Hamilton's principle is put to use to establish the size-dependent governing differential equations of motion.
By using Hamilton's principle, the size-dependent governing differential equations of motion and associated boundary conditions are derived.
The time-dependent governing equations for conservation of mass, momentum and energy together with turbulent kinetic energy and its dissipation rate are solved.
The different modes of heat transfer of the still were modeled and numerical solution for the time-dependent governing equations was performed using Runge-Kutta method of the 5th order.
The size-dependent governing differential equation is derived based on the nonlocal Euler Bernoulli beam theory with the thermal effect and the analytical formulations of the natural frequencies are deduced.
Employing the nonlocal strain gradient theory, the size-dependent governing equations accounting for the geometric nonlinearity and elastic medium are derived and the analytical solution for nonlinear frequency is presented.
The geometrically nonlinear size-dependent governing equation of system is derived in the framework of modified couple stress theory in conjunction with Euler-Bernoulli beam theory and the classical rule of mixture.
The size-dependent governing differential equations are derived and discretized along with various end supports by employing the principle of virtual work and the generalized differential quadrature (GDQ) method.
To this end, the size-dependent governing differential equations of cylindrical nanoshell based on von Karman Donnell-type of Karman Donnell-typeity are derived using a cofbination of Gurtin–Murdoch elasticity theory and the classical shell theory, and employing the principle of virtual workinematic
The number of recrossings of the overall barrier is temperature-dependent, governed by the microbarriers and not by the effective friction.
