Related papers: Nonlinear modes of clarinet-like musical instrumen…
This article uses a basic model of a reed instrument , known as the lossless Raman model, to determine analytically the envelope of the sound produced by the clarinet when the mouth pressure is increased gradually to start a note from…
Mechanical nonlinearities dominate the motion of nanoresonators already at relatively small oscillation amplitudes. Although single and coupled two-degrees-of-freedom models have been used to account for experimentally observed nonlinear…
We define a nonlinear thermodynamical formalism which translates into dynamical system theory the statistical mechanics of generalized mean-field models, extending investigation of the quadratic case by Leplaideur and Watbled. Under…
Modal synthesis methods are a long-standing approach for modelling distributed musical systems. In some cases extensions are possible in order to handle geometric nonlinearities. One such case is the high-amplitude vibration of a string,…
The dynamic mode decomposition (DMD) is a data-driven method used for identifying the dynamics of complex nonlinear systems. It extracts important characteristics of the underlying dynamics using measured time-domain data produced either by…
In the present paper, two existing nonlinear system identification methodologies are used to identify data-driven models. The first methodology focuses on identifying the system using steady-state excitations. To accomplish this, a…
The sound propagation is usually described by a linear homogeneous wave equation, though the air flow in a duct is described by the gas dynamics equations, using a variable cross section, which corresponds to a non linear non homogneous…
The resonances of forced dynamical systems occur when either the amplitude of the frequency response undergoes a local maximum (amplitude resonance) or phase lag quadrature takes places (phase resonance). This study focuses on the phase…
We present a first principle derivation of the coupled nonlinear Schr\"{o}dinger equations that govern the interaction between two families of modes with different transverse profiles in a generic whispering-gallery-mode resonator. We find…
Nonlinear effects are omnipresent in thin films of ion conducting materials showing up as a significant increase of the conductivity. For a disordered hopping model general physical mechanisms are identified giving rise to the occurrence of…
We prove the existence of nonlinear normal modes for general systems of two coupled nonlinear oscillators. Facilitating the comparison principle for ordinary differential equations it is shown that there exist exact solutions representing a…
Nonlinear diffusion is studied in the presence of multiplicative noise. The nonlinearity can be viewed as a ``wall'' limiting the motion of the diffusing field. A dynamic phase transition occurs when the system ``unbinds'' from the wall.…
The register tube marks the invention of the clarinet in the early eighteenth century, tripling the range of its ancestor, the chalumeau, and giving it the widest range among wind instruments. Opening this narrow tube causes the fundamental…
This work presents a nonlinear system identification framework for modeling the power extraction dynamics of wind turbines, including both freestream and waked conditions. The approach models turbine dynamics using data-driven power…
This paper aims at reviewing nonlinear methods for model order reduction of structures with geometric nonlinearity, with a special emphasis on the techniques based on invariant manifold theory. Nonlinear methods differ from linear based…
The paper takles a procedure which allow to extend some linear, wave type equations to the study of nonlinear models. More concretely, we present a practical way to generate the largest class of a given form of second order differential…
We study nonlinear resonance of coupled modes in nano-mechanical systems. To reveal the qualitative features of the dynamics, we consider the limiting cases, where the results can be obtained analytically. For 1:3 resonance, we find the…
Extensive studies have investigated the transition mechanism of boundary layers initiated by a single primary instability. In a real-world scenario, however, multiple primary instabilities of different physical nature would coexist and…
We propose a comprehensive model describing the Kerr nonlinear dynamics of an electric field in a cylindrical microresonator with an effective radius variation, coupled to a radiation source. The proposed system of equations for coupled…
The steady state motion of a folded pendulum has been studied using frequencies of drive that are mainly below the natural (resonance) frequency of the instrument. Although the free-decay of this mechanical oscillator appears textbook…