scholarly journals IMPROVED ANALYSIS OF A PROPPED CANTILEVER UNDER LATERAL VIBRATION

2021 ◽  
Vol 30 (4) ◽  
Author(s):  
Victor Okonkwo ◽  
Chukwurah Aginam ◽  
Charles Nwaiwu
Keyword(s):  
Dynamic Response ◽  
Dynamic Analysis ◽  
Continuous Systems ◽  
Lateral Vibration ◽  
Continuous Beam ◽  
Lumped Mass ◽  
Lagrange’S Equation ◽  
Continuous Beams ◽  
Lumped Masses ◽  
Stiffness Distribution

Continuous systems are sometimes analysed as lumped masses connected by massless elements. This reduces the structure’s degree of freedom and therefore simplifies the analysis. However this over simplification introduces an error in the analysis and the results are therefore approximate. In this work sections of the vibrating beam were isolated and the equations of the forces causing vibration obtained using the Hamilton’s principle. These forces were applied to the nodes of an equivalent lumped mass beam and the stiffness modification needed for it to behave as a continuous beam obtained. The beam’s stiffness was modified using a set of stiffness modification factors to . It was observed that by applying these factors in the dynamic analysis of the beam using the Lagrange’s equation, we obtain the exact values of the fundamental frequency irrespective of the way the mass of the beam was lumped. From this work we observed that in order to obtain an accurate dynamic response from a lumped mass beam there is need to modify the stiffness composition of the system and no linear modification of the stiffness distribution of lumped mass beams can cause them to be dynamically equivalent to the continuous beams. This is so because the values of the modification factors obtained for each beam segment were not equal. The stiffness modification factors were obtained for elements at different sections of the beam

scholarly journals Dynamic Analysis of Encastre Beams by Modification of the System’s Stiffness Distribution

2020 ◽  
Vol 5 (11) ◽  
pp. 1334-1342
Author(s):  
V. O. Okonkwo ◽  
C. H. Aginam ◽  
C. M. O. Nwaiwu
Keyword(s):  
Dynamic Analysis ◽  
Equations Of Motion ◽  
Continuous Systems ◽  
Complex Structures ◽  
Hamilton’S Principle ◽  
Equilibrium Equations ◽  
Lumped Mass ◽  
Hamilton's Principle ◽  
Lumped Masses ◽  
Stiffness Distribution

Numerical and energy methods are used to dynamically analyze beams and complex structures. Hamilton’s principle gives exact results but cannot be easily applied in frames and complex structures. Lagrange’s equations can easily be applied in complex structures by lumping the continuous masses at selected nodes. However, this would alter the mass distribution of the system, thus introducing errors in the results of the dynamic analysis. This error can be corrected by making a corresponding modification in the systems’ stiffness matrix. This was achieved by simulating a beam with uniformly distributed mass with the force equilibrium equations. The lumped mass structures were simulated with the equations of motion. The continuous systems were analyzed using the Hamilton’s principle and the vector of nodal forces {P} causing vibration obtained. The nodal forces and displacements were then substituted into the equations of motion to obtain the modified stiffness values as functions of a set of stiffness modification factors. When the stiffness distribution of the system was modified by means of these stiffness modification factors, it was possible to predict accurately the natural fundamental frequencies of the lumped mass encastre beam irrespective of the position or number of lumped masses.

Dynamic analysis of a helical gear reduction by experimental and numerical methods

2020 ◽  
Vol 68 (1) ◽  
pp. 48-58
Author(s):  
Chao Liu ◽  
Zongde Fang ◽  
Fang Guo ◽  
Long Xiang ◽  
Yabin Guan ◽  
...  
Keyword(s):  
Numerical Methods ◽  
Dynamic Analysis ◽  
Dynamic Behavior ◽  
Fourth Order ◽  
Numerical Models ◽  
Helical Gear ◽  
Operating Conditions ◽  
Dynamic Responses ◽  
Lumped Mass ◽  
Gear Mesh

Presented in this study is investigation of dynamic behavior of a helical gear reduction by experimental and numerical methods. A closed-loop test rig is designed to measure vibrations of the example system, and the basic principle as well as relevant signal processing method is introduced. A hybrid user-defined element model is established to predict relative vibration acceleration at the gear mesh in a direction normal to contact surfaces. The other two numerical models are also constructed by lumped mass method and contact FEM to compare with the previous model in terms of dynamic responses of the system. First, the experiment data demonstrate that the loaded transmission error calculated by LTCA method is generally acceptable and that the assumption ignoring the tooth backlash is valid under the conditions of large loads. Second, under the common operating conditions, the system vibrations obtained by the experimental and numerical methods primarily occur at the first fourth-order meshing frequencies and that the maximum vibration amplitude, for each method, appears on the fourth-order meshing frequency. Moreover, root-mean-square (RMS) value of the acceleration increases with the increasing loads. Finally, according to the comparison of the simulation results, the variation tendencies of the RMS value along with input rotational speed agree well and that the frequencies where the resonances occur keep coincident generally. With summaries of merit and demerit, application of each numerical method is suggested for dynamic analysis of cylindrical gear system, which aids designers for desirable dynamic behavior of the system and better solutions to engineering problems.

scholarly journals Time and Frequency Domain Dynamic Analysis of Offshore Mooring

