1,721,056 research outputs found
Frequency domain modeling of nonlinear end stop behavior in Tuned Mass Damper systems under single- and multi-harmonic excitations
No full textNonsmooth dynamics of a Tuned Mass Damper system with lateral stops are studied using an alternating frequency/time harmonic balancing (AFT-HB) method. To this end, an extremely stiff end stop nonlinearity is considered. The application range of AFT-HB is investigated by including up to 250 harmonics in the external force, as well as in the motion description. Numerical simulations are performed by making use of a Newmark time integration algorithm for numerical verification of the results. The results for single harmonic excitations are further verified with an existing pseudo-arclength path-following tool. Two excitation scenarios are considered: single harmonic- and a wide-spectrum excitation with uniform distribution and random phase correlation between the harmonics. The AFT-HB algorithm is found to accurately reproduce the time integration results, for all considered cases. Finally, insights are gained into the differences between the system responses to single- and multi-harmonic excitations.Accepted Author ManuscriptDynamics of Micro and Nano System
Nonlinear dispersion properties of metamaterial beams hosting nonlinear resonators and stop band optimization
No full textThe nonlinear dispersion properties of a metamaterial beam embedding nonlinear resonators
are investigated. The metamaterial beam incorporates a distributed array of local resonators
exhibiting softening or hardening cubic nonlinearity. The nonlinear dynamic behavior of the
metamaterial beam is first investigated asymptotically via the method of multiple scales, which
yields the closed-form nonlinear dispersion functions with the associated stop bands and the
nonlinear dispersive waves as a combination of acoustic and optical bending waves. The effects
of the resonators nonlinearity and the hosting beam nonlinear bending curvature on the stop
bands are investigated in terms of sensitivity with respect to the strength and type of resonators
nonlinearity. A full multi-variable optimization is carried out to study the nonlinear stop
band size variations with respect to the resonators nonlinearity and the acoustic/optical wave
amplitudes. The results show how the exploitation of the nonlinearities offers great possibilities
to enlarge the size of the stop bands compared to the corresponding linear case and, hence,
greatly enhance the energy absorption bandwidth
Nonlinear plane-wave expansion method for analyzing dispersion properties of piezoelectric metamaterial lattices with encapsulated resonators
Full text linksquare lattices encapsulating identical nonlinear resonators in each cell are investigated through an asymptotic treatment of the wave propagation equations. The nonlinear effects of the resonators, composed of suspended piezoelectric membranes with a central mass, are investigated through the introduction of a generalized nonlinear version derived from the plane-wave expansion (PWE) method. This method leads to nonlinear wave propagation equations and the analytical derivation of nonlinear dispersion functions using the method of multiple scales. Numerical simulations verify the validity of the analytical solutions. The proposed nonlinear PWE method is shown to overcomes the limitations of the popular approach based on the enforcement of the Floquet-Bloch theorem in the context of the cell projection method. While the latter provides the dispersion curves of the fundamental propagation mode, the nonlinear PWE delivers the nonlinear dispersion curves of all modes, offering a broader perspective into the design process for semi-adaptively programmable metamaterials aimed at controlling wave propagation
Buckling and postbuckling of extensible, shear-deformable beams: Some exact solutions and new insights
No full textThis paper presents exact solutions for the buckling loads and postbuckling states of extensible, shear deformable beams. The governing equation for the large-amplitude lateral deformation of beams in compression is expanded in Taylor series up to the cubic nonlinearity. Closed-form solutions in terms of the axial and shear stiffnesses are developed for statically determinate and statically indeterminate beams. Namely, pinned–pinned, cantilevered, clamped–clamped, and clamped–pinned beams are considered with the loaded end is a roller that is able to slide. The postbuckling response under a given axial load is exactly derived. The dependence of the buckling load on the length-to-radius of gyration is discussed. It is shown that the extensibility and the shear deformation significantly affect the buckling loads and the postbuckling response. For conventional materials with positive Poisson's ratio, the inclusion of the axial and shear deformation results in a meaningful reduction of the buckling load. It is further shown that the buckling load can be enhanced by designing artificial metamaterials materials with an effective negative Poisson's ratio
Asymptotic dynamic modeling and response of hysteretic nanostructured beams
