In this paper, the nonlinear dynamical behavior of an isotropic rectangular plate, simply supported on all edges under influence of a moving mass and as well as an equivalent concentrated force is studied. The governing nonlinear coupled PDEs of motion are derived by energy method using Hamilton’s principle based on the large deflection theory in conjuncture with the von-Karman strain-displacem...

in this paper, reduced order proper orthogonal decomposition method has been used for simulation of unsteady incompressible flow fields. after projection of the governing equations along pod modes, a low-dimensional dynamical system is achieved. normally, standard low-dimensional models, due to some reasons, do not predict time variations of flow field accurately. accuracy of dynamical system h...

Learning the governing equations in dynamical systems from time-varying measurements is of great interest across different scientific fields. This task becomes prohibitive when such data is moreover highly corrupted, for example, due to the recording mechanism failing over unknown intervals of time. When the underlying system exhibits chaotic behavior, such as sensitivity to initial conditions,...

In canonical models of Micro-Electro Mechanical Systems (MEMS), an event called touchdown whereby the electrical components of the device come into contact, is characterized by a blow up in the governing equations and a non-physical divergence of the electric field. In the present work, we propose novel regularized governing equations whose solutions remain finite at touchdown and exhibit addit...

This work presents the arguments for the possibility of approximating some discontinuous dynamical systems with continuous or even smooth dynamical systems. The discontinuous di€erential equation, which describes the system, is transformed into a di€erential inclusion and then into a di€erential equation with continuous or smooth right-hand side. As an example a generalization of the equations ...

We study a gradient-flow version of the Ginzburg-Landau equations with an addition of a compactly supported potential term. We consider initial data close to a magnetic vortex solution of the Ginzburg-Landau equations and find the dynamical law governing the motion of the vortex center in the presence of the potential.

The ability to discover physical laws and governing equations from data is one of humankind’s greatest intellectual achievements. A quantitative understanding of dynamic constraints and balances in nature has facilitated rapid development of knowledge and enabled advanced technological achievements, including aircraft, combustion engines, satellites, and electrical power. In this work, we combi...

The presence of nonlinear terms in the governing equations of a dynamical system usually leads to the loss of predictability, e.g. in numerical weather prediction. However, for the El Niño-Southern Oscillation (ENSO) phenomenon, in an intermediate coupled equatorial Pacific model run under the 1961–1975 and the 1981–1995 climatologies, the latter climatology led to longer-period oscillations, t...