Loads Moving on Beam Supported by Layered Elastic Foundation

1980 ◽  
Vol 102 (2) ◽  
pp. 295-302 ◽  
Author(s):  
V. N. Shah ◽  
R. D. Cook ◽  
T. C. Huang
Keyword(s):  
Dynamic Response ◽  
Equations Of Motion ◽  
Variable Coefficients ◽  
Moving Loads ◽  
Numerical Illustration ◽  
Concentrated Force ◽  
Winkler Model ◽  
First Case ◽  
Mass Damper ◽  
Pasternak Model

A finite element method is applied to analyze the dynamic response of a beam supported by layered inertial foundation and subjected to moving loads. The foundation is represented by the modified Pasternak model or by the Winkler model. The moving loads are simulated by a concentrated force, a point-mass or a spring-mass-damper system. The equations of motion are represented by a system of second-order ordinary differential equations with variable coefficients. Newmark’s method of constant average acceleration is used to integrate these equations. Two test cases are analyzed for numerical illustration. In the first case, the dynamic response of a beam supported by the modified Pasternak model and subjected to a moving concentrated force is analyzed. In the second, the dynamic response of a beam supported by the Winkler model and subjected to a moving spring-mass-damper system is analyzed. The results from these two cases are compared with those obtained by the transfer matrix method.

scholarly journals Dynamic Response Analysis of a Thin Plate with Partially Constrained Layer Damping Optimization under Moving Loads for Various Boundary Conditions

2021 ◽  
Vol 11 (7) ◽  
pp. 3282
Author(s):  
Yun Qin ◽  
Qinghua Song ◽  
Zhanqiang Liu ◽  
Jiahao Shi
Keyword(s):  
Dynamic Response ◽  
Loss Factor ◽  
Lagrange Equation ◽  
Differential Quadrature Method ◽  
Equations Of Motion ◽  
Shear Deformation Theory ◽  
Response Analysis ◽  
Constrained Layer Damping ◽  
Moving Loads ◽  
Damping Loss Factor

In this paper, the vibration analysis of a partially constrained layer damping plate subjected to moving loads is investigated. In addition, the first four order damping loss factor of the system is optimized with the location of partially constrained layer damping as a design variable. The equations of motion of a partially constrained layer damping plate are derived through the Lagrange equation based on first order shear deformation theory (FSDT). Next, using an extended Rayleigh–Ritz solution together with the penalty method expresses the unknown displacement terms, and the differential quadrature method is proposed to obtain the dynamic response of the system in the time domain. A multi-population genetic algorithm (MPGA) is employed to deal with the optimization of the damping loss factor of a partially constrained layer damping plate. To ensure the accuracy of the method presented in this study, the numerical results are comprehensively verified by experiments and open literature. The optimization results show that the damping loss factor increases when the position of the patch is close to the constraint boundary, and the best strategy is to optimize the low order damping loss factor of the system under moving loads. It is believed that the research results are of interest to engineering science.

Less=Moor: A Time-Efficient Computational Tool to Assess the Behavior of Moored Ships in Waves

2017 ◽  
Author(s):  
Yijun Wang ◽  
Alex van Deyzen ◽  
Benno Beimers
Keyword(s):  
Dynamic Response ◽  
Research Effort ◽  
Equations Of Motion ◽  
Line Tension ◽  
Mooring Line ◽  
Induced Response ◽  
Wave Forces ◽  
Computational Tool ◽  
The Time Domain ◽  
Nonlinear Equations Of Motion

In the field of port design there is a need for a reliable but time-efficient method to assess the behavior of moored ships in order to determine if further detailed analysis of the behavior is required. The response of moored ships induced by gusting wind and/or waves is dynamic. Excessive motion response may cause interruption of the (un)loading operation. High line tension may cause lines to snap, introducing dangerous situations. A (detailed) Dynamic Mooring Analysis (DMA), however, is often a time-consuming and expensive exercise, especially when responses in many different environmental conditions need to be assessed. Royal HaskoningDHV has developed a time-efficient computational tool in-house to assess the wave (sea or swell) induced dynamic response of ships moored to exposed berths. The mooring line characteristics are linearized and the equations of motion are solved in the frequency domain with both the 1st and 2nd wave forces taken into account. This tool has been termed Less=Moor. The accuracy and reliability of the computational tool has been illustrated by comparing motions and mooring line forces to results obtained with software that solves the nonlinear equations of motion in the time domain (aNySIM). The calculated response of a Floating Storage and Regasification Unit (FSRU) moored to dolphins located offshore has been presented. The results show a good comparison. The computational tool can therefore be used to indicate whether the wave induced response of ships moored at exposed berths proves to be critical. The next step is to make this tool suitable to assess the dynamic response of moored ships with large wind areas, e.g. container ships, cruise vessels, RoRo or car carriers, to gusting wind. In addition, assessment of ship responses in a complicated wave field (e.g. with reflected infra-gravity waves) also requires more research effort.

