Theoretical And Experimental Studies On The Parametrically Excited Vibrations Of Laminated Buckled Beams With A Lumped Mass

Beam structures are widely used in the fields of civil construction, machinery manufacturing, aerospace and other fields in recent years. With modern engineering structures increasingly become to be larger and lighter, people have more and more requirements on the stability and reliability of beam structures, thus the nonlinear vibration of the beam acquires more attention. Meanwhile, the nonlinear factors of the beam have great effect on the safety and lifespan of the structures. Therefore, the research on the nonlinear dynamics has very important significance for the rational design of engineering structures and reducing the impact of nonlinear factors.Chapter 1:The development, significance and methods of the nonlinear dynamic are introduced,besides, the research status of the theoretical and experimental study and problems of beam structures are also described.Chapter 2:Based on the Euler-Bernoulli beam theory and Reissner principle, the equations of the non-linear response of a composite laminated buckled beam with clamped ends and a lumped mass to an axial periodic excitation were obtained. By using the single-mode approximation and Galerkin’s method, the differential equation was derived, and the bifurcation diagram of displacement varying with the excitation amplitude was obtained by using the fourth-order Runga-Kutta algorithm. Moreover, the effect of size and locations of the concentrated mass on the natural frequency and period-doubling bifurcation was discussed.Chapter 3:The parametrically excited vibrations of a laminated buckled beam with fixed ends and a tipped mass when the external excitation frequency is close to the first-order frequency of the system are studied experimentally. We obtain the acceleration of the system by fixing the external excitation frequency and changing the excitation amplitude.Then we acquire the time history of displacement, phase and frequency spectrum via the signal processing software for data analysis. Thus the complexity of nonlinear phenomena of the system is verified.Chapter 4:The parametrically excited vibrations of delaminated laminated buckled beam with clamped ends and a lumped mass are experimentally studied. Then the nonlinear response of each group buckled beams at different excitation voltage are obtained. What’s more, the effects of delamination length on the first-order frequency, period-doubling bifurcation and chaotic motion are discussed.Finally: The conclusion of the study is summarized, the existing problems and future research directions are introduced.