1997.1441
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发表时间：
1998-04
影响因子：
4.7
通讯作者：
X. Tong;N. Mrad;B. Tabarrok
中科院分区：
文献类型：
--
作者：
X. Tong;N. Mrad;B. Tabarrok
摘要研究变截面圆拱的面内自由振动和强迫振动。利用薄梁的基尔霍夫假设和中性轴不可伸长，得到了等截面圆拱的封闭解。这个精确的解决方案是用于圆拱与阶梯形横截面，并适用于获得一个近似的解决方案，拱与非均匀横截面。对于自由振动，频率方程的解析形式是由拱一端的一些初始参数表示的一般解得到的;而对于强迫振动，系统的响应是通过求解一组只有三个未知数的代数方程得到的。算例表明了该方法的有效性和准确性。
Abstract Free and forced in-plane vibrations of circular arches with variable cross-sections are investigated. Using the Kirchhoff assumptions for thin beams and taking the neutral axis as inextensible, a closed form solution is obtained for circular arches of uniform cross-section. This exact solution is used for circular arches with stepped cross-sections and is applied to obtain an approximate solution for arches with non-uniform cross-sections. For free vibration, an analytic form of frequency equation is obtained by using the general solution expressed in terms of some initial parameters at one end of the arch; while for forced vibration, the system's response is obtained analytically by solving a set of algebraic equations with only three unknowns. Several examples are presented to illustrate the validity and accuracy of the method.