On Vibrations of a System With an Eigenfrequency Identical to That of One of Its Subsystems, Part 2

1996 ◽  
Vol 118 (3) ◽  
pp. 414-416
Author(s):  
A. V. Pesterev ◽  
L. A. Bergman
Keyword(s):  
Complex System ◽  
Free Vibration ◽  
Natural Frequency ◽  
Natural Frequencies ◽  
Companion Paper ◽  
Synthesis Methods ◽  
Interaction Forces ◽  
Modal Synthesis ◽  
Green’S Operator ◽  
Simple Systems

The problem of free vibration of a complex system with a natural frequency identical to that of one of its subsystems is further discussed. Such eigenvibrations need special consideration in many modal synthesis methods, as the Green’s operator of the resonating subsystem does not exist at subsystem natural frequencies. A general treatment of this problem has been given by the authors in a companion paper. In this supplement, the previous work is extended to include the case of interaction forces applied to the resonating subsystem at points where the corresponding eigenfunction of the subsystem has maxima. Examples of such eigenvibrations are presented for two simple systems. The differences between these examples and those of the previous paper are noted and discussed.

On Vibrations of a System With an Eigenfrequency Identical to That of One of Its Subsystems

1995 ◽  
Vol 117 (4) ◽  
pp. 482-487 ◽  
Author(s):  
A. V. Pesterev ◽  
L. A. Bergman
Keyword(s):  
Complex System ◽  
Natural Frequency ◽  
Matrix Equation ◽  
General Equation ◽  
Free Vibrations ◽  
Synthesis Methods ◽  
Characteristic Matrix ◽  
Substructure Synthesis ◽  
Modal Synthesis ◽  
Simple Systems

The free vibrations of a complex system with a natural frequency identical to that of one of its subsystems is discussed. Such eigenvibrations need special consideration in many modal synthesis methods as the characteristic matrix (equation) does not exist. Particular emphasis has been placed on the case where a resonating subsystem is subjected to forces from other subsystems, which has not received sufficient attention in the literature on substructure synthesis methods. Examples of such eigenvibrations for two simple systems are given. A general equation for system eigenfunctions corresponding to eigenfrequencies of the isolated subsystems is presented and discussed.

scholarly journals Effects of Elliptical Hole on the Correlation of Natural Frequency with Buckling Load of Basalt Laminates Composite Plates

2020 ◽  
Vol 27 (1) ◽  
pp. 216-225
Author(s):  
Buntheng Chhorn ◽  
WooYoung Jung
Keyword(s):  
Free Vibration ◽  
Natural Frequency ◽  
Natural Frequencies ◽  
Basalt Fiber ◽  
Orientation Angle ◽  
Elliptical Hole ◽  
Composite Plates ◽  
Buckling Load ◽  
Mode Shapes ◽  
Geometric Ratio

AbstractRecently, basalt fiber reinforced polymer (BFRP) is acknowledged as an outstanding material for the strengthening of existing concrete structure, especially it was being used in marine vehicles, aerospace, automotive and nuclear engineering. Most of the structures were subjected to severe dynamic loading during their service life that may induce vibration of the structures. However, free vibration studied on the basalt laminates composite plates with elliptical cut-out and correlation of natural frequency with buckling load has been very limited. Therefore, effects of the elliptical hole on the natural frequency of basalt/epoxy composite plates was performed in this study. Effects of stacking sequence (θ), elliptical hole inclination (ϕ), hole geometric ratio (a/b) and position of the elliptical hole were considered. The numerical modeling of free vibration analysis was based on the mechanical properties of BFRP obtained from the experiment. The natural frequencies as well as mode shapes of basalt laminates composite plates were numerically determined using the commercial program software (ABAQUS). Then, the determination of correlation of natural frequencies with buckling load was carried out. Results showed that elliptical hole inclination and fiber orientation angle induced the inverse proportion between natural frequency and buckling load.

Vibration of Beams with a Single Delamination under Axial Loading

2011 ◽  
Vol 675-677 ◽  
pp. 477-480
Author(s):  
Dong Wei Shu
Keyword(s):  
Free Vibration ◽  
Natural Frequency ◽  
Analytical Solutions ◽  
Axial Load ◽  
Natural Frequencies ◽  
Axial Loading ◽  
Composite Beams ◽  
Mode Shapes ◽  
Equilibrium Conditions ◽  
Monotonic Relation

In this work analytical solutions are developed to study the free vibration of composite beams under axial loading. The beam with a single delamination is modeled as four interconnected Euler-Bernoulli beams using the delamination as their boundary. The continuity and the equilibrium conditions are satisfied between the adjoining beams. The studies show that the sizes and the locations of the delaminations significantly influence the natural frequencies and mode shapes of the beam. A monotonic relation between the natural frequency and the axial load is predicted.

scholarly journals Analysis of Free Vibration of Hydraulic Opposing Cylinder Controlled by Servo Valve

