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A joint PD controller with additional feedback of joint acceleration and root strain of the beam is derived using a Lyapunov-type method.
The mathematical model that describes the lateral vibration of the beam is derived using the assumed mode method that coalesces with the Lagrange's equation.
Starting from the governing differential equations of motion in free vibration, the dynamic stiffness matrix of a uniform rotating Bernoulli Euler beam is derived using the Frobenius method of solution in power series.
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Nonlinear equations for a simply supported beam are derived using Ritz method in conjunction with minimum potential energy principle.
Based on the proposed model, the frequency responses of the displacement of the mounted mass and every beam are derived using a topological method.
The effect of light on the liquid crystal elastomer beam is modeled as an inhomogeneous and time-dependent light-induced contraction strain and the dynamic equations of the beam are derived using the Hamilton's principle.
A six order differential equation governing the apparent bending of sandwich beams is derived using Hamilton's principle.
The motion governing equation for FG beams is derived using the Hamilton's principle under the assumption of the Euler-Bernoulli beam theory.
Equations of motion governing wave motion in the bonded beams are derived using Hamilton's principle.
Considering the von Kármán geometric nonlinearity, governing equations of nano-beam are derived using Eringen's nonlocal theory and the modified couple stress theory is utilized to obtain the governing equations of microbeam.
A nodally-exact micropolar Timoshenko beam finite element is derived using the solution.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com