Theoretical And Experimental Investigation For Nonlinear Dynamics Of Z-shaped Folded Wings

With the rapid development of the aviation industry,it brings higher requirement to the capabilities of aircraft in the civil and military fields.New generation aircraft can perform in a variable flight environment(height,mach number,etc.)and perform multiple tasks(such as taking off or landing,cruising,maneuvering,hovering,attacking,etc.).Fixed wing aircraft can only meet the normal flight conditions in a specific airflow and airspace.Therefore,the concept of morphing aircraft comes into being.Morphing aircraft can be able to change the aerodynamic shape of the fuselage to improve comprehensive performance under different airflow conditions and flight environments.In this paper,the nonlinear dynamics theories and experimental methods are employed to study the dynamical behavior of Z-shaped folded wing combined with the current research situation on the morphing aircrafts in our country.In addition,the experimental model of Z-shaped folded wing has been designed and manufactured.We consider a Z-shaped folded wing composed of three consecutive elastic carbon-fiber reinforced laminated composite plates connected by rigid hinges,named inner wing,middle wing and outer wing,respectively.The inner wing is connected with the fuselage while the outer wing is free.With different flight mission,the middle wing can not only rotate around the hinges changing the folding angle,but also can be locked at any folding angle,meanwhile,the outer wing and the inner wing are always kept parallel so that the aircraft can always maintain the optimization of lift-drag ratios.The nonlinear governing equations of motion for the system are obtained based on the von Kármán equations and classical laminate plate theory.The governing equations are then discretized into a two degree-of-freedom nonlinear system using Galerkin's method.According to the finite element modal analysis results,a modal function is selected,and the dynamic equation is second-order discrete into a two-degree-of-freedom nonlinear system.The method of multiple scales is employed to obtain the averaged equation of motion for the system,and the effects of transverse excitations on the nonlinear dynamics of the Z-shaped folded wing are investigated through a comprehensive numerical simulation.Then,the experiment analyses are applied to verify the theoretical researches of the structure.The meaningful results are obtained by both the theoretical and experimental investigation,which are prerequisite for structural design and application.The main content of this dissertation can be summarized as following sections.(1)Consider a Z-shaped folded plate composed of three consecutive elastic carbon-fiber reinforced laminated composite plates.The inner side of inner wing is the fixed end,and the outermost end of the outer plate is the free end.Based on classical laminated plate theory,von Kármán's nonlinear theory,the nonlinear governing equations of the structure are established using Hamilton's principle.(2)Combining the finite element modal analysis results of Z-shaped folded wing,the first fifth order modes of the system is studied.The cases of primary parameter resonance and 1:1 inner resonance are considered.The method of multiple scales is employed to obtain the averaged equation of motion for the system.Finally,numerical methods are utilized to investigate the nonlinear dynamical characteristics of the Z-shaped folded wing.(3)Considering the resonance condition of 1:2 internal resonance of the system,the perturbation analysis of multi-scale is used to analyze the two-degree-of-freedom nonlinear system.The four-dimensional average equations of the system is obtained.Numerical simulation illustrates the complex dynamical responses of the Z-shaped folded wing with the bifurcation diagrams,wave-form diagrams,three-dimensional phase portraits,and Poincarèmap under some given conditions.(4)The operational modal experiment and vibration measurement are employed to verify the theoretical results.An experimental model of the Z-shaped folded wing is designed and manufactured.In this section,a series of experiments is employed not only to investigate the vibration mode shapes of the Z-shaped folded plate,but also to validate the theoretical analysis of the structure.We take the case of 1:2 internal resonance of the system at a folded angle of 60~o as a example,a vibration test experiment was performed on the experimental model,and the experimental results were compared with the theoretical analysis.(5)A series of modal experiments is designed to obtain the modal parameters of the Z-shaped folding wing model based on the PolyMAX algorithm,and the modal parameters are validated.This section select two different folded angle,90~o and 120~o respectively.Combining the Experimental Modal Analysis(EMA)and Operational Modal Analysis(OMA),the first five modal parameters are compared and identified,and the natural frequency,damping ratio,and mode shape of the system were obtained.