Study On Nonlinear Dynamics Of The Deploying Composite Laminated Cantilever Plates

In recent years, deploying cantilever beams or plates are being widely used in manyengineering fields, such as the deploying process of the solar array, the board type antenna,crane and the morphing wing. When subjected to the external loads, these structures can bedescribed by time-varying parameter systems which lose stability easier as compared tostationary systems. The instabilities will worsen the dynamic characteristics and reliabilityof the deploying cantilever beams or plates. Moreover, large amplitude vibrations of thedeploying composite laminated cantilever plates lead to the geometric nonlinearities.Therefore, it is necessary to study the nonlinear dynamics of deploying cantilever structures.In this paper, we investigate the complex nonlinear dynamic responses of a deployingcomposite laminated cantilever rectangular plate subjected to several external excitations onthe basis of the telescopic wings. The numerical simulations are used to analyze thetime-varying nonlinear characteristics of the deploying cantilevered laminated compositeplates. The governing equations of motion for a deploying piezoelectric composite laminatecantilever plate subjected to aerodynamic force and piezoelectric excitation are established,the influences of piezoelectric materials on the nonlinear dynamics of the deployingpiezoelectric composite laminate plate are investigated. The main contents of thisdissertation are as follows.(1) Based on Reddy’s third-order shear deformation plate theory and Hamilton’sprinciple, the nonlinear partial differential governing equations of motion for the deployingcomposite laminated cantilever rectangular plate subjected to the external excitations areestablished. After choosing suitble time dependent vibration mode-shape functions thatsatisfy the displacement boundray conditions, the Galerkin method is used to reduce thegoverning partial differential equations to a two-degree-of-freedom nonlinear ordinarydifferential equation with time-varying parameters.(2) Numerical simulations are performed for the nonlinear dynamic responses of thedeploying orthotropic composite laminated cantilever rectangular plate which subjected totransversal parametric excitations, first-order and third–order transversal aerodynamicspressures, respectively. The influences of different realistic parameters on the stability of thetelescopic cantilever rectangular orthotropic laminated composite plate are analyzed. Thenumerical results demonstrate that the deploying velocities, thickness and dampingcoefficients have great effects on the amplitudes of the nonlinear vibrations of the first-orderand second-order modes for the deploying composite laminated cantilever rectangular plateduring the deploying from2mto4m. The reasonable values of these parameters couldnot only suppress the amplitude of nonlinear vibration, but also can avoid the occurrence ofthe second jump phenomena of the amplitudes for the first-order and second-order modes during the deploying from2mto4m.(3) The nonlinear partial differential governing equations of motion for a deployingpiezoelectric composite laminated cantilever rectangular plate subjected to theaerodynamics loads, in-plane and piezoelectric excitations are established by usingHamilton’s principle. The aerodynamics loads acted on the deploying cantilever plateincluding first-order aerodynamics force and third-order aerodynamics force. Thetime-dependent mode-shape functions are chosen which satisfy the displacement boundaryconditions. Using Galerkin approach, the nonlinear partial differential governing equationsof motion for the deploying piezoelectric composite laminated cantilever rectangular plateare discretized to the two-degree-of-freedom nonlinear ordinary differential equations,respectively.(4) The nonlinear dynamic behaviors of the piezoelectric composite laminate platesubjected to the first-order and third-order aerodynamics force are investigated respectivelyusing numerical method, and the influences of piezoelectric actuators on the nonlineardynamics of the deploying plate are analyzed. The results show that the applied voltage hasgreat effects on the amplitudes of the nonlinear vibrations. When the value of appliedvoltage is positive, the deploying process of the piezoelectric composite laminate platebecomes more unstable. When the polarity of the applied voltage is changed to negative, notonly the increase of the amplitudes of first-order and second-order modes can be suppressed,but also the occurrence of the second jump phenomena of the amplitudes for the first-orderand second-order modes can be avoided during the deploying from2mto4m. Therefore,the appropriate selection of the piezoelectric parameters can suppress the nonlinear vibrationof deploying piezoelectric composite laminate cantilever plate. These results will be helpfulto the improvement of stability of the nonlinear vibrations for the deploying compositelaminated cantilever rectangular plates.