2021 ◽  
Author(s):  
Xiaoming Yuan ◽  
Weiqi Wang ◽  
Xuan Zhu ◽  
Bing Du ◽  
Lijie Zhang
Keyword(s):  
Free Vibration ◽  
Natural Frequency ◽  
Natural Frequencies ◽  
Transmission System ◽  
Normal Operation ◽  
Design Parameters ◽  
Analytical Relationship ◽  
Parameter Method ◽  
Mechanical Transmission ◽  
Servo Valve

Abstract The fluid transmission medium has large compressibility and low rigidity, and its physical properties are extremely sensitive to state parameters such as flow, pressure and temperature. Therefore, compared with the mechanical transmission system, the natural frequency of the fluid transmission system is relatively low and has time-varying characteristics. After a wide frequency range changing of the load frequency and long-term operation, the excitation frequency of the fluid transmission system is more likely to approach its natural frequency and causes resonance, which seriously affects the normal operation of the system. Therefore, taking the hydraulic opposing cylinder controlled by servo valve as the research object, based on the analytical relationship between the dynamic bulk modulus and the equivalent stiffness of oil, the vibration dynamics models and equations of the system is established by using the lumped parameter method. Through the free vibration analysis, the natural frequencies and main vibration modes of the system are determined and the sensitivity changes of the natural frequencies to the design parameters are revealed. The maximum error between the theoretical modal frequency and the experimental one is 3.77%, which verifies the correctness of the dynamic model of the system. This research can provide a theoretical reference for the optimization of the dynamic performance of the hydraulic transmission system.

Analysis of Free Vibration Characteristics and Mode Shapes of a Semi-Submersible Platform

2011 ◽  
Author(s):  
Jonas W. Ringsberg ◽  
Per Ernholm ◽  
Love Hogstro¨m
Keyword(s):  
Free Vibration ◽  
Natural Frequency ◽  
Fundamental Frequency ◽  
Natural Frequencies ◽  
Wave Spectrum ◽  
Shell Element ◽  
Element Model ◽  
Beam Element ◽  
Resonance Frequencies ◽  
Exciting Wave

The current investigation presents a global natural frequency and mode shape analysis of a semi-submersible platform. The purpose is to evaluate the separation in frequency between the semi-submersible’s global natural frequencies and the exciting wave spectrum. Two types of finite element models are compared: a beam element model and a shell element model. The main differences in the models are the level of resolution in details and model complexity. It is shown that both beam and shell element models can be used for the analysis. However, the beam element model is recommended for a first approximate assessment of the fundamental natural frequency and the interval/spectrum of global resonance frequencies compared to the wave spectrum. The shell element model is recommended when a more thorough analysis is required. In addition, the natural frequencies of the semi-submersible are calculated for free vibration in air. The fundamental frequency was 1.9 Hz for the beam element model and 1.5 Hz for the shell element model. When weights corresponding to a submerged structure in operation mode are considered, including the effects of added mass, the fundamental frequency for the first mode using the beam element model was decreased to 0.7 Hz, and to 0.6 Hz when using the shell element model. When compared to the DNV world wave spectrum’s highest frequency of 0.29 Hz it is concluded that the natural frequencies of the semi-submersible are at a sufficient distance from the exciting wave spectrum.

scholarly journals Theoretical Analysis on the Nonlinear Free Vibration of a Tri-Cross String

2017 ◽  
Vol 2017 ◽  
pp. 1-17
Author(s):  
Bo Pan ◽  
Jingda Tang ◽  
Ryuichi Tarumi ◽  
Fulin Shang ◽  
Yanbo Wang ◽  
...  
Keyword(s):  
Constitutive Equation ◽  
Theoretical Analysis ◽  
Free Vibration ◽  
Natural Frequency ◽  
Analytical Solutions ◽  
Vibration Amplitude ◽  
Natural Frequencies ◽  
Geometrical Nonlinearity ◽  
Governing Equations ◽  
Nonlinear Free Vibration

Here we present a theoretical analysis on the nonlinear free vibration of a tri-cross string system, which is an element of space net-antennas. We derived the governing equations from Hamilton’s principle and obtained a linearized solution by the standard perturbation method. The semi-analytical solutions of the governing equations have not been provided referring to the solution of plate vibrating problem. This analysis revealed that natural frequencies of the tri-cross string depend on the vibration amplitude due to the geometrical nonlinearity in the constitutive equation. The geometric parameters, such as the diameters and the lengths of the constituent strings, also affect the frequency through the nonlinearity of the tri-cross string. The nonlinear natural frequency shows coupled characteristic; that is, the natural frequency of the tri-cross string varies with that of the constituent strings, but the contribution of each constituent string to the natural frequency is in different proportions.

