Sound isolation properties of polycarbonate/clay and polycarbonate/silica nanocomposites

Abstract

The soundproofing properties of polycarbonate (PC)/nanoclay and PC/nanosilica nanocomposites were studied through testing and theoretical analysis. Nanocomposite sheets with a 3 mm thickness were fabricated by direct hot-compression molding process. The nanoclay and nanosilica particles were incorporated into the PC matrix by a twin-screw extruder. The dispersion efficiency of 1, 3 and 5 wt% nanoclay and nanosilica in the PC matrix was investigated by transmission electron microscopy. Dynamic mechanical analysis was performed for evaluation of mechanical properties of nanocomposites. Sound transmission loss (STL) was measured by an impedance tube over the frequency range of 1600–6300 Hz, and further employed in sound proofing characterizations of nanocomposites. A new finite element model was developed to model the sound transmission loss in impedance tube test. The results showed that the PC/3 wt% nanoclay and 3 wt% nanosilica nanocomposites had an average maximum increase of 5.5 and 6 dB in STL values in the stiffness control region (1600–3600 Hz), respectively. On the other hand, the PC/3 wt% nanoclay and PC/3 wt% nanosilica nanocomposites showed the same sound isolation characteristics in the frequency range of 1600–3600 Hz. In addition, the finite element model developed for modeling the sound transmission loss in the impedance tube demonstrated a good correlation between the theoretical curves and the experimental results in the stiffness control region for both nanocomposites.

Appendix

The stiffness matrix $\left[ K \right]^{(e)}$, mass matrix $\left[ M \right]^{(e)}$, displacement vector $\left[ u \right]^{(e)}$ and force vector $\left[ f \right]^{(e)}$ are defined as follows:

$$\left[ K \right]_{8 \times 8}^{(e)} = \left[ {\begin{array}{*{20}c} {\left[ {K_{rr} } \right]_{4 \times 4} } & {\left[ {K_{rz} } \right]_{4 \times 4} } \\ {\left[ {K_{zr} } \right]_{4 \times 4} } & {\left[ {K_{zz} } \right]_{4 \times 4} } \\ \end{array} } \right]^{(e)} \left[ M \right]_{8 \times 8}^{(e)} = \left[ {\begin{array}{*{20}c} {\left[ {M_{rr} } \right]_{4 \times 4} } & 0 \\ 0 & {\left[ {M_{zz} } \right]_{4 \times 4} } \\ \end{array} } \right]^{(e)}$$

$$\left[ u \right]_{8 \times 1 }^{(e)} = \left[ {\begin{array}{*{20}c} {\left\{ {u_{{r_{m} }} } \right\}_{4 \times 1} } \\ {\left\{ {u_{{z_{m} }} } \right\}_{4 \times 1} } \\ \end{array} } \right]^{(e)} \left[ f \right]_{8 \times 1 }^{(e)} = \left[ {\begin{array}{*{20}c} {\left\{ {f_{{r_{m} }} } \right\}_{4 \times 1} } \\ {\left\{ {f_{{z_{m} }} } \right\}_{4 \times 1} } \\ \end{array} } \right]^{(e)}$$

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As an example, below is the two matrix elements of the stiffness matrix $\left[ K \right]_{8 \times 8}^{(e)}$:

$$\left[ {K_{rr} } \right]_{4 \times 4} = \left( {K_{b} + \frac{4}{3}G} \right)\int \limits_{0}^{b} \int \limits_{0}^{a} \left\{ {\frac{{\partial N_{m} }}{\partial x}} \right\}\frac{{\partial N_{m} }}{\partial x} 2\pi x\left( {x + r_{1} } \right){\text{d}}x{\text{d}}y + \left( {K_{b} - \frac{2}{3}G} \right)\int \limits_{0}^{b} \int \limits_{0}^{a} \left\{ {\frac{{\partial N_{m} }}{\partial x}} \right\}N_{m} 2\pi {\text{d}}x{\text{d}}y + \left( {K_{b} - \frac{2}{3}G} \right)\int \limits_{0}^{b} \int \limits_{0}^{a} \left\{ {N_{m} } \right\}\frac{{\partial N_{m} }}{\partial x}2\pi {\text{d}}x{\text{d}}y + \left( {K_{b} + \frac{4}{3}G} \right)\int \limits_{0}^{b} \int \limits_{0}^{a} \left\{ {N_{m} } \right\}N_{m} \frac{2\pi }{{\left( {x + r_{1} } \right)}}{\text{d}}x{\text{d}}y + G\int \limits_{0}^{b} \int \limits_{0}^{a} \left\{ {\frac{{\partial N_{m} }}{\partial y}} \right\}\frac{{\partial N_{m} }}{\partial y} 2\pi \left( {x + r_{1} } \right){\text{d}}x{\text{d}}y$$

$$\left[ {K_{rz} } \right]_{4 \times 4} = \left( {K_{b} - \frac{2}{3}G} \right)\int \limits_{0}^{b} \int \limits_{0}^{a} \left\{ {\frac{{\partial N_{m} }}{\partial x}} \right\}\frac{{\partial N_{m} }}{\partial y} 2\pi x\left( {x + r_{1} } \right){\text{d}}x{\text{d}}y + \left( {K_{b} - \frac{2}{3}G} \right)\int \limits_{0}^{b} \int \limits_{0}^{a} \left\{ {N_{m} } \right\}\frac{{\partial N_{m} }}{\partial y}2\pi {\text{d}}x{\text{d}}y + G\int \limits_{0}^{b} \int \limits_{0}^{a} \left\{ {\frac{{\partial N_{m} }}{\partial y}} \right\}\frac{{\partial N_{m} }}{\partial x} 2\pi \left( {x + r_{1} } \right){\text{d}}x{\text{d}}y$$

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