9 - Relationships between vibration frequencies of higher-order plate theories and classical thin plate theory

Abstract

Publisher Summary This chapter discusses that recent advances into the subject of plate vibration have focused on shear deformable plates that are somewhat more complicated to analyze compared with the classical thin plate theory. Fueled by the availability of powerful computers, researchers have developed computer codes for analysis of shear deformable plated structures that involve a relatively larger number of degrees of freedoms. In order to check the validity, convergence, and accuracy of their numerical techniques and software, it is necessary to have exact benchmark vibration frequencies of shear deformable plates. The chapter provides exact vibration frequency relationships that convert the classical plate solutions into their corresponding shear deformable plate solutions. The chapter presents exact vibration frequency relationships between CPT and higher-order plate theories FSDT and TSDT. These relationships not only furnish insights into how the various design variables influence the vibration frequencies, but they also provide valuable benchmark shear deformable plate frequencies upon supplying the corresponding CPT solutions.