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This paper investigates the free vibrations of double beams, consisting of upper and lower beams, which are discretely connected by N springs. In the theoretical analysis, the modal analysis approach is employed to determine the expressions for the natural frequencies and vibrational modes of the system. In the numerical calculation, two cases, Cases A and B, are examined. In Case A, the two beams are connected by a single spring, while in Case B they are connected by two springs. In Case A, when the two beams have identical materials and dimensions, as the spring constant K1 increases, the natural frequencies of the odd-order vibrational modes are constant because the two beams vibrate in phase in their vibrational modes and the connecting spring is not stretched. The natural frequencies of the even-order vibrational modes are increased with the increase of K1 because the two beams vibrate out of phase. When the spring is attached at the middle of the beams, the natural frequencies p4n-1 (n=1, 2, ...) equal p4n. In addition, when K1 reaches the specific values K1,n in this case, a set of three natural frequencies satisfies p4n-2=p4n-1=p4n, and a magnitude relationship of the natural frequencies is switched when K1 crosses the value K1,n. In Case B, when two springs are attached in symmetry with respect to the midpoints of the beams, a set of two natural frequencies satisfies p2n=p2n+1 for the specific values of the spring constants even if the springs are not attached to the positions of the nodes of the independent beams. The validity of the theoretical analysis was confirmed by comparing the theoretical results with the results obtained by the FEM analysis for Case A. 1. 緒 言 異なる世帯が共通の建物に居住するタイプの集合住宅のような住宅構造物では,振動に起因する音の問題が重 要な課題となっている.例えば,上階の居住者の飛び跳ねなどにより発生する床振動が床と天井を結ぶ吊り要素 を介して,天井を振動させ,下階の室内に音として放射される.そのため,床,天井に対してインピーダンスの (松岡 他,1998).放射音の観点では,天井の振動モードが対称モードの場合には天井から室内への放射効率は高く,非 対称モードの場合は小さくなることが分かっている(田中,2009).それに対して,天井下の室内が閉空間と想定さ れる場合には天井の振動と室内音の連成問題となり,放射音とは逆に天井が対称モードのときに室内音が小さく, 非対称モードで音が大きくなることが報告されている(眞田他,2014).このように住宅構造物では天井の振動と 室内音は密接な関係にあり,天井の振動モードを正確に把握することは工学的に重要な問題である. *1 正員,倉敷化工(株)(〒712-8555 岡山県倉敷市連島町矢柄四の町 4630) *2 正員,フェロー,広島大学大学院 工学研究科(〒739-8527 広島県東広島市鏡山 1-4-1) *3 正員,広島大学大学院 工学研究科 E-mail of corresponding author: tikeda@hiroshima-u.ac.jp 加藤 隆一,池田 隆,原田 祐志 Received: 11 March 2017; Revised: 10 June 2017; Accepted: 24 July 2017 1 *2,*3 Department of Mechanical Systems Engineering, Graduate school of Engineering, Hiroshima University 1-4-1 Kagamiyama, Higashi-Hiroshima-shi, Hiroshima 739-8527, Japan No.17-00109 [DOI: 10.1299/transjsme.17-00109], J-STAGE Advance Publication date : 9 August, 2017

Free vibrations of double beams discretely connected by multiple springs