Real systems are often complex, nonlinear, and noisy in various fields, including mathematics, natural science, and social science. We present the symplectic entropy (SymEn) measure as well as an analysis method based on SymEn to estimate the nonlinearity of a complex system by analyzing the given time series. The SymEn estimation is a kind of entropy based on symplectic principal component ana...

Gaussian beams and wave packets are formally equivalent to high-frequency solutions of the linear wave equation with complex-valued phase functions. The theory of weakly nonlinear high-frequency waves is extended in this paper to allow for complex phase solutions. The procedure is similar to nonlinear geometrical optics and the nonlinearity causes the phase to vary, leading to the development o...

The dynamics of beams that undergo large displacements is analyzed in frequency domain and comparisons between models derived by isogeometric analysis and p-FEM are presented. The equation of motion is derived by the principle of virtual work, assuming Timoshenko’s theory for bending and geometrical type of nonlinearity. As a result, a nonlinear system of second order ordinary differential equa...

this paper presents a nonlinear model of a clamped-clamped microbeam actuated by an electrostatic load with stretching and thermoelastic effects. the frequency of free vibration is calculated by discretization based on the differential quadrature (dq) method. by separating the real and imaginary parts of frequency, the quality factor of thermoelastic damping is calculated. both the stretching a...

torsion of many symmetric structures, which were designed based on the seismic codes, is due to their asymmetricity induced during inelastic behavior. although the structure was designed symmetrically assuming elastic based criteria, different factors such as material inconsistency in structure, construction details discrepancy and construction errors may result in asymmetric behavior in inelas...

Recently, a new model of propagation of the light through the so-called weakly three-dimensional Cole-Cole nonlinear medium with short-range nonlocality has been proposed. In particular, it has been shown that in the geometrical optics limit, the model is integrable and it is governed by the dispersionless Veselov-Novikov (dVN) equation. Burgers-Hopf equation can be obtained as 1+1-dimensional ...