Experimental investigation of resonantly forced oscillations of a two-degree-of-freedom structure
Abstract An experimental study of the response of a two-degree-of-freedom structure with quadratic non-linearities and a two-to-one internal resonance to an external harmonic excitation is presented. When the excitation frequency was close to the lower natural frequency of the structure, periodic, quasi-periodic, and chaotic responses were observed. Fourier spectra, time-dependent modal decompositions, and Poincare maps were used to analyze the amplitude- and phase-modulated motions of the structure.
We derive asymptote solution of a homogeneous and isotropic universe governed by the quadratic form of the field equation of $f(T)$ gravity. We explain how the higher order of the torsion can provide an origin for late accelerated phase of the universe in the FRW. The solution makes the scalar torsion $T$ to be a function of the cosmic time $t$. We show that for the equation of state $p=\omega \rho$ with $\omega\neq -1$ the scale factor represent late phase of universe. We perform the cosmological studies and show how the quadratic form of $f(T)$ effect on the behavior of these studies.