MS8.3 - Dynamic Stability, Multistability and Buckling-induced Smart Applications

Curvilinear reinforcement fibres allow tailoring the elastic properties of composite laminates in space, leading to Variable Stiffness Composite Laminates (VSCL). This work intends to analyse if variable stiffness composites can be used to increase the critical aerodynamic pressure, under which aeroelastic instabilities develop on circular cylindrical composite shells. The airflow is considered to be supersonic and along the shell’s axial direction. A linear mathematical model for thin circular cylindrical VSCL shells is developed for that purpose. The representation of the aerodynamic pressure caused by the supersonic airflow is derived recurring to a linearised piston theory, with a correction term to account for the shell’s curvature. The p-version of the finite element method is used, resulting in a set of second order ordinary differential equations of motion. These equations are transformed into a set of first order differential equations of motion in state space coordinates. Writing the solution to these equations as the product of a vector of coefficients by an exponential function of L*t, where L is a complex parameter and t represents time, a generalised eigenvalue problem is defined. If the real part of any eigenvalue L is positive, then the shell will not return to its undeformed configuration after a perturbation: an aeroelastic instability occurred. In the numerical tests, convergence and verification analyses are performed. The values of the present approach are compared with the ones computed by other authors in conventional, constant stiffness, composite laminate shells. The required number of degrees of freedom of the present p-version FEM model is relatively low. However, the large number of circumferential waves in some modes of interest leads to an increase in this number, if one wishes that the model is able to represent not only the modes involved in instabilities but also all modes until those. Four types of curvilinear fibre paths are explored. The geometry of the shell and most airflow parameters are fixed, in the numerical tests; the shell ends are either considered to be both clamped or both simply supported. An iterative procedure – using the free stream pressure as parameter - is applied to find fibre path parameters that result in an increase of critical flutter pressure for each type of fibre path. Limitations in the fibre path turning radius, due to manufacturing restraints and fibre buckling, are considered. The values of the critical aerodynamic pressure are found to be very sensitive to changes in the fibre path and it is shown that substantial increases can be achieved by using curvilinear fibres. Hence, variable stiffness composite laminates present a great capacity to postpone aeroelastic instabilities in the supersonic regime.

The present work is concerned with the dynamic instabilities arising when a circular cylindrical shell containing a dense fluid is subjected to a seismic excitation of harmonic type. Typical Fluid Structure Interaction studies focused on the interactions between elastic structures and fluids are focused on inviscid or Newtonian fluids (compressible or incompressible). However, the Nature shows many examples where the Newtonian fluid models cannot be considered, e.g. blood, blood plasma, oil and many other examples are non-natural products of common use: toothpaste, paint, shampoo, melted butter, starch suspensions, corn starch. For such reason here the focus are non-Newtonian fluids and their interactions with vibrating structures. An intensive experimental campaign is aimed to understand the complex interactions arising from the interaction between the elastic vibrating structure and the fluid. The structure under investigation is a polymeric thin circular cylindrical shell clamped at the bottom to a shaking table, through a vibration table adapter, the top of shell is closed with a heavy rigid disk, which imposes a rigid body motion to the top, preserves the circular shape to the top and generates strong inertia forces due to the seismic excitation. Experiments are carried out with and without fluid, which is a mixture of water and corn starch flour, also known as oobleck. The dynamic scenario of the system is analyzed for different excitation levels and frequencies and different fluid levels: empty, partially, and full-filled. Modal testing is carried out in order to identify modal shapes and natural frequencies and quantify changes in the system modal properties vs fluid filling. The system dynamic instabilities are analyzed by exciting the system with a high amplitude base oscillation that pumps high energy into the system; the excitation consists in a stepped sine sweep procedure, which spans a frequency region where several natural frequencies are present and strong resonance phenomena can take place; different excitation levels have been considered in order to induce phase transitions in the fluid. The onset of complex dynamics has been detected using Fourier spectra and bifurcation diagrams of the Poincaré maps: when the fluid-solid transition takes place, the entangled non-Newtonian fluid rheology results in a complex dynamic scenario: period-doubling cascades, quasiperiodic and chaotic responses have been observed.

Quasi-zero stiffness (QZS) isolators exploit the kinematic nonlinearity to increase the vibration attenuation with respect to a linear suspension. This paper presents an experimental study on a quasi-zero stiffness QZS isolator under base excitations. Stepped-sine tests have been performed to characterize the system and determine the isolator transmissibility. The system parameter identification has been carried out by fitting a model, based on the Duffing equation with viscous damping and dry friction, to the experimental data. Then, the isolator performance was verified under realistic earthquake signals. A satisfactory acceleration attenuation can be observed from the analysis of the time histories whilst a non-negligible presence of dry friction, leading to stick-slip phenomena and affecting the activation of the isolator at low frequencies, has been observed.