Elements main unknowns consist in displacements and electric potential that are approximated above the beam cross-section via Lagrange's polynomials in a layer-wise sense.
At the receiver, the GPS signals from different paths will add in a phase-wise sense, causing fluctuations in the signal amplitude and phase.
The correction terms are obtained by using the exact homogenous solution of the composite beam problem as the interpolation functions which impose the zero-slip constraint between the two components in the point-wise sense.
Let v0 be the lowest vertex (in a component-wise sense) shared by y, y′ and let ak+ (ak−) be the sum of positive (negative) elements of row k of A, excluding the diagonal.
It is assumed that only a finite number of point-wise sensing and actuation devices, suitably located in an equi-spaced manner along the 1-dimensional spatial domain of interest, is available.
The state of the closed-loop system is shown to feature an exponential ISS property with respect to mismatched disturbances thereby constituting a new result in the DPsettinging, capturing point-wise sensing and actuation.
A fully condensed elemental equilibrium equations as mathematical exactness in the piece-wise linear sense is explicitly derived within AFEM formulation.
The hierarchical beam model is derived within the framework of the Carrera Unified Formulation (CUF), which makes use of Lagrange polynomials to express the three-dimensional (3D) displacement field via arbitrary order approximation of pure displacement variables at each layer over the cross section, in a Layer-Wise (LW) sense.
The wise person, sensing her intention, responded, "I cannot say whether the bird is alive or dead, but I can say that the fate of the bird is in your hands".
Right from the music's start, as with Buddy Holly's "That'll Be The Day" ("when I die…") and "Not Fade Away", its wisest minds sensed a reckoning would come one day.
