# Euler’s equation

Xem 1-20 trên 37 kết quả Euler’s equation
• ### Free vibration of functionally graded beams resting on winkler foundation around the buckling domain

This paper investigates free vibration of functionally graded beams (FG beams) resting on Winkler foundation around the buckling domain. The governing equations of motion based on Euler–Bernoulli and Timoshenko beam theories together with Von Karman’s strain–displacement relation are derived from Lagrange’s equations.

• ### Study on effects of road conditions on the lateral instability of tractor semitrailer vehicle during turning maneuver

This paper establishes a dynamic model of tractor semitrailer vehicle, based on Multi-Body System Method analysis and Newton-Euler equations with Burckhardt’s tire model. This model is applied to evaluate the effect of road conditions on lateral instability of the tractor semitrailer vehicle during turning maneuver.

• ### Analysis rollover condition of tractor semitrailer while turning maneuver with high forward speed

In this paper, a full dynamic model of tractor semitrailer is developed based on Multi-body System Method and Newton-Euler equations. The rollover condition is based on the load transfer ratio which corresponds to the load transfer between the left and the right sides of the vehicle.

• ### Theoretical approach to the performance analysis of a low-specific speed pump as turbine based on hydraulic losses

This paper focuses on building a theoretical method, based on the calculation of hydraulic losses to predict the energy performance of a Low-specific speed Pump as Turbine (PaT) quickly and accurately that supported for the PaT’s impeller design. The Euler equation is built with the analysis of hydraulic loss calculation and flow phenomena passing on the machine.

• ### An adaptive sliding mode controller for a class of MIMO Euler-Lagrange systems with variable parameters

This paper presents a method to synthesize the adaptive sliding mode controller for a class of MIMO Euler-Lagarance systems with variable parameters. We perform a Taylor series expansion of a class of MIMO Euler-Lagarance systems into nonlinear state-space equations, considering cases of varying parameters and unmeasured external disturbances.

• ### Numerical scheme for transient seepage analysis under unsaturated conditions

This study attempts to develop a numerical scheme for 2-D transient analysis under unsaturated conditions. First, the unsaturated groundwater flow was described using the mass conservation law. Then, the Finite Difference Method and Backward Euler approximation were applied for space and time discretization, respectively.

• ### On models with wobbling disk for brake squeal

The presented models are more generalized in terms of damping, in-plane vibration, and asymmetry. The equations of motion for a 2DOF case that are compact enough are presented. It is shown that asymmetric coefficients of kinetic friction may have stabilizing effect while softening the tangential pads’ supports can either stabilize or destabilize the trivial solution of the system.

• ### Nonlinear vibration of nonlocal strain gradient nanotubes under longitudinal magnetic field

The nonlinear free vibration of embedded nanotubes under longitudinal magnetic field is studied in this paper. The governing equation for the nanotube is formulated by employing Euler–Bernoulli beam model and the nonlocal strain gradient theory. The analytical expression of the nonlinear frequency of the nanotube is obtained by using Galerkin method and the equivalent linearization method with the weighted averaging value. The accuracy of the obtained solution has been verified by comparison with the published solutions and the exact solution.

• ### Vibration under variable magnitude moving distributed masses of non-uniform bernoulli–euler beam resting on pasternak elastic foundation

The dynamic response to variable magnitude moving distributed masses of simply supported non-uniform Bernoulli–Euler beam resting on Pasternak elastic foundation is investigated in this paper. The problem is governed by fourth order partial differential equation with variable and singular coefficients. The main objective of this work is to obtain closed form solution to this class of dynamical problem.

• ### Plasticity based interface model for failure modelling of unreinforced masonry under cyclic loading

In this work our objective is to understand the failure behaviour of unreinforced masonry under in-plane cyclic loading. For this purpose we proposed a plasticity based interface model consists of a single yield surface criteria which is a direct extension of Mohr–Coulomb criteria with a tension cut and compression cap and a back stress vector is introduced as a mixed hardening law variable in the adopted yield surface to capture the unloading/reloading behaviour of masonry under cyclic loading.

