1,721,031 research outputs found
Nonsmooth dynamics of a double-belt friction oscillator
No full textTo investigate the dynamics of these systems, a model of a visco-elastic oscillator dragged by two different rough belts moving with constant velocity and possibly colliding on a rigid obstacle (DBO) is proposed and analysed. Two types of external excitation have been considered: in the first case energy is uniquely transferred from the moving supports to the mass via a velocity-dependent friction force (autonomous PSS); in the second case a harmonic driving force is also applied to the mass (non-autonomous PSS). The interactions between the mass and the belts and the collisions on the obstacle lead to multiple discontinuity boundaries in the phase plane: aim of this study is to investigate how the number and positions of the discon-tinuity boundaries affect the dynamics of the system and the associated bifurcation scenarios
Nonlinear dynamics and bifurcations of an axially moving beam
No full textThe present paper analyzes the dynamic behavior of a simply supported beam subjected to an axial transport of mass. The Galerkin method is used to discretize the problem; a high dimensional system of ordinary differential equations with linear gyroscopic part and cubic nonlinearities is obtained. The system is studied in the sub and super-critical speed ranges with emphasis on the stability and the global dynamics that exhibits special features after the first bifurcation. A sample case of a physical beam is developed and numerical results are presented concerning the convergence of the series expansion, linens subcritical behavior, bifurcation analysis and stability, and direct simulation of global postcritical dynamics. A homoclinic orbit is found in a high dimensional phase space and its stability and collapse are studied
Nonlinear strategies for longitudinal control in the stabilization of an oscillating suspended cable
No full textThe feasibility of reducing vibrations in suspended cables by an imposed longitudinal displacement of one support is investigated through an analytical model. A noncollocated active control scheme is considered where modal amplitudes describing transverse oscillations are used in the feedback control action at the boundary. A 2DOF nonlinear model of the cable is used to design state-feedback controller. Linear and nonlinear velocity feedback and feedback bilinearisation are shown to produce a nonlinear and bilinear actively-damped system, respectively. The controlled system performance is analysed comparing the effectiveness of the different strategies on both control demand and response amplitudes in the stabilization of the equilibrium position. Control spillover effects are commented through an enlarged 8DOF modal description of the controlled cable oscillations
Buckling of composite laminated plates via a refined higher-order theory
No full textThe buckling stresses and mode shapes of rectangular laminated composite plates
are investigated employing a global higher-order theory. The displacement field is expanded
along the thickness direction in a complete polynomial series with arbitrary
degree whereas the series coefficients, function of the in-plane coordinates, are expressed,
according to Ritz method, as a superposition of admissible functions. Expressing the
energy functionals in terms of the generalized coordinate, the expressions of the elastic
and geometric stiffness matrices are obtained. The problem is suitably nondimensionalized
so as to single out the independent parameters affecting the buckling behaviour.
The convergence properties of the adopted discretization scheme are investigated first
considering simply supported orthotropic three-layer symmetric composite plates under
a transverse distributed load. It is shown that higher-order terms in the thickness direction
are needed for convergence. Variations of the lowest buckling loads with the
width-to-thickness ratio and with the ratio between the in-plane elastic moduli are also
investigated to ascertain the sensitivity of the buckling behavior with respect to these parameters.
The semi-analytical solutions are compared with those obtained using a finite
element code (NASTRAN) for the three- and four-layer plates and a good agreement is
found
Nonlinear behaviour of a suspended cable under stationary and non-stationary loading
No full textIn cables, time-varying forces cause large amplitude oscillations involving mainly the low
modes. The contribution of higher modes may arise due to either internal coupling phenomena or peculiar
spatial distribution of the loading. Using analytical reduced models and finite element models, the paper
explores the relevance of the modal interactions in both planar and spatial response to harmonical in-
plane excitation and to out-of-plane wind turbulence with its spatial distribution
Shallow versus nonshallow cables: linear and nonlinear vibration performance
No full textA mechanical model describing large motions of non-shallow cables
around the initial catenary configurations is proposed. An exact
kinematic formulation accounting for finite axis extensions while
neglecting bending and torsional deformations is adopted whereas the material is assumed to be linearly hyperelastic. The nondimensional
mechanical parameters governing the motions of non-shallow cables are
obtained via a suitable nondimensionalization and the regions of
their physically plausible variations are portrayed. The spectral
properties of linear vibrations around the initial static
configurations are first discussed. Then, the responses to
primary-resonance excitations of either the lowest symmetric or
skew-symmetric modes are investigated employing the method of
multiple scales directly applied to the partial-differential
equations of motion and boundary conditions. A detailed analysis of
these responses is documented shedding light onto the importance of
the quadratic non-linearities in non-shallow regimes which may entail
significant non-linear spatial corrections to the leading first-order
motions
Nonsmooth dynamics of oscillators with frictional contacts: analyses and experiments
No full textThe model of a non-smooth oscillator, which exhibits different discontinuity boundaries in the phase space, is considered in order to investigate the dynamics of vibrating systems characterized by the occurrence of multiple frictional contacts. A test set-up of the model has been built and its behaviour is experimentally investigated to find out the existence of the non-standard bifurcations predicted by the theoretical analyses and the influence of other parameters, as the friction coefficient, the non-ideal energy source, the variation of the normal contact force during the oscillations. Based on measurements performed, a good qualitative agreement with the responses of the theoretical model has been observed
Mitigation of human-induced vibrations in suspension footbridges via multiple tuned mass dampers
No full textThe dynamic response of suspension footbridges to pedestrian-induced excitations and its passive
mitigation are investigated. The linearized equations of motion are obtained from a nonlinear
model and the Gal ̈erkin discretization approach is employed to solve both the free and forced elastodynamic
problems. First, the leading characteristics of the Singapore Suspension Foobridge,
whose lowest two modes possess closely-spaced frequencies near the so-called crossover condition,
are outlined. Further it is shown the effectiveness of the multiple tuned mass dampers (TMD)
architecture. To this end, the frequency-response functions as well as direct integration of the
equations of motion are employed to predict the response of the footbridge by itself and with the
addition of the TMDs under various scenarios of pedestrian excitation, namely, walking, running
and jumping
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