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Spatial derivatives in the equation of motion are expressed with generalized differential quadrature method.
With such an approach, the equations of motion are expressed as a linear, time-invariant system.
The derivatives present in the equation of motion are expressed in terms of displacements using finite-difference schemes.
First, the coupled deterministic equations of motion are expressed in the bases given by the uncoupled elements' eigenmodes.
In the present 3D axisymmetric model, the equations of motion are expressed by expanding the displacement field using Fourier series in the circumferential direction.
The governing equations of motion are expressed in the state space formulation and are then solved by employing the reverberation-ray matrix method.
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The equation of motion is expressed in non-dimensional matrix form.
The equation of motion is expressed in terms of dimensionless quantities.
Partial derivatives in the equation of motion is expressed with generalized differential quadrature method and time integration is carried out using Newmark average acceleration method.
The effect of convective motion is expressed entirely through changing amplitude and time scales, both of which are given in terms of a single time varying factor.
Using the random process orthogonal expansion method and the concept of random functions, initial earthquake ground motion is expressed as a random process based on only one random variable.
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