Stability of parametric vibrations of laminated composite plates
The dynamic stability of laminated composite plates subjected to arbitrary periodic loads is studied based on the first-order shear deformation plate theory. The in-plane load is taken to be a combination of periodic biaxial and bending stress. A set of second-order ordinary differential equations with periodic coefficients of Mathieu-Hill type is formed to determine the regions of dynamic instability based on Bolotin's method. Numerical results reveal that the dynamic instability is significantly affected by the modulus ratio, number of layer, static and dynamic load parameters. The effects of various important parameters on the instability region and dynamic instability index are investigated.
Dynamic Stability of Rectangular Plates Subjected to Pulsating Follower Forces
The dynamic stability of isotropic and nonsymmetric laminated plates with four free edges subjected to pulsating follower forces is discussed. The results are obtained using the first-order shear deformation theory. The discretized equation of motion is obtained by the finite element method, and then the method of multiple scales is adopted to investigate the dynamic instability regions. The effects of Poisson ratio as well as aspect and thickness ratios on the dynamic instability region for isotropic plates are investigated. The influences of aspect ratio, lamination angle, and the number of layers for nonsymmetric, cross-ply, and angle-ply laminated plates are also studied.
Mechanics of deformable directed surfaces
Abstract The paper develops a simple, yet complete and consistent non-linear dynamic thermo-elastic shell theory based on the concepts of a two-dimensional directed continuum. The constitutive equations are postulated in a general form. Stress-strain relations are derived using the equation of energy balance and the two entropy production inequalities, which are rewritten in a special form. The linear theory is discussed in detail. The structure of the stress-strain relations is presented in the most general form and then specialized to concrete examples, in particular, to the classical shell theory, using their invariance properties with respective to certain symmetry groups. The elastic moduli are determined by demanding the coincidence of the frequency dispersion surfaces obtained using the two-dimensional theory with the lowest foils of the corresponding surfaces resulting from the three-dimensional theory of elasticity.