No full textThe nonlinear dynamic response of carbon nanotube (CNT)/polymer nanocomposite beams to harmonic base excitations is investigated asymptotically via the method of multiple scales. The hysteresis associated with the CNT/polymer interfacial frictional sliding is described by a 3D mesoscopic theory reduced via a uniaxial strain assumption for a beam in pure plane bending. Such reduction leads to a Bouc–Wen-like hysteretic moment–curvature relationship. The generalized memory-dependent constitutive law is developed asymptotically and, subsequently, introduced in two archetypal cases of nonlinear beam models. A beam model is tailored for axially restrained, extensible beams (e.g., hinged–hinged beams) for which the dominant geometric nonlinearity is associated with the multiplicative effect of the tension with the bending curvature. The second model is valid for inextensible beams (e.g., cantilever beams) dominated by inertia and curvature nonlinearities. The piece-wise integration of the moment–curvature relationship yields an exponential law which is treated asymptotically to obtain the quadratic and cubic curvature contributions. The ensuing asymptotic equations of motion in the unknown deflection field are discretized according to the Galerkin method employing the eigenmode directly excited near its primary resonance to thus obtain a piece-wise reduced-order model (ROM). The method of multiple scales applied to the ROM yields the asymptotic response together with the frequency response functions for the lowest mode. A parametric study unfolds rich nonlinear dynamic responses in terms of behavior charts highlighting regions of hardening and softening behavior, regions of single-valued stable behavior and regions of multi-valued multi-stable behavior. Such richness of responses is caused by the unusual and unique combination of material and geometric nonlinearities
A review on buckling and postbuckling of thin elastic beams
No full textThis paper provides a review of models and solutions for the buckling and postbuckling of beams available from the 50s of the last century to date. Beams with axially unrestrained (movable) ends and restrained (immovable) ends are covered. In each class, the formulation of the nonlinear buckling problem for the buckling loads and the postbuckling states is discussed and the underlying assumptions are highlighted. For relatively large-amplitude buckling of beams with movable ends, approximate analytical solutions up to the third order are presented and compared with the exact solutions expressed in terms of elliptic integrals. For beams with immovable ends, buckling involves midplane stretching that makes the nonlinear buckling problem takes the same form of the standard eigenvalue problem and, hence, exact solutions are affordable. This review combines the research outcomes on buckled beams from two scientific viewpoints: the structural dynamics and the nonlinear vibration viewpoints, respectively. Moreover, it presents in one place the formulation and the exact solutions for the buckling of beams to serve as an on-demand resource for researchers concerned with the buckling and postbuckling of beams
Optimal resonator damping for wave propagation control in mechanical metamaterials
No full textA novel approach to the optimal damping of linearly damped resonators embedded in metamaterial systems is proposed with the aim of minimizing the metamaterials’ response when the external excitation frequency lies within one of the bandgaps. The equation governing wave propagation in the metamaterial system is obtained via a Galerkin projection combined with the quasi-periodicity ansatz of the Floquet–Bloch theorem. It is shown that an optimality criterion can be obtained for the resonator damping for any excitation frequency by extending the Den Hartog theory of fixed points in the frequency response functions. A numerical example of a honeycomb metamaterial is discussed to show how the proposed method works in a practical application. A full numerical optimization is carried out to study the quality factor of the metamaterials’ response with respect to the resonator damping ratio while proving its effectiveness. © 2023 Elsevier Lt
Advances in nonlinear acoustic/elastic metamaterials and metastructures
Full text linkAcoustic/elastic metamaterials exhibit a wealth of unusual properties conducive to wave manipulation. This review outlines state-of-the-art developments from FPUT chains, granular crystals to nonlinear acoustic metamaterials (NAMs). It mainly discusses key advances made in the domain of NAMs for wave manipulation, vibration control and sound attenuation given the blooming interest in exploring how nonlinearity offers possibilities for discovering novel wave phenomena, principles and properties that potentially go well beyond linear metamaterials and the relevant linear theories. NAMs reveal intriguing wave phenomena, revolutionizing our understanding of wave behavior including the breakdown of reciprocity, stationary invariance and space–time invariance, and have the potential to promote superior engineering performance like ultra-low and ultra-broadband vibration reduction. An overview of present research and further challenges are provided in fields such as calculation methods, amplitude-dependent bandgaps, self-adaptive bands, nonreciprocal wave control, harmonic control, chaotic dynamics, vibration and sound attenuation, practical design, experimental implementation, and practical applications. © The Author(s) 2024
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