REJECT} \mathrm{b}$ 1209 2001 89-98 89 (Teruaki ONO) 1 $LR$ $LR$ $\mathrm{f}\ovalbox{\tt\small $L$ $L$ $L$ R $LR$ (Sp) (Map) (Acr) $(105\cross 105\cross 2\mathrm{m}\mathrm{m})$ (A1) $1$) ) $2$
90 2 3) $D_{L} \frac{\partial^{4}w}{\mathrm{a}^{4}}+2d_{lr}\frac{\partial^{4}w}{\ ^{2}\Phi^{2}}+D_{R} \frac{\partial^{4}w}{\phi^{4}}+\phi\frac{\partial^{2}w}{\partial t^{2}}=0$ (1) $D_{L}$ $L$ $D_{R}$ $R$ Du $LR$ $D_{K}$ $LR$ $D_{L}= \frac{e_{l}h^{3}}{12(1-\mu_{lr}\mu_{rl})}$ $D_{R}= \frac{e_{r}h^{3}}{12(1-\mu_{lr}\mu_{m_{d}})}$ DLR=DL\mu RL+2Dk=DRAR+ $D_{k}= \frac{g_{lr}h^{3}}{12}$ $w$ $x$ $L$ $f$ $R$ 12 \rho $E$ $G$ \mu $E^{\iota}= \frac{e}{1-\mu_{lr}\mu_{rl}}$ $D_{LR}=(E_{L} \cdot\mu_{rl} +2G_{LR}\mathrm{I}\frac{h^{3}}{12}$ $=(E \sim\mu_{1}+2g_{lr})\frac{h^{3}}{12}$ (1) $\ovalbox{\tt\small REJECT}$ $\frac{h^{3}}{12}[e_{l}\frac{\partial^{4}w}{\mathrm{a}^{4}}+2(\prime E\cdot\mu+2G_{LR}) \frac{\partial^{4}w}{\ ^{2}\Phi^{2}}+E_{R} \frac{\partial^{4}w}{\phi^{4}}]+$ \partial a2w2 $=0(1 )$ (1) \mbox{\boldmath $\omega$} $\omega^{2}=\frac{1}{\mu}(\frac{a^{4}d_{l}}{l_{l}^{4}}+\frac{\sqrt{}^{4}d_{r}}{l_{r}^{4}}+\frac{2a^{2}\beta^{2}d_{lr}}{l_{l}^{2}l_{r}^{2}})$ (2) $\mathit{1}_{l}=l$ $l_{r}\subset R$ ; ; $a$ $\beta=$ $\varpi=\frac{a^{2}}{l^{2}}\sqrt{\frac{d_{l}+d_{r}+2d_{lr}}{\rho h}}$ (3) 3 $\mathrm{l}\mathrm{m}\mathrm{s}$ $25\cdot 20\mathrm{k}\mathrm{H}\mathrm{z}$ 30 1/3 4) 1/3 $5\mathrm{m}\mathrm{s}$ 2 1st 1st
91 1 1/3 (1) Sp (2) Map (3) Acr (4) Al
92 4 (SPL) 2-5 $05123155\mathrm{k}\mathrm{H}\mathrm{z}$ 5 $SPL$ $P_{o}$ $\mathrm{l}\mathrm{m}\mathrm{s}$ (1) Sp Acr $5\mathrm{k}\mathrm{H}\mathrm{z}$ $\mathrm{a}1$ lkhz $5\mathrm{k}\mathrm{H}\mathrm{z}$ $2\mathrm{k}\mathrm{H}\mathrm{z}$ (2) Sp Acr Po $[]\ovalbox{\tt\small REJECT}$ (3) Map Al Po fime (ms) 2 3 4 5
$\hat{\vee\dot{\mapsto}\infty\in}$ $ \mathrm{j}$ $\hat{\vee\mapsto\infty\xi}$ $\hat{\grave{\approx\vee-\iota\infty \mathrm{o}}\infty}$ 93 $f_{\mathit{1}l}$ Sp Map Sp ( ) 5 $\delta(\mathrm{d}\mathrm{b}/\mathrm{s})$ \mbox{\boldmath $\delta$} 67 $f$ \mbox{\boldmath $\delta$} \mbox{\boldmath $\delta$} $f_{\mathit{1}l}$ \beta s)=k/f Sp Acr Map Al $\theta^{l}$ \mbox{\boldmath $\tau$} ( \mbox{\boldmath $\delta$}) o) $\mathrm{f}$ (Hz) $\mathrm{f}$(hz) 6 7 \Re