Dynamics Simulation and Analysis of Transition Stage of Tilt-Rotor Aircraft

2016 ◽  
Vol 842 ◽  
pp. 251-258 ◽  
Author(s):  
Muhammad Rafi Hadytama ◽  
Rianto A. Sasongko
Keyword(s):  
Dynamic Response ◽  
Equations Of Motion ◽  
Flight Dynamics ◽  
Dynamics Simulation ◽  
Tilt Rotor ◽  
Vertical Takeoff And Landing ◽  
Improved Stability ◽  
Simulation Results ◽  
Vtol Aircraft ◽  
Vertical Takeoff

This paper presents the flight dynamics simulation and analysis of a tilt-rotor vertical takeoff and landing (VTOL) aircraft on transition phase, that is conversion from vertical or hover to horizontal or level flight and vice versa. The model of the aircraft is derived from simplified equations of motion comprising the forces and moments working on the aircraft in the airplane's longitudinal plane of motion. This study focuses on the problem of the airplane's dynamic response during conversion phase, which gives an understanding about the flight characteristics of the vehicle. The understanding about the flight dynamics characteristics is important for the control system design phase. Some simulation results are given to provide better visualization about the behaviour of the tilt-rotor. The simulation results show that both transition phases are quite stable, although an improved stability can give better manoeuver and attitude handling. Improvement on the simulation model is also required to provide more accurate and realistic dynamic response of the vehicle.

Research on the Selecting Control Sections of Internal Force Envelope by Simulation

2012 ◽  
Vol 226-228 ◽  
pp. 1467-1471
Author(s):  
Hai Xiang Lu ◽  
Jing Hua Diao ◽  
Zeng Zhi Li
Keyword(s):  
Simulation Optimization ◽  
Internal Force ◽  
Moving Loads ◽  
Concentrated Force ◽  
Live Loads ◽  
Concentrated Couple

The simulation optimization of internal force envelope in plane bar structure subjected to complex moving loads, including arbitrary concentrated force, concentrated couple, linearly distributed force and etc, was mainly discussed. By means of Vsap2011, the plane bar structure analyzing software, the effects of internal force envelope’s control sections on the solving precision of internal force envelope were analyzed. The research had reached to some important conclusions that in order to the obtain higher solving precision of internal force envelope, the element passed by moving loads should be divided by steps; more than enough dividing points should be inserted between load acting points for the element arbitrarily distributed with live loads; the element without any loads should be divided by defined interval when its both ends are rigid-jointed, while it should not be divided when its single or both ends are hinged-jointed.

scholarly journals Steady and unsteady flow of non-newtonian fluid in curved pipe with triangular

2006 ◽  
Vol 3 (3) ◽  
pp. 470-480
Author(s):  
Baghdad Science Journal
Keyword(s):  
Unsteady Flow ◽  
Pressure Gradient ◽  
Secondary Flow ◽  
Cross Section ◽  
Numerical Study ◽  
Equations Of Motion ◽  
Curved Pipe ◽  
First Case ◽  
Stable Flow ◽  
Flow Cross

This paper deals with numerical study of the flow of stable and fluid Allamstqr Aniotina in an area surrounded by a right-angled triangle has touched particularly valuable secondary flow cross section resulting from the pressure gradient In the first case was analyzed stable flow where he found that the equations of motion that describe the movement of the fluid

scholarly journals Multiple shooting method in stability analysis of non-prismatic multi-segment columns

2013 ◽  
Vol 12 (4) ◽  
pp. 225-232
Author(s):  
Ryszard Hołubowski ◽  
Andrzej Merena
Keyword(s):  
Finite Element Method ◽  
Stability Analysis ◽  
Shooting Method ◽  
High Efficiency ◽  
Variable Coefficients ◽  
Multiple Shooting ◽  
System Of Differential Equations ◽  
The Finite Element Method ◽  
Concentrated Force ◽  
Multiple Shooting Method

The application of multiple shooting method in stability analysis of non-prismatic multi-segment columns with pinned ends loaded with a concentrated force applied to the upper node has been presented. Numerical analyses were carried out for an exemplary three-segment column by solving the system of differential equations with variable coefficients and parameter. The results were compared with the solution obtained by using SOFiSTiK software based on the finite element method. The analyses show that considering the stiffness changes along the length can have a significant influence on the values of critical loads and thus change the resistance of the column. The advantage of the proposed method is its high efficiency and easy description of stiffness changes.

scholarly journals Multi-moving Loads Induced Vibration of FG Sandwich Beams Resting on Pasternak Elastic Foundation

2021 ◽  
Vol 18 (9) ◽  
Author(s):  
Wachirawit SONGSUWAN ◽  
Monsak PIMSARN ◽  
Nuttawit WATTANASAKULPONG
Keyword(s):  
Dynamic Response ◽  
Elastic Foundation ◽  
Excitation Frequency ◽  
Beam Theory ◽  
Equation Of Motion ◽  
Functionally Graded ◽  
Sandwich Beams ◽  
Moving Loads ◽  
Layer Thickness Ratio ◽  
Pasternak Elastic Foundation

The dynamic behavior of functionally graded (FG) sandwich beams resting on the Pasternak elastic foundation under an arbitrary number of harmonic moving loads is presented by using Timoshenko beam theory, including the significant effects of shear deformation and rotary inertia. The equation of motion governing the dynamic response of the beams is derived from Lagrange’s equations. The Ritz and Newmark methods are implemented to solve the equation of motion for obtaining free and forced vibration results of the beams with different boundary conditions. The influences of several parametric studies such as layer thickness ratio, boundary condition, spring constants, length to height ratio, velocity, excitation frequency, phase angle, etc., on the dynamic response of the beams are examined and discussed in detail. According to the present investigation, it is revealed that with an increase of the velocity of the moving loads, the dynamic deflection initially increases with fluctuations and then drops considerably after reaching the peak value at the critical velocity. Moreover, the distance between the loads is also one of the important parameters that affect the beams’ deflection results under a number of moving loads.

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