Free Vibration of Initially Stressed Circular Disks

1965 ◽  
Vol 87 (2) ◽  
pp. 258-264 ◽  
Author(s):  
C. D. Mote
Keyword(s):  
Free Vibration ◽  
Natural Frequency ◽  
Variable Thickness ◽  
Transverse Vibration ◽  
Fundamental Mode ◽  
Natural Frequencies ◽  
Thermal Environment ◽  
Vibration Characteristics ◽  
Initial Stresses ◽  
Circular Disks

The approximate free vibration characteristics of centrally clamped, variable thickness disks are analyzed by the Rayleigh-Ritz technique. Natural frequencies of transverse vibration are computed, taking into consideration rotational and thermal in-plane stresses as well as purposely induced initial stresses. Initial stresses can significantly raise the minimum disk natural frequency throughout a prescribed rotational and thermal environment. The fundamental mode of disk vibration is one of zero nodal circles and either zero, one, or two nodal diameters, depending upon the disk geometry and the rotational-thermal environment.

scholarly journals Analysis of Fiberglass Winding Angle on Natural Frequency of Free Vibration of Cylindrical Shell with Asymmetric Boundary Conditions

2013 ◽  
Vol 274 ◽  
pp. 65-69 ◽  
Author(s):  
Zhi Wei Wang ◽  
Bo Wu ◽  
Yan Fu Wang ◽  
S.M. Bosiakov
Keyword(s):  
Cylindrical Shell ◽  
Free Vibration ◽  
Boundary Conditions ◽  
Natural Frequency ◽  
Natural Frequencies ◽  
Circular Cylindrical Shell ◽  
Geometrical Parameters ◽  
Glass Fiber Reinforced Plastic ◽  
Glass Fiber Reinforced ◽  
Winding Angle

In order to obtain approximate solution of natural frequencies for the free vibration of anisotropic circular cylindrical shells made of GFRP (glass fiber-reinforced plastic) with asymmetric boundary conditions, Love’s theory and energy method are used. Computation results show that the fundamental natural frequency comes from different vibration modes while the winding angle varies, the effect of number of axial half waves is stronger than number of circumferential waves on natural frequency of free vibration of anisotropic circular cylindrical shell. The effect of shell’s geometrical parameters is also investigated on natural frequencies.

The Influence of a Cracked Blade on Rotor’s Free Vibration

2008 ◽  
Vol 130 (5) ◽  
Author(s):  
Yi-Jui Chiu ◽  
Shyh-Chin Huang
Keyword(s):  
Free Vibration ◽  
Natural Frequency ◽  
Natural Frequencies ◽  
Bending Moment ◽  
Rotor System ◽  
Coupled Modes ◽  
Mode Localization ◽  
Coupled Vibrations ◽  
Crack Location ◽  
Blade System

The influence on the coupled vibrations among shaft, disk, and blades of a rotor system due to a cracked blade was investigated analytically. On the shaft-disk-blade system, without a cracked blade, there exist three types of coupled modes, shaft disk blade (SDB), disk blade (DB), and blade-blade. A cracked blade was found to change not only the natural frequencies but also the types of coupled modes. First, the DB modes disappeared and were replaced by SDB modes. Second, in some modes the disk experienced mode localization due to the cracked blade. Numerical results showed that natural frequencies varied with the blade’s crack location and depth. At no bending moment places the crack imposed no effect. The crack affected the natural frequency slightly until its depth reached as deep as 70% then the frequency dropped abruptly.

scholarly journals Free vibration analysis of isotopic rectangular plate with one edge free of support (CSCF and SCFC plate)

2014 ◽  
Vol 3 (1) ◽  
pp. 30 ◽  
Author(s):  
Stanley I Ebirim ◽  
J C Ezeh ◽  
M Owus Ibearugbulem
Keyword(s):  
Aspect Ratio ◽  
Free Vibration ◽  
Natural Frequency ◽  
Natural Frequencies ◽  
Shape Function ◽  
Ritz Method ◽  
Dimensional Parameter ◽  
Fundamental Natural Frequency ◽  
Aspect Ratios ◽  
Significant Difference

The paper presents a theoretical formulation based on Ibearugbulems shape function and application of Ritz method. In this study, the free vibration of simply supported plate with one free edge was analyzed. The Ibearugbulems shape function derived was substituted into the potential energy functional, which was minimized to obtain the fundamental natural frequency. Aspect ratios from 0.1 to 2.0 with 0.1 increments were considered. The values of fundamental natural frequencies of the first mode were determined for different aspect ratio. For aspect ratio of 1.0, the value of non-dimensional parameter of fundamental natural frequency obtained was 23.86. Comparison was made for values of non-dimensional parameter of fundamental natural frequencies obtained in this study with those of previous research works. It was seen that there is no significant difference between values obtained in this study with those of previous studies. Keywords: fundamental natural frequency; Ibearugbulems shape function; CSCF plate; Ritz method; SCFC plate.

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