Free and forced vibration of simply supported, orthotropic sandwich panel

A three-dimensional (3-D) sandwich panel, which is characterized by two thin flat sheets and a core sandwiched between them, is a relatively complex structure. The degree of complexity depends on the type of core used. Despite the complexity, the dynamic flexural behavior of a 3-D, thin-walled sandwich panel may be represented by the response of an equivalent two-dimensional (2-D), homogeneous, orthotropic, thick-plate continuum, provided its plan size is many times larger than its depth. Seven elastic constants represent the homogeneous, orthotropic, thick-plate continuum. These constants vary with the core configuration. In this paper, a truss-core sandwich panel unit, which departs from conventional forms, is introduced. Elastic constants for the truss-core panel have been derived and are presented. Using these equivalent constants in conjunction with a closed-form solution, free and forced vibration response of the sandwich panel as an orthotropic, thick-plate continuum are derived. A double series solution is used for the simply supported orthotropic thick plate. This technique requires considerably less computational effort than 2-D or 3-D finite element analysis. Numerical examples show that the closed-form solution is in excellent agreement with finite element results, thus, validating both the accuracy and effectiveness of the transformation and closed-form solution.