• ### Modeling and analysis of vibration of a gold nano-beam under two-temperature theory

The present problem deals with the thermo-elastic interaction of a gold nano-beam resonator induced by ramp-type heating under the two temperature theory of generalized thermoelasticity. The governing equations are constructed in the context of two-temperature three-phase-lag model (2T3P) and two-temperature Lord-Shulman (2TLS) model of generalized thermoelasticity.

• ### Dynamic model with a new formulation of coriolis/centrifugal matrix for robot manipulators

The paper presents a complete generalized procedure based on the Euler-Lagrange equations to build the matrix form of dynamic equations, called dynamic model, for robot manipulators. In addition, a new formulation of the Coriolis/centrifugal matrix is proposed. The link linear and angular velocities are formulated explicitly. Therefore, the translational and rotational Jacobian matrices can be derived straightforward from definition, which make the calculation of the generalized inertia matrix more convenient.

• ### Boundary conditions for hyperbolic systems of partial differentials equations

An easy-to-apply algorithm is proposed to determine the correct set(s) of boundary conditions for hyperbolic systems of partial differential equations. The proposed approach is based on the idea of the incoming/outgoing characteristics and is validated by considering two problems. The first one is the well-known Euler system of equations in gas dynamics and it proved to yield set(s) of boundary conditions consistent with the literature. The second test case corresponds to the system of equations governing the flow of viscoelastic liquids.

• ### Curves whose pseudo spherical indicatrices are elastic

The pseudo spherical indicatrix of a curve in Minkowski 3-space emerges as three types: The pseudo spherical tangent indicatrix, principal normal indicatrix, and binormal indicatrix of the curve.

• ### Numerical approach for solving space fractional order diffusion equations using shifted Chebyshev polynomials of the fourth kind

In this paper, a new approach for solving space fractional order diffusion equations is proposed. The fractional derivative in this problem is in the Caputo sense. This approach is based on shifted Chebyshev polynomials of the fourth kind with the collocation method.

• ### P-elastica in the 3-dimensional lorentzian space forms

R Huang worked the p-elastic in a Riemannian manifold with constant sectional curvature. In this work, we solve the Euler-Lagrange equation by quadrature and study the Frenet equation of the p-elastica by using the Killing field in the three dimensional Lorentzian space forms.

• ### On the compression softening effect of prestressed beams

The main objective of the present paper is to study the transverse vibration of the prestressed beams. The differential equation of the transverse vibration of the Euler-Bernoulli beam is developed, in which the initial axial strain in every cross section of the beam is taken into account, so that the initial normal stress is not equal to zero. We have proposed some formulae to determine the natural frequencies of the prestressed beam.

• ### Calculation of transonic flows around profiles with blunt and angled leading EDGES

Transonic flow is a mixed flow of subsonic and supersonic regions. Because of this mixture, the solution of transonic flow problems is obtained only when solving the differential equations of motion with special treatments for the transition from subsonic region to supersonic region and vice versa. We built codes solving the full potential equation and Euler equations by applying the finite difference method and finite volume method, and also associated with software Fluent to consider the viscous effects.

• ### Rayleigh’s quotient for multiple cracked beam and application

Rayleigh’s quotient for Euler-Bernoulli multiple cracked beam with different boundary conditions has been derived from the governed equation of free vibration. An appropriate choosing of approximate shape function in terms of mode shape of uncracked beam and specific functions satisfying conditions at cracks and boundaries leads to an explicit expression of natural frequencies through crack parameters that can simplify not only the analysis of natural frequencies of cracked beam but also the crack detection problem.

• ### Comparative study of numerical schemes for strong shock simulation using the Euler equations

This study presented the implementation of some typical finite difference schemes solving the compressible Euler equations. As categorized in, the numerical methods will be studied are the Flux Difference scheme, whose Roe’s Approximate Riemann Solver is the representative; the Flux Vector Splitting scheme, whose Steger-Warming method is the representative; the Flux Limited Method.