Nonlinear oscillations, bifurcations and chaos of functionally graded materials plate

The bifurcations and chaotic dynamics of a simply supported symmetric cross-ply composite laminated piezoelectric rectangular plate are studied for the first time, which are simultaneously forced by the transverse, in-plane excitations and the excitation loaded by piezoelectric layers. Based on the Reddy’s third-order shear deformation plate theory, the nonlinear governing equations of motion for the composite laminated piezoelectric rectangular plate are derived by using the Hamilton’s principle. The Galerkin’s approach is used to discretize partial differential governing equations to a two-degreeof-freedom nonlinear system under combined the parametric and external excitations. The method of multiple scales is employed to obtain the four-dimensional averaged equation. Numerical method is utilized to find the periodic and chaotic responses of the composite laminated piezoelectric rectangular plate. The numerical results indicate the existence of the periodic and chaotic responses in the averaged equation. The influence of the transverse, in-plane and piezoelectric excitations on the bifurcations and chaotic behaviors of the composite laminated piezoelectric rectangular plate is investigated numerically.

Periodic and chaotic dynamics of composite laminated piezoelectric rectangular plate with one-to-two internal resonance

In this paper, we use the asymptotic perturbation method based on the Fourier expansion and the temporal rescaling to investigate the nonlinear oscillations and chaotic dynamics of a simply supported rectangular plate made of functionally graded materials (FGMs) subjected to a through-thickness temperature field together with parametric and external excitations. Material properties are assumed to be temperature-dependent. Based on the Reddy’s third-order plate theory, the governing equations of motion for the plate are derived using the Hamilton’s principle. The Galerkin procedure is employed to obtain a two-degree-of-freedom nonlinear system including the quadratic and cubic nonlinear terms. The resonant case considered here is 1:2 internal resonance, principal parametric resonance-1/2 subharmonic resonance. Based on the averaged equation in polar coordinate form, the stability of steady state solutions is analyzed. The phase portrait, waveform and Poincare map are used to analyze the periodic and chaotic motions of the FGM rectangular plate. It is found that the FGM rectangular plate exhibits the chaotic motions under certain circumstances. It is seen that the nonlinear dynamic responses of the FGM rectangular plate are more sensitive to transverse excitation. The excitation force can be used as a controlling factor which can change the response of the FGM rectangular plate from periodic motion to the chaotic motion.

Complicated nonlinear responses of a simply supported FGM rectangular plate under combined parametric and external excitations

In this paper, the nonlinear oscillations and chaotic dynamics of a parametrically excited simply supported symmetric cross-ply laminated composite rectangular thin plate are further investigated. ...

Further studies on nonlinear oscillations and chaos of a symmetric cross-ply laminated thin plate under parametric excitation

Analysis on nonlinear vibrations near internal resonances of a composite laminated piezoelectric rectangular plate

The present investigation deals with nonlinear dynamic behavior of a parametrically excited simply supported rectangular symmetric cross-ply laminated composite thin plate for the first time. The governing equation of motion for rectangular symmetric cross-ply laminated composite thin plate is derived by using von Karman equation. The geometric nonlinearity and nonlinear damping are included in the governing equations of motion. The Galerkin approach is used to obtain a two-degree-of-freedom nonlinear system under parametric excitation. The method of multiple scales is utilized to transform the second-order non-autonomous differential equations to the first-order averaged equations. Using numerical method, the averaged equations are analyzed to obtain the steady state bifurcation responses. The analysis of stability for steady state bifurcation responses in laminated composite thin plate is also given. Under certain conditions laminated composite thin plate may have two or multiple steady state bifurcation solutions. Jumping phenomenon occurs in the steady state bifurcation solutions. The chaotic motions of rectangular symmetric cross-ply laminated composite thin plate are also found by using numerical simulation. The results obtained here demonstrate that the periodic, quasi-periodic and chaotic motions coexist for a parametrically excited fore-edge simply supported rectangular symmetric cross-ply laminated composite thin plate under certain conditions.

Local and global nonlinear dynamics of a parametrically excited rectangular symmetric cross-ply laminated composite plate

Investigation of cooling performance degradation of impingement/effusion structure on pressure side of nozzle guide vane

To expand the application of light-weight and high-strength polymer matrix composites in the fields of aerospace, shipbuilding and transportation, it has designed and fabricated a new-type carbon fiber fabric/hollow glass beads/epoxy resin (CFF/HGB/EP) composite with a three-layer sandwich structure, consisting of an upper composite layer (CFF/EP), core layer (HGB/EP) and lower composite layer (CFF/EP). The effects of the CFF/EP layer and the HGB content on the sandwich composites were explored through a systematic investigation of the mechanical properties and microstructure. The results indicate that the density of the sandwich composite can be reduced to 0.83 g cm−3, while the flexural, impact, and tensile strength of the sandwich composite can be increased by 227%, 156%, and 118% compared with pure epoxy resin, respectively. The great improvement of mechanical properties of the sandwich composite makes its application in various industries more promising. 

Investigation on preparation and mechanical properties of carbon fiber fabric/hollow glass beads/epoxy resin sandwich composite laminates

With the rapid development of 3D sensing and reconstruction technologies, point cloud compression has become an active research area. When designing compression methods for point cloud attributes, the reconstructed geometry information is commonly used to guide the attribute compression. Specifically, the geometric distance between points is widely applied in different forms to assist attribute prediction. However, due to the complicated spatial distributions of 3D point clouds, using distance as the sole feature may not be optimal. In this paper, the spatial distribution of point clouds is further considered to derive a distribution-driven attribute pre-diction. Experimental results show that the proposed method can significantly improve the coding efficiency of G-PCC. The proposed method has been adopted in the technologies under consideration (TuC) for MPEG G-PCC and will be included in the second version of the G-PCC specification.

Jing Lu

Papers

Local and global nonlinear dynamics of a parametrically excited rectangular symmetric cross-ply laminated composite plate

Investigation of cooling performance degradation of impingement/effusion structure on pressure side of nozzle guide vane

Investigation on preparation and mechanical properties of carbon fiber fabric/hollow glass beads/epoxy resin sandwich composite laminates

Distribution-Driven Predictor Screening For Point Cloud Attribute Compression

Competitive adsorption behavior and mechanisms of coexisting EDTA-Cu(Ⅱ) and EDTA-Cr(Ⅲ) on ferrihydrite