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c, Energy as a function of displacement along the shear-mode coordinate.
The frequency modulated (FM) oscillator output is a function of displacement.
These findings include typical strengths and failure modes, as well as stiffness and/or friction coefficient values as a function of displacement, for all the test specimens.
When the damping is light, one term in the Fokker-Planck equation for the joint density function of displacement, velocity and acceleration is negligibly small.
Failure due to combined shear, tensile and compressive stresses are considered through a constitutive damaging contact model that incorporates traction separation as a function of displacement discontinuity.
The joint probability density function of displacement and velocity is sought by trying approximate solutions to the Fokker-Planck-Kolmogorov equation.
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All derivations are based upon the Fourier-series representations of the fundamental solutions, including Green's function of displacements and its derivatives.
These equations are solved for two kinds of boundary conditions and the unknown assumed functions of displacement field are found.
Since the system parameters are functions of displacement, the present study, from a purely mathematical viewpoint, is thus a genuine non-linear inverse vibration problem.
These results were analyzed in several ways: trajectories, Poincaré maps, probability density functions of displacement and velocity, root mean square responses and Lyapunov exponents.
The common practice in developing a locking-free curved beam element is to ensure that its interpolation functions of displacement explicitly satisfy the inextensible bending mode condition for the membrane locking-free instead of the rigid body modes.
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