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{\partia

Size: px

Start display at page:

Download "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{\partia"

きょういちいくのや
5 years ago
Views:

$REJECT} \mathrm{b}$ 1209 2001 89-98 89 (Teruaki ONO) 1 $LR$ $LR$ $\mathrm{f}\ovalbox{\tt\small$

1 REJECT} \mathrm{b}$ (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) $1$) ) $2$

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

3 91 1 1/3 (1) Sp (2) Map (3) Acr (4) Al

4 92 4 (SPL) 2-5 $ \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)

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

6 $7^{\ovalbox{\tt\small REJECT}}$ $\langle$ 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 $\mathrm{p}_{\mathrm{m}}$ $J\triangleright$

7 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

8 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 $T_{t}$

9 $\mathrm{p}$ $\mathrm{g}/\mathrm{c}\mathrm{m}^{3}$ 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 Soda glass Aluminum Alumina 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

10 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 $\mathrm{j}\mathrm{p}\mathrm{n}$ $(\mathrm{e}) (1993)$ 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)

42 1 ( ) 7 ( ) $\mathrm{s}17$ $-\supset$ 2 $(1610?\sim 1624)$ 8 (1622) (3 ), 4 (1627?) 5 (1628) ( ) 6 (1629) ( ) 8 (1631) (2 ) $\text{ }$ ( ) $\text{

$42 1 ( ) 7 ( ) $\mathrm{s}17$ $-\supset$ 2 $(1610?\sim 1624)$ 8 (1622) (3 ), 4 (1627?) 5 (1628) ( ) 6 (1629) ( ) 8 (1631) (2 ) $\text{ }$ ( ) $\text{$ 26 [\copyright 0 $\perp$ $\perp$ 1064 1998 41-62 41 REJECT}$ $=\underline{\not\equiv!}\xi*$ $\iota_{arrow}^{-}\approx 1,$ $\ovalbox{\tt\small ffl $\mathrm{y}