2021 ◽  
Vol 9 (7) ◽  
pp. 781
Author(s):  
Shi He ◽  
Aijun Wang
Keyword(s):  
Dynamic Analysis ◽  
Frequency Domain ◽  
Time Domain ◽  
Linearization Method ◽  
Euler Method ◽  
Single Component ◽  
Hydrodynamic Drag ◽  
Lumped Mass ◽  
Mooring Lines ◽  
The Time Domain

The numerical procedures for dynamic analysis of mooring lines in the time domain and frequency domain were developed in this work. The lumped mass method was used to model the mooring lines. In the time domain dynamic analysis, the modified Euler method was used to solve the motion equation of mooring lines. The dynamic analyses of mooring lines under horizontal, vertical, and combined harmonic excitations were carried out. The cases of single-component and multicomponent mooring lines under these excitations were studied, respectively. The case considering the seabed contact was also included. The program was validated by comparing with the results from commercial software, Orcaflex. For the frequency domain dynamic analysis, an improved frame invariant stochastic linearization method was applied to the nonlinear hydrodynamic drag term. The cases of single-component and multicomponent mooring lines were studied. The comparison of results shows that frequency domain results agree well with nonlinear time domain results.

A Simplified Model of SSI Dynamic Analysis

2012 ◽  
Vol 446-449 ◽  
pp. 334-339
Author(s):  
Zhi Ying Zhang ◽  
Ying Li ◽  
Qing Sun
Keyword(s):  
Dynamic Analysis ◽  
Soil Structure ◽  
Design Method ◽  
Simplified Model ◽  
Lumped Mass ◽  
Foundation Soil ◽  
Linear Elastic ◽  
Lumped Mass Method ◽  
Actual Mechanism ◽  
Seismic Design Method

Aiming at the problem of dynamic analysis of SSI system, the dynamic influence of different parts of foundation soil is studied on the linear elastic assumption according to the actual mechanism of Soil-Structure Interaction (SSI); in addition, a simplified model on the condition of the lumped mass method is put forward and the corresponding motion equations of SSI system are built, which can be a reference for the structural seismic design method considering SSI effect.

DYNAMIC BEHAVIOR OF TELESCOPIC CRANES BOOM

2013 ◽  
Vol 13 (01) ◽  
pp. 1350010 ◽  
Author(s):  
IOANNIS G. RAFTOYIANNIS ◽  
GEORGE T. MICHALTSOS
Keyword(s):  
Dynamic Response ◽  
Dynamic Analysis ◽  
Dynamic Behavior ◽  
Analytical Model ◽  
Constant Velocity ◽  
Steel Beam ◽  
Continuum Approach ◽  
Theoretical Formulation ◽  
Modal Superposition ◽  
Superposition Technique

Telescopic cranes are usually steel beam systems carrying a load at the tip while comprising at least one constant and one moving part. In this work, an analytical model suitable for the dynamic analysis of telescopic cranes boom is presented. The system considered herein is composed — without losing generality — of two beams. The first one is a jut-out beam on which a variable in time force is moving with constant velocity and the second one is a cantilever with length varying in time that is subjected to its self-weight and a force at the tip also changing with time. As a result, the eigenfrequencies and modal shapes of the second beam are also varying in time. The theoretical formulation is based on a continuum approach employing the modal superposition technique. Various cases of telescopic cranes boom are studied and the analytical results obtained in this work are tabulated in the form of dynamic response diagrams.

Accelerometer correction for the dynamic analysis of damped multi-degree of freedom systems

1969 ◽  
Vol 59 (4) ◽  
pp. 1591-1598
Author(s):  
G. A. McLennan
Keyword(s):  
Dynamic Response ◽  
Dynamic Analysis ◽  
Degrees Of Freedom ◽  
Degree Of Freedom ◽  
Exact Method ◽  
Three Degrees Of Freedom

Abstract An exact method is developed to eliminate the accelerometer error in dynamic response calculations for damped multi-degree of freedom systems. It is shown that the exact responses of a system can be obtained from the approximate responses which are conventionally calculated from an accelerogram. Response calculations were performed for two typical systems with three degrees of freedom for an assumed pseudo-earthquake. The results showed that the approximate responses may contain large errors, and that the correction developed effectively eliminates these errors.

scholarly journals Application of Laplace Transform to the Free Vibration of Continuous Beams

2017 ◽  
Vol 63 (1) ◽  
pp. 163-180 ◽  
Author(s):  
H.B. Wen ◽  
T. Zeng ◽  
G.Z. Hu
Keyword(s):  
Free Vibration ◽  
Laplace Transform ◽  
Reaction Force ◽  
Bending Moment ◽  
Frequency Equation ◽  
Simplified Model ◽  
Continuous Beam ◽  
Transform Method ◽  
Continuous Beams ◽  
Vibration Problems

AbstractLaplace Transform is often used in solving the free vibration problems of structural beams. In existing research, there are two types of simplified models of continuous beam placement. The first is to regard the continuous beam as a single-span beam, the middle bearing of which is replaced by the bearing reaction force; the second is to divide the continuous beam into several simply supported beams, with the bending moment of the continuous beam at the middle bearing considered as the external force. Research shows that the second simplified model is incorrect, and the frequency equation derived from the first simplified model contains multiple expressions which might not be equivalent to each other. This paper specifies the application method of Laplace Transform in solving the free vibration problems of continuous beams, having great significance in the proper use of the transform method.

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