Dragan Milosavljević

FREE VIBRATIONS ANALYSIS OF COMPOSITE LAMINATE PLATES USED IN AUTOMOTIVE INDUSTRY

The paper describes the process of applying mathematical methods for obtaining analytic solutions in dynamic problems of free vibrations of composite laminate materials which are used in automotive industry. For selected high-order deformation theories the paper presents mathematical method for analytic solving of partial differential equations of motion. The procedure of obtaining results by combining symbolic and numerical values of relevant variables was implemented. Through a kind of comparative analysis, the emphasis was put on the use of HSDTs based on shape functions. Comparative values of results obtained using different shape functions are presented in tabular form. The paper considers simply supported thin, moderately thick and thick laminate plates. Moreover, it shows the influence of the laminate class of symmetry on the method of obtaining results. Simply supported laminate plates were primarily considered, specifically symmetric and anti-symmetric cross-ply laminate plates.

ACOUSTICAL TENSOR AND ELASTIC WAVE PROPAGATION IN ANISOTROPIC MATERIALS USED IN AUTOMOTIVE INDUSTRY

Mechanical behaviour of anisotropic media may be seen the best through its behaviour during bulk wave propagation. Such waves may be decomposed into finite plane waves propagating along arbitrary direction n in solid. Properties of these waves are determined by dependence between propagation direction and constitutive properties of media. Three types of such waves may be distinguished in connection to three displacement vectors, which determine acoustic polarization. The most of dynamical systems are naturally nonlinear; here we are going to write Reimann-Christoffel equation. This equation represents propagation condition of bulk waves as set of three homogeneous linear equations. Materials used in present analysis are fibre reinforced with one or two families of continuous fibres. Often used represent of such materials is epoxy resin carbon fibres composite whose material constants are determined with ultrasound methods.

Elastic waves in multilayered plate reinforced by inextensible fibres

In this article the propagator matrix method is employed to obtain the overall transfer matrix which gives dependence of displacements and stresses on the one face of the multilayered plate in terms of those on the opposite face. Attention is restricted to waves propagating in the plane parallel to stress free plate faces where we examine waves travelling at any angle to one of the families of fibres. The plate is of finite thickness but of infinite lateral extent. Each of the laminae is formed from same material reinforced by one family of inextensible fibres laying in the plane of the laminae. Results are presented for eight-ply laminated plate with symmetric arrangements of the laminae. Frequency spectrum for first 10 modes is presented for specific plate with (π/2, −π/4, π/4, 0)s lay up, and specific fibre reinforced material.

Dynamic Behaviour of Fibre Reinforced Circular Cylinders and Shells

In recent years there has been considerable activity in the study of the dynamic behaviour of composite materials. Here we shall consider with fibre-reinforced composite materials which have an important property that they are anisotropic, and in many cases this anisotropy may be very strong, in the sense that mechanical properties depend strongly on direction. A continuum model of such materials was developed by Spencer [1], [2], and wave propagation in a plate reinforced by one family of fibres was examined by Green [3] and Green and Milosavljevie [4], [5]. The dynamic behaviour of a plate reinforced by two families of fibres was examined by Milosavljevie [6], [7] and [8].