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.

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.

Free vibration analysis and post-critical free vibrations of nanocomposite rotating beams reinforced with graphene platelet

2021 ◽  
pp. 107754632110511
Author(s):  
Arameh Eyvazian ◽  
Chunwei Zhang ◽  
Farayi Musharavati ◽  
Afrasyab Khan ◽  
Mohammad Alkhedher
Keyword(s):  
Natural Frequency ◽  
Thermal Environment ◽  
Rotational Velocity ◽  
Equations Of Motion ◽  
Free Vibration Analysis ◽  
Beam Theory ◽  
Weight Fraction ◽  
Free Vibrations ◽  
Graphene Platelet ◽  
The Impact

Treatment of the first natural frequency of a rotating nanocomposite beam reinforced with graphene platelet is discussed here. In regard of the Timoshenko beam theory hypothesis, the motion equations are acquired. The effective elasticity modulus of the rotating nanocomposite beam is specified resorting to the Halpin–Tsai micro mechanical model. The Ritz technique is utilized for the sake of discretization of the nonlinear equations of motion. The first natural frequency of the rotating nanocomposite beam prior to the buckling instability and the associated post-critical natural frequency is computed by means of a powerful iteration scheme in reliance on the Newton–Raphson method alongside the iteration strategy. The impact of adding the graphene platelet to a rotating isotropic beam in thermal ambient is discussed in detail. The impression of support conditions, and the weight fraction and the dispersion type of the graphene platelet on the acquired outcomes are studied. It is elucidated that when a beam has not undergone a temperature increment, by reinforcing the beam with graphene platelet, the natural frequency is enhanced. However, when the beam is in a thermal environment, at low-to-medium range of rotational velocity, adding the graphene platelet diminishes the first natural frequency of a rotating O-GPL nanocomposite beam. Depending on the temperature, the post-critical natural frequency of a rotating X-GPL nanocomposite beam may be enhanced or reduced by the growth of the graphene platelet weight fraction.

A Survey of Modal Synthesis Methods

1971 ◽  
Author(s):  
Gary C. Hart ◽  
Walter C. Hurty ◽  
Jon D. Collins
Keyword(s):  
Synthesis Methods ◽  
Modal Synthesis

Study on the Stress-Stiffening Effect and Modal Synthesis Methods for the Dynamics of a Spatial Curved Beam

2016 ◽  
Vol 83 (8) ◽  
Author(s):  
Jianshu Zhang ◽  
Xiaoting Rui ◽  
Bo Li ◽  
Gangli Chen
Keyword(s):  
Small Deformation ◽  
Dynamics Simulation ◽  
Variation Principle ◽  
Synthesis Methods ◽  
Curved Beam ◽  
The Finite Element Method ◽  
High Rotational Speed ◽  
Modal Synthesis ◽  
Geometric Stiffening ◽  
Stiffening Effect

In this paper, based on the nonlinear strain–deformation relationship, the dynamics equation of a spatial curved beam undergoing large displacement and small deformation is deduced using the finite-element method of floating frame of reference (FEMFFR) and Hamiltonian variation principle. The stress-stiffening effect, which is also called geometric stiffening effect, is accounted for in the dynamics equation, which makes it possible for the dynamics simulation of the spatial curved beam with high rotational speed. A numerical example is carried out by using the deduced dynamics equation to analyze the stress-stiffening effect of the curved beam and then verified by abaqus software. Then, the modal synthesis methods, which result in much fewer numbers of coordinates, are employed to improve the computational efficiency.

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