変形綱細線のマトリクス法振動解析

抄録

Flexurally vibrating bars used for mechanical filter are generally supported at their nodal points with slender steel wires. These wires are in many cases straight, but sometimes curved wires are used (Fig. 1). Their characteristics in vibration have not yet made clear. For the support wire of a mechanical filter, the consideration of the static stiffness of the wires and the frequency range to be practically utilized determines whether or not the curved wires are better than straight ones. On the otherhand, the curved wire is also used in practice as a bridging coupler over the adjoining resonators for the mechanical filter with attenuation-poles characteristic (Fig. 2). As the coupler of a narrow-band mechanical filter, a ∩︀-shaped coupler is suitable for practical use because the stresses are less concentrated at its curved portion than a ⊓︀-shaped coupler. This paper deals with the analysis of these curved wires and attempts to make their vibration characteristics clear. For the matrix analysis applied effectively in this paper, the straight portions of the wire are considered as a single section whereas the curved portions are divided into several elements approximated by a series of straight sections (Fig. 3 to 5). In the first part of this paper, the models of the curved wires and the matrices for the straight section are presented. Two different matrix equations are presented. Two different matrix equations are separately utilized for the segment. That is, one is Equation (1), which is used for the calculation of the dynamic characteristics and the other is Equation (5), for the calculation of static characteristics. In the second part of the paper, methods of calculating the input impedances, the resonant and the antiresonant frequencies are described (Figs. 6 and 7). Finally, the numerical results are demonstrated (Tables 1 and 3, Figs. 8 to 13). From these results, the following conclusions are drawn. (1) In the application to the support wire, the stiffness of the curved wire is less than that of the straight wire, so that curved support wire less affects the resonant mode of the vibration, but its frequency range is narrower than that of the straight support. In addition, the curved support wire may not always be superior from the point of the resilience against the rigid body vibration due to external shock. (2) Concerning the application to the bridging coupler, the coupling stiffness is greatly affected by very small change of the curvature. The resonances and anti-resonances appear repeatedly at narrow internals in the frequency characteristics (Figs. 11 and 12). (3) A coupler of the ∩︀-shape is superior to that of the ⊓︀-shape for the narrow-band filter applications, because it can provide small coupling stiffness (Table 3). (4) The equivalent circuit and element values of tee type are based on the numerical results.