Vibration of aerospace composites

This chapter deals with the study of composite vibration. The axial and flexural vibrations of anisotropic composite plates are fully coupled, which is substantially different from the case of isotropic metallic plates in which the axial and flexural vibrations are decoupled and can be studied independently. The displacements and stress resultants are defined in terms of the motion and loading of composite-plate midsurface. The equations of motion are derived in terms of stress resultants. The strains were expressed in terms of midsurface strains and curvatures. ABD matrices derived in one of the previous chapters are used to express the relation between stress resultants and midsurface strains and curvatures. Eventually, the vibration equations for an anisotropic laminated composite plate are derived in terms of displacements, mass distribution, and the ABD matrix components. The same approach is repeated for isotropic plates to allow direct comparison with the axial and flexural plate vibration formulations existing in literature. The composite-plate vibration equations are solved for the special case of orthotropic composites which permit the decoupling between the axial and flexural motions. The flexural vibration of simply supported (SS) orthotropic composite plates is studied in order to derive natural frequencies and modeshapes. The dynamic response of SS orthotropic composite plates is studied through normal mode expansion in terms of natural frequencies and modeshapes. Several worked-out numerical examples are presented including unidirectional and crossply composite plates. Natural frequencies, modeshapes, and dynamic response for uniformly distributed excitation and point-load excitation are given. The calculations for similar isotropic aluminum plates are offered for comparison. Vibration of free composite plates is treated with the finite element method. Problems and exercises as well as a list of references and bibliography conclude the chapter.