$7^{\ovalbox{\tt\small REJECT}}$ $\langle$ q $\backslash \backslash$ $\mathfrak{v}$ $\mathrm{f}(\mathrm{h}\mathrm{z})$ 94 2 $2\pi$ -1 $\omega\delta$ (4) $\Phi^{l}$ ( $S$ ) $f_{\mathit{1}l}$ $f\mathit{1}r$ $f_{ll}$ $f_{lr}$ $f$ ( ) ( $\backslash \backslash$ $L$ $Q_{L\mathit{1}}\mathit{1}$ Sp 0007 Acr 006 Map 001 Al 0001 Acr $Q^{-l}$ $\mathrm{s}\mathrm{p}$ $\theta^{\mathit{1}}$ 6 $\langle$ Acr Sp Map Map Al \mbox{\boldmath $\delta$} $P_{m}$ $P_{m}$ $\theta^{\mathit{1}}$ $Q^{\mathit{1}}$ 8 $\theta^{l}$ (1) Sp f (2) Map f $\theta^{l}$ (3) Acr $\theta^{l}$ (4) Al HMeinel 8 ] $\mathrm{f}\mathrm{b}$ Sp Map $\mathrm{p}_{\mathrm{m}}$ $J\triangleright$
95 5) Sp $\mathrm{q}^{-1}$ (1) 6) STimoshenko $EI \frac{\partial^{4}w}{\mathrm{a}^{4}}+p4\frac{\partial^{2}w}{\alpha^{2}}-\beta\frac{\partial^{4}w}{\mathrm{a}^{2}a^{2}}-\frac{;ei}{k G}\frac{\partial^{4}w}{\mathrm{a}^{2}a^{2}}+\frac{\rho^{2}I}{kG}\frac{\partial^{4}w}{\alpha^{4}}=0$ (5) 3 45 k 083 (1) $a)= \frac{m^{2}h}{2\sqrt{3}l^{2}}\sqrt{\frac{e}{\sqrt}}$ (6) Goens $E_{A}$ $E_{A}$ $T$ 7) $E=E_{A}\cdot T$ (7) $T=1+ \frac{1}{12}(\frac{h}{l})^{2}mf(m)(mf(m)+6)+\frac{1}{12}(\frac{h}{l})^{2}mf(m)(mf(m)-2)\frac{e}{kg}$ (8) $\frac{h}{l})^{2}$ $\frac{\frac{1}{12}(\frac{h}{l})^{2}m^{4}\frac{e}{kg}}{1+\frac{1}{12}(\frac{h}{l})^{2}m^{2}(1+\frac{e}{kg})}$ $m$ $\mathrm{f}(m)=\tanh(m/2)$ ( ) ; $\mathrm{f}(m)=\coth(m/2)$ ( ) $T$ 2 34 E/G $ _{/}\mathrm{a}$ $E/G$ Map $L$ EvGL T Sp
96 Sp $\mathrm{s}\mathrm{p}$ 3 8) $\sigma^{\mathit{1}}$ Sp Acr $Q^{\mathit{1}}$ (1) 9) $G= \frac{e}{2(1+\mu)}$ (9) $D= \frac{eh3}{12(1-\mu)2}$ $E = \frac{e}{1-\mu^{2}}$ (9) $E \frac{h^{3}}{12}(\frac{\partial^{4}w}{\mathrm{a}^{4}}+2\frac{\partial^{4}w}{\ ^{2}\Phi^{2}}+ \frac{\partial^{4}w}{\phi^{4}})+\sqrt h\frac{\partial^{2}w}{\partial t^{2}}=0$ (10 ) $\omega=\sqrt{\frac{d}{\sqrt h}}(\frac{a^{2}}{l_{l}^{2}}+\frac{\sqrt{}^{2}}{l_{r}^{2}})=\frac{a^{2}}{l_{l}^{2}}\sqrt{\frac{e I_{RT}}{A_{RT}\rho}}+\frac{\sqrt{}^{2}}{l_{R}^{2}}\sqrt{\frac{E I_{LT}}{A_{LT}\sqrt}}$ (11) $A$ ; $I$ ) ; $\epsilon(\mathrm{n}\sim\cdot 1)\pi$ $\neq(\mathrm{n}_{2^{-}}1)_{\pi}(\mathrm{n}1$ $\mathrm{n}\mathrm{z}=234$ $\omega=\frac{a12}{l^{2}}\sqrt{\frac{d}{\phi}}=\frac{a^{2}\prime}{l^{2}}\sqrt{\frac{e I}{A\rho}}$ (12) $\theta^{\mathit{1}}$ Table 1 Acr $f_{\mathit{1}l}$ Sp $T_{t}$
