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In this paper, we consider the multiplicity of homoclinic solutions for the following damped vibration problems $$ \ddot{x}(t)+B\dot{x}(t)-A(t)x(t)+H_{x}(t,x(t))=0,$$ where $A(t)\in (\mathbb{R},\mathbb{R}^{N})$ is a symmetric matrix for all $t\in \mathbb{R}$, $B=[b_{ij}]$ is an antisymmetric $N \times N$ constant matrix, and $H(t,x)\in C^{1}(\mathbb{R}\times B_{\delta},\mathbb{R})$ is only locally defined near the origin in $x$ for some $\delta>0$. With the nonlinearity $H(t,x)$ being partially sub-quadratic at zero, we obtain infinitely many homoclinic solutions near the origin by using a Clark's theorem.