Effect of Local Modifications on the Vibration Characteristics of Linear Systems

1968 ◽  
Vol 35 (2) ◽  
pp. 327-332 ◽  
Author(s):  
J. T. Weissenburger
Keyword(s):  
Linear System ◽  
Eigenfunction Expansion ◽  
Natural Frequencies ◽  
Original System ◽  
Vibration Characteristics ◽  
Concentrated Mass ◽  
Linear Eigenvalue Problem ◽  
Local Modification ◽  
Linear Spring ◽  
New System

A method is presented for predicting the effect of a local modification such as the addition or removal of a concentrated mass or linear spring on the vibration characteristics of a linear system. The method, which is mathematically applicable to any linear eigenvalue problem, is rigorous even for large changes and has its basis in an eigenfunction expansion of the solution of the modified system in terms of the eigenfunctions of the unmodified system. Given the natural frequencies and modes of the original system, the characteristic function of the modified system is of such a form that it may be solved with a significant reduction in work as compared with direct treatment of the new system.

scholarly journals Stochastic Natural Vibration Analyses of Free-Form Shells

2019 ◽  
Vol 9 (15) ◽  
pp. 3168
Author(s):  
Bingbing San ◽  
Yunlong Ma ◽  
Zhi Xiao ◽  
Dongming Feng ◽  
Liwei Yin
Keyword(s):  
Elastic Modulus ◽  
Shape Optimization ◽  
Shell Thickness ◽  
Natural Vibration ◽  
Natural Frequencies ◽  
Vibration Characteristics ◽  
Free Form ◽  
Probability Models ◽  
Geometric Imperfection ◽  
Natural Vibration Characteristics

This work investigates the natural vibration characteristics of free-form shells when considering the influence of uncertainties, including initial geometric imperfection, shell thickness deviation, and elastic modulus deviation. Herein, free-form shell models are generated while using a self-coded optimization algorithm. The Latin hypercube sampling (LHS) method is used to draw the samplings of uncertainties with respect to their stochastic probability models. ANSYS finite element (FE) software is adopted to analyze the natural vibration characteristics and compute the natural frequencies. The mean values, standard deviations, and cumulative distributions functions (CDFs) of the first three natural frequencies are obtained. The partial correlation coefficient is adopted to rank the significances of uncertainty factors. The study reveals that, for the free-form shells that were investigated in this study, the natural frequencies is a random quantity with a normal distribution; elastic modulus deviation imposes the greatest effect on natural frequencies; shell thickness ranks the second; geometrical imperfection ranks the last, with a much lower weight than the other two factors, which illustrates that the shape of the studied free-form shells is robust in term of natural vibration characteristics; when the supported edges are fixed during the shape optimization, the stochastic characteristics do not significantly change during the shape optimization process.

Dynamic Characteristics Analysis for the Headstock of a Vertical Machining Center

2016 ◽  
Vol 836-837 ◽  
pp. 348-358
Author(s):  
Zhe Li ◽  
Song Zhang ◽  
Yan Chen ◽  
Peng Wang ◽  
Ai Rong Zhang
Keyword(s):  
Dynamic Characteristics ◽  
Natural Frequencies ◽  
Vibration Characteristics ◽  
Numerical Control ◽  
Vibration Test ◽  
Machining Accuracy ◽  
Modal Test ◽  
Machining Center ◽  
Characteristics Analysis ◽  
Nc Machine

Dynamic characteristics of numerical control (NC) machine tools, such as natural frequency and vibration property, directly affect machining efficiency and finished surface quality. In general, low-order natural frequencies of critical components have significant influences on machine tool’s performances. The headstock is the most important component of the machine tool. The reliability, cutting stability, and machining accuracy of a machining center largely depend on the structure and dynamic characteristics of the headstock. First, in order to obtain the natural frequencies and vibration characteristics of the headstock of a vertical machining center, modal test and vibration test in free running and cutting conditions were carried out by means of the dynamic signal collection and analysis system. According to the modal test, the first six natural frequencies of the headstock were obtained, which can not only guide the working speed, but also act as the reference of structural optimization aiming at frequency-shift. Secondly, by means of the vibration test, the vibration characteristics of the headstock were obtained and the main vibration sources were found out. Finally the corresponding vibration reduction plans were proposed in this paper. That provides the reference for improving the performance of the overall unit.

