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A high-fidelity finite difference approximation of the dynamic beam equation is derived.
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A refined laminated beam constitutive equation is derived that takes into account the breadth direction strains.
From the derived governing equation, a dispersive equation is derived for a viscoelastic Timoshenko beam.
The frequency equation is derived on the basis of Timoshenko beam theory.
Using Euler Bernoulli beam (EBB) model, Hamilton׳s principle and nonlocal piezoelasticity theory, the higher order governing equation is derived.
Using Euler Bernoulli beam (EBB) model, Hamilton's principle and nonlocal piezoelasticity theory, the higher order governing equation is derived.
In this study, a new design equation is derived to predict the shear strength of slender reinforced concrete (RC) beams without stirrups using gene expression programming (GEP).
Then Mathieu equation is derived from the homogeneous structural equation.
High-order CSPCW solutions, termed here high-order quasi-Gaussian cylindrical beams, which exactly satisfy the Helmholtz equation, are derived analytically.
A set of differential equations is derived by finite element formulation for this oscillating beam.
The final system of equations is derived by a combination of equations for both the beam and the elastic foundation in the global coordinate.
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