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Showing 1 to 20 of 27 for “"Hamilton's principle"”.
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Deformation theory analysis of a dynamically loaded rigid-plastic cantilever
… what was claimed to be an extension of Hamilton's Principle (normally considered to be restricted to conservative systems) to rigid-plastic structural dynamics. A comment by Professor A.R.S. Ponter, however, has led to the present study. Professor Ponter queried whether Taya and Mura had …
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Dinâmica de estruturas prismáticas laminares - consideração de cargas móveis
… The formulation of the problem makes use of Hamilton's principle and the linear theory of thin plates. Associated with the Fourier series, the finite element method is used to discretize the spatial variables. The resulting system of ordinary differential equations is integrated by means of …
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The permanent deformation of steel portal frames subjected to impulsive loading
… theoretical predictions. The use of the extended Hamilton's principle for mode form solutions is discussed.
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Geometric discretization schemes and differential complexes for elasticity
… volume- preserving discrete deformations, we use Hamilton's principle on this configuration manifold. The discrete Euler-Lagrange equations are obtained without using Lagrange multipliers.
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Numerical relativity from a gauge theory perspective
… symmetries of the continuous action. Applying Hamilton's principle of stationary action gives discrete field equations on the mesh. For each gauge degree of freedom there is a corresponding discrete constraint; the remaining discrete evolution equations exactly preserve these constraints under …
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Nonlinear free vibration of beams by one-dimensional and elasticity solutions
… The equation of motion is derived depending on Hamilton's principle. A validation of the Ritz method formulation has been conducted by comparison with the Euler–Bernoulli beam theory. The impact of three-dimensional beam length has been investigated as well. In terms of nonlinear analysis, a …
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Variationally consistent methods for Lagrangian dynamics in continuum mechanics
… scheme is developed from a variational principle based on Hamilton's principle of stationary action. Such methods ensure conservation of linear and angular momentum, which lead to more physically consistent simulations.
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Resposta dinâmica e estabilidade de tubos com escoamento interno
… use of an updated lagrangian formulation for the principle of virtual work the incremental equations of motion are deduced. These equations are linearized about the equilibrium configuration and the free vibration problem is discussed, showing that an integral of motion exists when the pipes have …
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Towards A Mobile Damping Robot For Vibration Reduction of Power Lines
… we model the conductor and the MDR by using Hamilton's principle and we consider the two-way nonlinear interaction between the MDR and the cable. The MDR is driven by a Proportional-Derivative controller to the optimal vibration location (i.e, antinodes) as the wind characteristics vary. The …
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Applications of Second-Order Necessary and Sufficient Conditions to Optimal Trajectories
… example variational problems are investigated: Hamilton's Principle for several dynamic systems, including a circular orbit in an inverse-square gravitational field and projectile motion in a uniform field, as well as a simple example of Zermelo's problem. For those solutions that satisfy …
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Transient analysis and vibration suppression of a cracked rotating shaft with ideal and nonideal motor passing through a critical speed
… of motion and boundary conditions are derived by Hamilton's Principle. To eliminate the spatial dependence, the Extended Galerkin Method is applied. Longitudinal vibration, shear deformation and torsional vibration are neglected. In the second part of this study, the vibration suppression of a …
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Investigation of a Mobile Damping Robot for Electric Transmission Lines
… in MATLAB using equations of motion obtained via Hamilton's Principle. We discuss the design and validation of an appropriate test bench and MDR prototype. We also experimentally investigate the ability of the MDR prototype to transport a mass along a conductor to antinode locations. Experimental …
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Investigation of Zinc Oxide Nanowires for Impedance Based Structural Health Monitoring
… voltage was applied to the composite. Using Hamilton's Principle and Galerkin's method of weighted residuals, a mathematical model was derived to estimate piezoelectric constants for the composites from the experimental data. Piezoelectric properties were determined using vibrational testing …
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Large Deflection Inextensible Beams and Plates and their Responses to Nonconservative Forces: Theory and Computations
… a new beam and plate model is derived using Hamilton's Principle to lay the structural framework for a nonlinear, large deflection aeroelastic model. Two boundary conditions of the beam are explored: cantilevered and free-free. For a plate, the cantilevered boundary condition is considered. …
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Free Vibration of Bi-directional Functionally Graded Material Circular Beams using Shear Deformation Theory employing Logarithmic Function of Radius
… deformations of the beam are derived by using Hamilton's principle. Assuming a time harmonic variation of the displacements, and by utilizing the generalized differential quadrature method (GDQM) the free vibration problem is reduced to solving an algebraic eigenvalue problem whose solution …
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Feedback Control of Multi-Story Structures under Seismic Excitations
… the state space. A combination of the extended Hamilton's principle and the Hierarchical Finite Element Method (HFEM) was used to derive the discrete differential equations of motion. This method exhibits superior accuracy with fewer degrees of freedom (DOF). The discrete equation were realized …
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Analysis and Compensation of Imperfection Effects in Piezoelectric Vibratory Gyroscopes
… vibratory gyroscopes, were studied. Hamilton's principle and the Rayleigh-Ritz method provided an effective approach for modeling the coupled electromechanical dynamics of piezoelectric resonators. This method produced accurate results when applied to an imperfect piezoelectric …
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Modeling and Analysis of a Cantilever Beam Tip Mass System
… excitation are developed using generalized Hamilton's principle. Using a Galerkin's discretization scheme, the discretized equation for the first mode is developed for simpler representation assuming linear and nonlinear boundary conditions. We solve the distributed parameter and discretized …
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Axisymetric vibrations of homogeneous and sandwich spherical shells with a hole at the center
Based on Hamilton's principle and the theory of elasticity, both linear and nonlinear governing equations of motion are derived for elastic spherical shells. Most of the analysis is focused on the free axisymmetric vibrations of homogeneous and sandwich shallow spherical shells. The nonlinear …
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Towards a Self-Powered Structural Health Monitoring Smart Tire
… harvester model was derived using extended Hamilton's principle and the linear constitutive relations of piezoelectric materials. Comparison of model with experimental data at increasing loading conditions demonstrated the monotonic increase in voltage output, with linear asymptotes at …
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