In this paper, the first attempt is made to obtain some new analytic free vibration solutions of rectangular sandwich panels within the symplectic solution framework, which are difficult to tackle within the conventional analytic solution framework. The sandwich panels with honeycomb and truss cores are first treated as equivalent thick plates. The governing dual equation is then established within the Hamiltonian system. Subsequently, the original problem is converted into two subproblems whose analytic solutions are acquired by applying the variable separation and symplectic eigen expansion. The superposition yields the final analytic free vibration solution, with the emerging coefficients determined according to the equivalence between the original problem and the superposition. The natural frequency and mode shape solutions by the present symplectic superposition method are quantitatively shown via numerical and graphical results, respectively, and are all well validated by consistency with classical solutions, experimental results, or the numerical solutions by the refined finite element modeling. Besides providing the new results that can serve as benchmarks, the effects of the size parameters on the natural frequencies of the sandwich panels are also analyzed. Since the developed method gives up the assumption of any trial solutions and follows a rigorous derivation to yield new analytic solutions, it provides opportunities for solving more intricate problems of sandwich panels and shells.

本文首次尝试在辛解框架内获得矩形夹芯板的一些新的解析自由振动解，这些解在传统解析解框架内难以解决。具有蜂窝和桁架芯的夹芯板首先被视为等效厚板。然后在哈密顿系统内建立控制对偶方程。随后，将原问题转化为两个子问题，通过变量分离和辛特征展开获得其解析解。叠加产生最终的解析自由振动解，新出现的系数根据原始问题和叠加之间的等价性确定。本辛叠加方法的固有频率和振型解分别通过数值和图形结果定量显示，并且都通过与经典解、实验结果或精细有限元建模的数值解的一致性得到很好的验证。除了提供可作为基准的新结果外，还分析了尺寸参数对夹芯板固有频率的影响。由于所开发的方法放弃了任何试验解决方案的假设并遵循严格的推导以产生新的分析解决方案，它为解决夹层板和壳的更复杂问题提供了机会。并且都通过与经典解、实验结果或精细有限元建模的数值解的一致性得到了很好的验证。除了提供可作为基准的新结果外，还分析了尺寸参数对夹芯板固有频率的影响。由于所开发的方法放弃了任何试验解决方案的假设并遵循严格的推导以产生新的分析解决方案，它为解决夹层板和壳的更复杂问题提供了机会。并且都通过与经典解、实验结果或精细有限元建模的数值解的一致性得到了很好的验证。除了提供可作为基准的新结果外，还分析了尺寸参数对夹芯板固有频率的影响。由于所开发的方法放弃了任何试验解决方案的假设并遵循严格的推导以产生新的分析解决方案，它为解决夹层板和壳的更复杂问题提供了机会。