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Free and forced nonlinear oscillations of a two-layer composite beam with interface slip
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Nonlinear free dynamics of a two-layer composite beam with different boundary conditions
Get PDFThe nonlinear free vibrations of a two-layer elastic composite beam are investigated. Different boundary conditions, both symmetric and not symmetric with respect to the beam midpoint, equal on both layers and different on each layers, are considered. The analysis is developed by means of the multiple time scale method, and at each order of the asymptotic development, we obtain different information. The first order terms provide the linear natural frequencies. The first, the second and the third natural frequencies are computed explicitly. The next order terms, on the other hand, provide the nonlinearity coefficients measuring the nonlinear amplitude dependence of the natural frequencies, i.e. the curvature of the backbone curve. Both the linear frequencies and the nonlinear coefficients are found to be dependent on two dimensionless parameters only and, for boundary conditions different on each layer, also of the ratio between the axial stiffnesses of each layer
Nonlinear vibrations of an extensional beam with tip mass in slewing motion
No full textDynamics of a rotor composed of a flexible beam attached to a slewing rigid hub is presented in the paper. Dynamics of the structure is studied for a slender beam model, based on extended Bernoulli–Euler theory, which takes into account a nonlinear curvature, coupled transversal and longitudinal oscillations and non-constant angular velocity of the hub. Moreover, to demonstrate a general case for dynamical boundary conditions, lumped mass fixed at the beam tip is added. The partial differential equations (PDEs) are derived from Hamilton principle of the least action. The analytical solutions of the PDEs are obtained by the multiple time scale method applied directly to PDEs. Forced vibrations around selected resonance zones are studied and the influence of beam rotation, preset angle, hub radius, tip mass is presented. Hardening and softening phenomena, respectively for the first and the second mode, are obtained for various angular velocity values
Hardening vs. softening dichotomy of a hinged-simply supported beam with one end axial linear spring: Experimental and numerical studies
No full textThe aim of this paper is to validate experimentally a nonlinear model of a kinematically excited hinged-simply supported beam with a spring subjected to one end. An experimental setup configuration enables to test different variants of axial boundary conditions: first a typical simply supported beam (no spring), and next two different spring systems. The prototype is kinematically excited with different amplitudes of excitation and then full frequency response curves are drawn wherein hardening/softening dichotomy is recognized. A set of mechanical properties of the system is identified and then used to reproduce tests with finite element simulations. Consequently numerical vs. experiment results are compared. The analysis demonstrates amplitude dependent damping as well as that the natural frequency depends on environmental conditions, and thus may change over experiments
Longitudinal–transversal internal resonances in Timoshenko beams with an axial elastic boundary condition
Get PDFThe internal resonances between the longitudinal and transversal oscillations of a forced Timoshenko beam with an axial end spring are studied in depth. In the linear regime, the loci of occurrence of 1 : ir, ir∈ N, internal resonances in the parameters space are identified. Then, by means of the multiple time scales method, the 1 : 2 case is investigated in the nonlinear regime, and the frequency response functions and backbone curves are obtained analytically, and investigated thoroughly. They are also compared with finite element numerical simulations, to prove their reliability. Attention is paid to the system response obtained by varying the stiffness of the end spring, and it is shown that the nonlinear behaviour instantaneously jumps from hardening to softening by crossing the exact internal resonance value, in contrast to the singular (i.e. tending to infinity) behaviour of the nonlinear correction coefficient previously observed (without properly taking the internal resonance into account)
Experimental nonlinear dynamic regimes for energy harvesting from cantilever bistable shells
No full textAn experimental campaign on a cantilever composite bistable shell with a piezoelectric patch is reported in the paper. The considered shell is characterized by two stable configurations far apart in terms of natural frequencies and geometries. Harmonic forcing is applied at the shell's clamped side through an electrodynamic shaker and the dynamic response is measured through an embedded strain gauge. Different dynamic regimes are encountered by performing excitation frequency and amplitude sweeps. The resonance scenarios around the two natural frequencies corresponding to the stable configurations show different softening behavior. The excitation amplitude threshold level for snap-through motion is identified. Experimental power generation maps plotted on the excitation frequency–amplitude plane are created to provide useful design insights for vibration energy harvesting purposes
Nonlinear experimental dynamics of a pentastable composite cantilever shell
No full textA composite shell with conical geometry, featuring opposite curvatures in its free (undeformed) configuration, is studied. Prestress is applied by first flattening and then clamping one of the curved edges, leading to a morphing structure. The shell exhibits five distinct static equilibria, referred to as configurations I, J, L, S, and I∗. Based on experimental measurements and numerical models, the rich potential energy topology is qualitatively reconstructed. The linear dynamics of the cantilevered shell is investigated at first through various scenarios of kinematic excitation over a wide range of frequencies (up to 100 Hz). Frequency response curves, time series, phase portraits, Poincaré maps, fast Fourier transforms and largest Lyapunov exponents are used to investigate in-well, cross-well, and global nonlinear dynamics. Depending on the forcing amplitude and frequency, one-way and reversible snap-through is observed. The extensive experimental campaign allows to unveil the dynamic interplay among the observed five stable configurations
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