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Using the latter as the asymptotic parameter and employing modal superposition, a formal methodology based on perturbation methods is developed to ascertain the stability and instability characteristics.
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To reduce calculation time due to the complexity of the track model, involving a large number of elements and degrees-of-freedom, a complex-valued modal superposition with a truncated mode set is applied before the impulse response functions are calculated at various positions along the crossing panel.
The overall simulation procedure is based on a decomposition into the nonlinear stationary rolling case, the eigenvalue analysis in the deformed state, and the calculation of the noise radiation including a modal superposition approach with an excitation by deterministic functions.
The clamped boundary condition along the panel edge introduces the modal superposition theory and a double Fourier series solution for the STL is obtained by employing the weighted residual (Galerkin) method.
The method uses a modal superposition technique for the bridge components.
In the multimode method, equations of motion for the coupled wind-bridge system are first represented using a modal superposition technique.
The formulation uses a geometric damage model, perturbation of mode shapes and natural frequencies, and a modal superposition technique to obtain and solve the governing differential equation.
A modal superposition technique and the Newmark-β method are used in the numerical analysis to compute the dynamic response of composite beams.
Based on a finite element (FE) model of a standard turnout design, a complex-valued modal superposition of track dynamics is applied using the first 500 eigenmodes of the turnout model.
A complex modal superposition is adopted to decouple the equations of motion of the linear track model with a non-proportional spatial distribution of viscous damping.
The transient interaction problem is numerically solved by use of an extended state-spacer vector approach in conjunction with a complex modal superposition for the track.
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