Inertia force effect on longitudinal vibrations of underground pipelines

The effect of the inertia term on the longitudinal displacements of an underground pipeline is shown for various cases of pipe fastening when a seismic wave propagates along its axis. The problem is solved by analytical and numerical methods. The pipe-soil interaction is assumed to be elastic (shear stress generated in soil is proportional to the relative displacement between the pipe and soil).

Parametric investigation of twin tube magnetorheological dampers using a new unsteady theoretical analysis

In the present work, a new unsteady analytical model is developed for magnetorheological fluid flow through the annular gap which is opened on the piston head of twin tube magnetorheological damper, considering fluid inertia term into the momentum equation. This new unsteady model is based on Stokes’ second problem that is extended for magnetorheological fluid flow between finite oscillating parallel plates under the pressure gradient. A quasi-static analysis is also developed for magnetorheological fluid flow in twin tube damper, to compare its results with present unsteady solution and to show the effect of magnetorheological fluid inertia. The obtained results are validated experimentally and then, a parametric study is presented using both unsteady and quasi-static analysis. The effect of fluid inertia term is investigated on force–displacement and force–velocity loops, magnetorheological fluid velocity profile, pressure drop, phase difference between pressure drop and flow rate and change of plug thickness with time duration. According to the obtained results, quasi-static analysis included considerable error respect to new unsteady analysis as the gap height, magnetorheological fluid density, excitation frequencies and amplitudes are increased and yield stress is decreased. It is found that the plug thickness is considerably affected by inertia term of magnetorheological fluid.

Determination of natural frequencies and mode shapes of a wind turbine rotor blade using Timoshenko beam elements

When simulating a wind turbine, the lowest eigenmodes of the rotor blades are usually used to describe their elastic deformation in the frame of a multi-body system. In this paper, a finite element beam model for the rotor blades is proposed which is based on the transfer matrix method. Both static and kinetic field matrices for the 3-D Timoshenko beam element are derived by the numerical integration of the differential equations of motion using a Runge–Kutta fourth-order procedure. In the general case, the beam reference axis is at an arbitrary location in the cross section. The inertia term in the motion differential equation is expressed using appropriate shape functions for the Timoshenko beam. The kinetic field matrix is built by numerical integration applied on the approximated inertia term. The beam element stiffness and mass matrices are calculated by simple matrix operations from both field matrices. The system stiffness and mass matrices of the rotor blade model are assembled in the usual finite element manner in a global coordinate system accounting for the structural twist angle and possible pre-bending. The program developed for the above-mentioned calculations and the final solution of the eigenvalue problem is accomplished using MuPAD, a symbolic math toolbox in MATLAB®. The natural frequencies calculated using generic rotor blade data are compared with the results proposed from the FAST and ADAMS software.

Determination of Natural Frequencies and Mode Shapes of a Wind Turbine Rotor Blades using Timoshenko Beam Elements

In the simulation of a wind turbine, the lowest eigenmodes of the rotor blades are usually used to describe their elastic deformation in the frame of a multibody system. In this paper, a finite element beam model for the rotor blades based on the transfer matrix method is proposed. Both static and kinetic field matrices for the 3D Timoshenko beam element are derived by numerical integration of the differential equations of motion using RUNGE KUTTA 4th order procedure. The beam reference axis in the general case is at an arbitrary location in the cross section. The inertia term in the motion differential equation is expressed using appropriate shape functions for the Timoshenko beam. The kinetic field matrix is built by numerical integration applied on the approximated inertia term. The beam element stiffness and mass matrices are calculated by simple matrix operations from both field matrices. The system stiffness and mass matrices of the rotor blade model are assembled in the usual finite element manner in a global coordinate system with the accounting for structural twist angle and possibly pre-bending. The program developed for the above calculations and the final solution of the eigenvalue problem is accomplished using MuPAD, a symbolic math toolbox of MATLAB®. The calculated natural frequencies using generic rotor blade data are compared with the results proposed from FAST and ADAMS software.

On the Influence of Piston and Cylinder Density in Tribodynamics of a Radial Piston Digital Fluid Power Displacement Motor

In the past three decades an increasing amount of research has been performed in the field of tribodynamics of fluid power pumps and motors. The main incentives for this research are optimization of reliability and efficiency through the study of loss and wear mechanisms. These mechanisms are very difficult to study experimentally, whereby modeling and simulation are necessary. The modeling of tribodynamics is a multiphysics problem involving multibody dynamics, fluid mechanics, thermodynamics and solid mechanics. Consequently, the simulation durations can easily become impractical for parametric analysis or optimization. The coupling between multibody dynamics and fluid mechanics depend on the formulation of the solid body motion equations, where two approaches have historically been used. One approach is where the external forces on any lubricated joint are balanced by the fluid forces, such that solid body inertia is neglected. The other approach includes the inertia terms in the calculation of microdynamics. The inclusion of inertia terms entails a need for smaller time steps in comparison to the force balance approach, wherefore it is of interest to analyze the influence of the inertia term. In this paper the influence of the inertia term on the lubrication gaps of a radial piston motor are studied by a parametric analysis of the piston and cylinder density in a multibody tribodynamic simulation model. The motor is modeled as a digital fluid power displacement machine and a series of full-stroke displacement simulations are used as basis for the parametric analysis. From the parametric analysis a change, in the minimum film thickness as function of piston and cylinder density, is shown for certain operating modes of the digital fluid power displacement motor. This indicate a need for careful assessment of the applicability, of the force balance condition, if it is used in multibody tribodynamic simulations of radial piston digital fluid power displacement motors.