Vibration Modeling of Machine Tool Spindles: A Calibrated Dynamic Stiffness Matrix Method

2013 ◽  
Vol 651 ◽  
pp. 710-716 ◽  
Author(s):  
Omar Gaber ◽  
Seyed M. Hashemi
Keyword(s):  
Stiffness Matrix ◽  
Natural Frequencies ◽  
Dynamic Stiffness ◽  
Dynamic Stiffness Matrix ◽  
Spring Element ◽  
Linear Spring ◽  
Beam Bending ◽  
The Stability ◽  
Spinning Speed ◽  
Vibration Modeling

The effects of spindles vibrational behavior on the stability lobes and the Chatter behavior of machine tools have been established. The service life has been observed to reducethe system natural frequencies. An analytical model of a multi-segment spinning spindle, based on the Dynamic Stiffness Matrix (DSM) formulation, exact within the limits of the Euler-Bernoulli beam bending theory, is developed. The system exhibits coupled Bending-Bending (B-B) vibration and its natural frequencies are found to decrease with increasing spinning speed. The bearings were included in the model usingboth rigid, simply supported, frictionless pins and flexible linear spring elements. The linear spring element stiffness is then calibrated so that the fundamental frequency of the system matches the nominal value.

Free Vibration of Thin-Walled Open Section Beams With Unconstrained Damping Treatment

1981 ◽  
Vol 48 (1) ◽  
pp. 169-173 ◽  
Author(s):  
S. Narayanan ◽  
J. P. Verma ◽  
A. K. Mallik
Keyword(s):  
Free Vibration ◽  
Cross Section ◽  
Transverse Vibration ◽  
Natural Frequencies ◽  
Vibration Characteristics ◽  
Numerical Results ◽  
Simply Supported ◽  
Clamped Beams ◽  
Thin Walled ◽  
Open Cross Section

Free-vibration characteristics of a thin-walled, open cross-section beam, with unconstrained damping layers at the flanges, are investigated. Both uncoupled transverse vibration and the coupled bending-torsion oscillations, of a beam of a top-hat section, are considered. Numerical results are presented for natural frequencies and modal loss factors of simply supported and clamped-clamped beams.

scholarly journals Vibrational Analysis on Hemp and Okra Fibres Mixed Glass Fiber Polyester Composite

2021 ◽  
Vol 8 (11) ◽  
pp. 55-62
Author(s):  
Putti Venkata Siva Teja ◽  
Badatala Ooha ◽  
Kondeti Sravanth
Keyword(s):  
Glass Fiber ◽  
Natural Frequency ◽  
Natural Frequencies ◽  
Fiber Composite ◽  
Fem Analysis ◽  
Vibration Characteristics ◽  
Mode Shapes ◽  
Machine Component ◽  
Free System ◽  
Glass Fiber Composite

In transverse vibrations the element moves to and fro in a direction perpendicular to the direction of the advance of the wave. To determine the vibration characteristics i.e., natural frequencies and mode shapes, modal analysis is a process for a structure or a machine component while is being designed. In real life, aero planes, missiles, rockets, space vehicles, satellites, sub marines etc are modeled as free-free mechanical systems. In this paper an attempt was made to compare natural frequency for two composite materials- ladies finger with Glass fiber composite and Hemp with Glass fiber composite by taking as cantilever beams. The cantilever beam which is fixed at one end is vibrated to obtain the natural frequency, mode shapes at four different modes. A simple low cost demonstration experiment is performed in this paper by using common apparatus in order to compare theoretical, numerical (FEM analysis) profiles of two free-free thin two rectangular composite beams of dimensions 305*49.5* 7 in mm. Keywords: Natural frequencies, Mode shapes, Vibration characteristics, Ladies finger fiber, Hemp fiber, Glass fiber, FEM analysis, Free-Free system.

scholarly journals Automatic Course Scheduling System in Universities Based on Hybrid Genetic-Ant Colony Algorithm

2021 ◽  
Vol 2066 (1) ◽  
pp. 012079
Author(s):  
Yanbei Duan ◽  
Wenjie Lu
Keyword(s):  
Hybrid Algorithm ◽  
Ant Colony Algorithm ◽  
Operation Time ◽  
Original System ◽  
Colleges And Universities ◽  
Ant Colony ◽  
Scheduling System ◽  
Course Scheduling ◽  
System A ◽  
New System