$\mathrm{p}$ $\mathrm{g}/\mathrm{c}\mathrm{m}^{3}$ Hz $\mathrm{f}_{1\mathrm{b}}$ $\mathrm{f}_{1\mathrm{p}}$ $\triangle \mathrm{f}_{1}$ $\triangle \mathrm{f}_{1}$ $\mathrm{q}_{\mathrm{b}}^{\cdot}1$ Qpl $\mathrm{q}_{\mathrm{b}}^{-1}$ 97 1 $\mathrm{f}_{1\mathrm{b}}$ Material $\mathrm{f}$ $\mathrm{o}_{\mathrm{p}}^{-\prime}$ Hz Hz % $\cross $\triangle \mathrm{q}^{\cdot}1$ $\triangle \mathrm{q}^{1}$ 10^{\theta}$ $\mathrm{x}103$ $\cross 103$ % Acrylic resin 118 3785458 79521 581 513 68 117 Soda glass 249 88589687829 935 198 196 0016 08 Aluminum 269 9361 10877 1516 162 102 143 041 402 Alumina 391 195042197 2466 126 0152 164 149 979 Cer $105\mathrm{x}\mathrm{l}05\mathrm{x}2(\mathrm{t})\mathrm{m}\mathrm{m}$ $\star\triangle \mathrm{f}_{1}=\mathrm{f}_{1\mathrm{p}}\cdot \mathrm{f}_{1\mathrm{b}}$ $\triangle \mathrm{q}^{\cdot}1=\mathrm{q}\mathrm{p}1-$ 1 105(1)xl6(w)x2(t) $\mathrm{m}\mathrm{m}$ 7 $Q_{L}- \mathit{1}$ E\phi $(EJ\sqrt)/Q_{L^{\mathit{1}}}M\mathrm{B}^{S}$ Eh $Q_{L^{\mathit{1}}}-$ $Q_{L^{l}}-$ Sp EJd EiGLT 8 $L$ $ _{\sqrt}\mathrm{a}$ 1) T Ono Frequency responses of wood for musical instruments in relation to $(\mathrm{e})17183\cdot 193(1996)$ the vibrational properties J Acoust Soc $\mathrm{j}\mathrm{p}\mathrm{n}$ 2) T Ono bansient response of wood for musical instruments and its $\mathrm{j}\mathrm{p}\mathrm{n}$ $(\mathrm{e})20117\cdot 124$ mechanism in vibrational property J Acoust Soc
die 98 (1999) 3) R F S Hearmon The elasticity of wood and plywood in Forest Products Research Special Report No 7(His Majesty s Stationary Office London 1948) Part I 4) T Ono Effects of varnishing on acoustical characteristics of wood used for musical instrument soundboards J Acoust Soc $\mathrm{j}\mathrm{p}\mathrm{n}$ $(\mathrm{e})14397-407(1993)$ 5) H Meinel Regarding the sound quality of violins and ascientific basis for violin construction J Acoust Soc Am 29 $817\cdot 822(1957)$ 6) S Timoshenko p302 (1972) 7) E Goens $\ddot{\mathrm{u}}\mathrm{b}\mathrm{e}\mathrm{r}$ Bestimmung des Elastizit\"atsmoduls von St\"aben mit Hflfe von Biegungsschwingungen Ann Phys 11 $649\cdot 678$ (1931) 8) T Ono The dynamic rigidity modulus and internal ffiction of several woods in torsional vibration Mokuzai Gakkaishi 26 9) P126(1971) $139\cdot 145$ (1980)