Free vibration study of sandwich plates using a family of novel shear deformable dynamic stiffness elements: limitations and comparison with the finite element solutions

Framework for Dynamic‐Stiffness‐Based Free Vibration Analysis of Plate‐Like Structures

“…e overview of the dynamic stiffness method is presented in this section. For more details, the reader is referred to authors' previous work [27][28][29][30][31][32][33].…”

“…where L denotes the length of the corresponding boundary line (2a or 2b), s is related to x or y coordinate, while H ij is the projection matrix composed of the Fourier base functions. Now, the components of the projection vectors are the Fourier coefficients in the series expansion (see [27][28][29][30][31][32][33] for details). e relation between the projection vectors q ij and Q ij and the vector of integration constants C ij is obtained as…”

“…and F ij D , the number of terms in the Fourier series expansion in equation 9should be the same as the number of terms in the general solutions given in equation 7. Since integrals given in equation 8 [27][28][29][30][31][32][33]). Consequently, the code execution is significantly accelerated.…”

“…In a series of contributions, dynamic stiffness matrices for a completely free rectangular plate element based on the FSDT [27] and higher-order shear deformation theory (HSDT) [28], as well as for the plate element ongoing in-plane vibrations [29], have been developed by the authors. Recently, the above formulations have been broadened to the free transverse vibration analysis of sandwich [30], symmetric cross-ply laminated composite plates [31,32], and composite stiffened plate assemblies and GFRP beams with or without straight through cracks [33].…”

Linear and Nonlinear Dynamic Analyses of Sandwich Panels with Face Sheet‐to‐Core Debonding

“…This makes the dynamic analysis of the sandwich panels more challenging than that of the laminates. Furthermore, high physical and geometrical mismatching is also an obstacle to handle sandwich panels using the equivalent single layer (ESL) two-dimensional (2D) finite element [3,4] or dynamic stiffness element [5] models. In 2 Shock and Vibration this regard, models adopting mixed theories or the layer-wise (LW) approach are preferable for sandwich structures [6].…”