We give aderivation of the nonlinear spring equation mx - f(x) = 0 where f(x) represents the restoring force and m is the mass of a weight attached to the spring. This derivation shows that even powers may appear in the Maclaurin expansion of the restoring force function. We demonstrate...
This note discusses the boundary in the frequency--amplitude plane for boundedness of solutions to the forced spring Duffing type equation For fixed initial conditions and fixed parameter results are reported of a systematic numerical investigation on the global stability of solutions to the initial ...
By means of the Lagrange's equation,the nonlinear vibration equation of spring oscillator is established.Using the first kind of complete ellipse integral,the exact solution of the nonlinear spring oscillator period is got,and the curves of the exact solution of the period varying with amplitude,or...
In the second group, an exact equation for determining \( \chi \) is proposed, that is, a nonlinear function that relates the hysteresis factor to the physical parameters of the system. The third category considers those models that, from considering a simple assumption, provide an explicit ...
a Diatomic NAM model composed of periodic linear base m b coupled with Duffing oscillators m r through the nonlinear spring k 1 x + k 2 x 3, where k 1 and k 2 are the linear and nonlinear stiffness coefficients, respectively. b Its band structure. Here, the passbands become ...
Inverse scattering transform for the multi-component nonlinear schro¨dinger equation with nonzero boundary condi- tions. Stud Appl Math 2010;126:245-302.B. Prinari, G. Biondini, and A. D. Trubatch, Inverse scattering transform for the multi-component non- linear Schro¨dinger equation with ...
We assume that the coecients of the system (1)+(2) satisfy the neces- sary Lipschitz and linear growth conditions for the solution of the Zakai equation (see [16] or [3]) to exist and be unique and that h is a continuous bounded function. We also assume that the domain gu2 ...
We want to study the dynamics of a simple linear harmonic micro spring which is under the influence of the quantum Casimir force/pressure and thus behaves as a (an) nonlinear (anharmonic) Casimir oscillator. Generally, the equation of motion of this nonlinear micromechanical Casimir oscillator has...
0frequency-amplitude plane for boundedness of solutions to the forced spring Duffing type equation xe + x + εx~3 = F cos ωt For fixed initial conditions and for representative fixed values of the parameter ε, the results are reported of a systematic numerical investigation into the global ...
"A nonlinear approach to solution of Reynolds equation for elastic distortion analysis to spring-supported thrust bearing", STLE, Tribol Trans 1994; 37(4):802-10.Sinha A N,Athre K,Biswis S.A nonlinear approach to solutionof Reynolds equation for elastic distortion analysis to spring-supported ...