The objective of this textbook is to develop the
fundamental concepts needed for the dynamic analysis of composite materials and composite structures. The book has been established for the undergraduate upper-levels and graduate level in Mechanical
The basic elements needed to investigate the dynamic
behaviour of laminate and sandwich materials and structures are developed in References 1 and 2 of this textbook. Chapter 1 summarizes these basic elements. First the chapter gives elements on the
constituents and the architecture of composite materials, and then introduces the mechanical behaviour of composite materials. Next the chapter considers the fundamental theories for modelling the
mechanical behaviour of laminate and sandwich materials.
Chapter 2 treats the dynamics of systems with one degree
of freedom. The topics considered are of general interest and practical usefulness for analyzing the dynamic behaviour of structures using mode superposition.
Chapter 3 develops the one-dimensional flexural vibrations
of laminate or sandwich plates. This type of vibrations concerns the bending vibrations of beams and the vibrations of plates under cylindrical bending. The chapter considers the natural modes of
beam vibrations and their properties. Beam vibrations with low damping are then analysed, introducing the modal coordinates. The effects of transverse shear are analysed in the case of cylindrical
Chapter 4 analyses the flexural vibrations of rectangular
laminate plates, with damping neglected. Analytical solutions for the free vibrations of plates are derived in a few particular cases. Then, the chapter develops the Ritz’s method to obtain
approximate solutions for the natural modes of rectangular plates with various conditions along the edges. The analysis of the dynamic behaviour of composite structures needs to evaluate the bending
stiffnesses of composite materials. Chapter 4 shows how the stiffnesses can be estimated from the experimental analysis of rectangular plate vibrations. The problems and the difficulties of the
evaluation are extensively discussed.
In fact, it is necessary to consider the damping of
materials in the investigation of the dynamic behaviour of composite structures. Damping in composite materials is considered in Chapter 5, first, as function of the constituents. Then, bending
vibrations of damped laminate beams are studied using viscous friction model and complex stiffness. Damping properties of orthotropic beams and plates are analyzed as function of material
An extended experimental investigation of damping of
composites is developed in the case of unidirectional glass and Kevlar fibre composites in Chapter 6. A procedure for measuring laminate damping from the bending vibrations of beams is presented.
Next, discussion is developed on the experimental results obtained. Temperature effect is also considered.
Inserting viscoelastic layers in composite laminates
improves significantly the damped dynamic properties of the laminates. Chapter 7 develops an extended analysis in the case of rectangular plates which allows to investigate the processes induced by
interleaving viscoelastic layers.
The dynamic analysis of complex structures needs to use
the finite element method. Chapter 8 provides the basic concepts of the finite element formulation applied to the dynamic analysis of composite structures. The formulation has been developed so as to
make the chapter self-contained.
Finite element formulation derives the numerical equations
of the dynamic behaviour of composite structures. Chapter 9 analyzes the numerical procedures used to solve these equations. Direct integration and mode superposition are presented. Examples of
engineering applications are reported as illustrations.
Chapter 10 develops an extensive analysis of the damping
of sandwich materials. First, modelling of sandwich materials and structures is implemented. Experimental investigation is next carried out in the case of sandwich materials constituted of a foam
core and laminate skins.
The purpose of Chapter 11 is to report a general
formulation of the different concepts introduced in the present textbook by applying these concepts to the analysis of the damping of different laminates and sandwich materials and to the analysis of
the vibrations of a simple shape structure.
2015, Jean-Marie Berthelot