Abstract Scheduling is the daily work of the Ministry of Education in Colleges and universities. In the past ten years, the scale of our colleges and universities has expanded rapidly, but the teaching resources are relatively limited. Many schools are facing the problem of insufficient classroom resources and teachers resources. The current way of organizing courses is increasingly difficult to make full use of existing resources to solve the changing needs and inefficiencies, which need to be improved urgently. This paper applies the hybrid Genetic-Ant algorithm to the automatic course scheduling system in Colleges and universities, and uses the cross-function to design and build the automatic course scheduling system in Colleges and universities. And select a college’s course scheduling system from this city for research, and use the Genetic-Ant hybrid algorithm to improve the original system to form a new system, called the original system A, and called the improved new system B, to compare the operation time and system suitability of the two systems. The results show that the fitness of system B is better than that of system A. When the scheduling unit is 100, the fitness of system A is 181, and system B is 203. When the scheduling unit is 400, the fitness of system B is 14 higher than that of system A. When the scheduling unit is 800, the fitness of system B is 64 higher than that of system A. Thus, the hybrid algorithm of genetic ant colony can improve the rationality of the curriculum.

Hydro-Elastic Vibration of Partially Liquid-Filled or Partially Liquid- Surrounded Composite Cylindrical Shells

2011 ◽  
Vol 462-463 ◽  
pp. 1127-1133
Author(s):  
Zhu Shan Shao ◽  
Guo Wei Ma ◽  
Zhan Ping Song
Keyword(s):  
Natural Frequencies ◽  
Cylindrical Shells ◽  
Hydrodynamic Pressure ◽  
Elastic Vibration ◽  
Vibration Characteristics ◽  
Radius Ratio ◽  
Liquid Density ◽  
External Work ◽  
Love’S Shell Theory ◽  
Composite Cylindrical Shells

Vibration characteristics of partially liquid-filled or partially liquid-surrounded composite cylindrical shells are investigated in this paper. Using Rayleigh-Ritz energy method and Love’s shell theory, eigenvalue equation of the problem is derived, and the polynomial for natural frequencies of such shells is further obtained. The external work by the hydrodynamic pressure, which is introduced by liquid sloshing, is taken into account in the energy function. Hydro-elastic vibration characteristics of a composite cylindrical shell are studied by using the present method. Effects of liquid level, liquid density, fiber orientation, length-to-radius ratio, and thickness-to-radius ratio on the natural frequencies are analyzed and graphically presented.

A Unified Frequency Equation and the Motion Analysis of a Moving Flexible Beam Carrying a Concentrated Mass

1999 ◽  
Author(s):  
S. Park ◽  
J. W. Lee ◽  
Y. Youm ◽  
W. K. Chung
Keyword(s):  
Natural Frequencies ◽  
Equations Of Motion ◽  
Frequency Equation ◽  
Open Loop ◽  
Mode Shapes ◽  
Flexible Beam ◽  
Lumped Mass ◽  
Concentrated Mass ◽  
Forcing Function ◽  
The Mathematical Model

Abstract In this paper, the mathematical model of a Bernoulli-Euler cantilever beam fixed on a moving cart and carrying an intermediate lumped mass is derived. The equations of motion of the beam-mass-cart system is analyzed utilizing unconstrained modal analysis, and a unified frequency equation which can be generally applied to this kind of system is obtained. The change of natural frequencies and mode shapes with respect to the change of the mass ratios of the beam, the lumped mass and the cart and to the position of the lumped mass is investigated. The open-loop responses of the system by arbitrary forcing function are also obtained through numerical simulations.

Free Vibrations of Constrained Beams

1952 ◽  
Vol 19 (4) ◽  
pp. 471-477
Author(s):  
Winston F. Z. Lee ◽  
Edward Saibel
Keyword(s):  
Natural Frequencies ◽  
Degree Of Approximation ◽  
Free Vibrations ◽  
Frequency Equation ◽  
Continuous Beam ◽  
Concentrated Mass ◽  
Simple Manner ◽  
Natural Modes ◽  
Modes Of Vibration ◽  
Rigid Supports

Abstract A general expression is developed from which the frequency equation for the vibration of a constrained beam with any combination of intermediate elastic or rigid supports, concentrated masses, and sprung masses can be found readily. The method also is extended to the case where the constraint is a continuous elastic foundation or uniformly distributed load of any length. This method requires only the knowledge of the natural frequencies and natural modes of the beam supported at the ends in the same manner as the constrained beam but not subjected to any of the constraints between the ends. The frequency equation is obtained easily and can be solved to any desired degree of approximation for any number of modes of vibration in a quick and simple manner. Numerical examples are given for a beam with one concentrated mass, for a beam with one sprung mass, and a continuous beam with one sprung mass.

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