Natural Frequency and Vibration Modal Analysis of Composite Laminated Plate

2013 ◽  
Vol 711 ◽  
pp. 396-400
Author(s):  
Long Sheng Zhao ◽  
Jin Wu Wu
Keyword(s):  
Natural Frequency ◽  
Good Accuracy ◽  
Natural Frequencies ◽  
Equation Of Motion ◽  
Theory Method ◽  
Laminated Plate ◽  
Simply Supported ◽  
Composite Laminated Plate ◽  
Experiment Method ◽  
Vibration Modal

In this paper,a layer-wise theory is used to analyze the natural frequency and vibration modal of the composite laminated plate. Layer-wise theory assumes that displacement is continue through thickness direction and has good accuracy to analyze free vibration. The frequency and vibration modal are acquired while building the equation of motion according to layer-wise theory. Through comparing layer-wise theory and other theories, numerical results show that layer-wise theory is credible to analyze composite laminated plate. At the same time, experiment is used in this paper to acquire the natural frequencies and vibration modal of a simply supported composite laminated plate. Lastly, combination of the theory method and experiment method canprobably predict the natural frequencies and vibration modal.

The Control of Parametric Vibration in a Simply Supported Beam

1987 ◽  
Vol 109 (3) ◽  
pp. 315-318
Author(s):  
J. S. Burdess
Keyword(s):  
Numerical Simulation ◽  
Theoretical Analysis ◽  
Perturbation Method ◽  
Natural Frequency ◽  
Multiple Scales ◽  
Equation Of Motion ◽  
Control Law ◽  
Parametric Vibrations ◽  
Simply Supported ◽  
Multiple Scales Perturbation Method

The paper shows how unstable parametric vibrations of a uniform beam can be controlled. A control law is proposed and it is shown that the beam can be made to vibrate at a present amplitude at its natural frequency. The beam is modelled by its first mode and a solution to the governing equation of motion is derived by applying the multiple scales perturbation method. The results of the theoretical analysis are verified by a numerical simulation.

Research on the Natural Frequency Solving Method of the Simply Supported Beam Bridge with Cracks

2013 ◽  
Vol 437 ◽  
pp. 51-55
Author(s):  
Ping Yi Sun ◽  
Yan Hua Wang ◽  
Han Bing Liu ◽  
Guo Jin Tan
Keyword(s):  
Natural Frequency ◽  
Natural Frequencies ◽  
Beam Model ◽  
Euler Beam ◽  
Simply Supported Beam ◽  
Simply Supported ◽  
Solution Methods ◽  
Element Approach ◽  
Experimental Values ◽  
Beam Bridge

Two kinds of natural frequency solution methods for the simply supported beam bridge with cracks are presented respectively based on the Bernoulli-Euler beam model and the finite element approach. Multiple groups of crack damages are supposed on the experimental simply supported steel I-beam, and the natural frequencies of the experimental beam are measured in all the crack cases. By comparing the calculated natural frequencies respectively obtained by the above two methods with the experimental values, the characteristics of the two kinds of natural frequency solving methods are evaluated.

The NAVMI Factor and Natural Frequency of a Circular Plate Exposed to Water in Flexural Vibration

2011 ◽  
Vol 199-200 ◽  
pp. 1445-1450
Author(s):  
Hui Juan Ren ◽  
Mei Ping Sheng
Keyword(s):  
Boundary Condition ◽  
Natural Frequency ◽  
Circular Plate ◽  
Natural Frequencies ◽  
Integration Method ◽  
Flexural Vibration ◽  
The Other ◽  
Additional Mass ◽  
Simply Supported ◽  
Higher Order Modes

The expression of NAVMI factor and the natural frequency of a circular plate, which is placed in a hole of an infinite grid wall with one side exposed to water, are derived from the viewpoint of the additional mass. 10 Nodes Gauss-Legender integration method and the iteration method are employed to obtain the numerical results of the NAVMI factors, AVMI factors and the natural frequencies. It can be found from the results that NAVMI factors of the first two order modes are far bigger than those of the other modes when the boundary condition of a circular plate is certain. The first two order modal NAVMI factors of the circular plate with clamped and simply supported boundary conditions are far bigger than those of the circular plate with free-edged boundary condition, and the NAVMI factors are almost the same for the three order or much higher order modes regardless of the boundary condition. It is also observed that the natural frequencies of the circular plate exposed to water are smaller than those exposed to air, and the natural frequencies of the circular plate exposed to water with both sides are smaller than those of the circular plate exposed to water with one side.

scholarly journals Vibration Modal Analysis and Optimization of the Motor Base

2018 ◽  
Vol 175 ◽  
pp. 03046 ◽  
Author(s):  
Meiling Qiu ◽  
Dafang Wang ◽  
Hui Wei ◽  
Xiu Liang ◽  
Yue Ma
Keyword(s):  
Modal Analysis ◽  
Natural Frequency ◽  
Vibration Frequency ◽  
Natural Frequencies ◽  
Mechanical Equipment ◽  
Boundary Constraints ◽  
Vibration Modal ◽  
Different Thickness

When the motor works normally, its base will vibrate. The structure will generate the resonance and result in damage of the mechanical equipment when the vibration frequency reaches the natural frequency. The article which is based on the modal analysis of the motor base compares the natural frequencies in different boundary constraints in order to select appropriate way to install the motor base, and optimizes the motor base by contrasting different effects on the natural frequencies of the different thickness of the ribbed plates for selecting reasonable structure to prevent resonance.

Vibratory Bending of Damped Laminated Plates

1969 ◽  
Vol 91 (4) ◽  
pp. 1081-1090 ◽  
Author(s):  
R. A. Ditaranto ◽  
J. R. McGraw
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Natural Frequencies ◽  
Laminated Plates ◽  
Simultaneous Equations ◽  
Laminated Plate ◽  
Partial Differential ◽  
Simply Supported ◽  
First Case ◽  
Viscoelastic Layers

The natural frequencies and associated composite loss factor have been determined for a finite-length laminated plate having alternate elastic and viscoelastic layers. Partial differential equations in terms of the variables of the plate are derived and, with the loading equation for a freely vibrating plate, a set of simultaneous partial differential equations is formed. Of two solutions considered the first is general and the second satisfies the boundary condition for a simply supported plate. In both cases, the resulting algebraic simultaneous equations are complex since the shear modulus of the viscoelastic material is a complex expression. In the first case, the expressions could not be solved directly since the value of the eigenvalues depended upon the boundary conditions, whereas the eigenvalues for the simply supported plate could be easily chosen. The simply supported case is solved and the results plotted for specific dimensionless parameters.

The Natural Frequency of Vibration of Curved Rectangular Plates

1954 ◽  
Vol 5 (2) ◽  
pp. 101-110 ◽  
Author(s):  
P. J. Palmer
Keyword(s):  
Natural Frequency ◽  
Pressure Wave ◽  
Natural Frequencies ◽  
Dynamic Pressure ◽  
Mode Frequency ◽  
Rectangular Plates ◽  
Simply Supported ◽  
Distributed Pressure

SummaryThe natural frequency of vibration of curved rectangular plates, with both simply-supported and fixed edges, is evaluated for the fundamental extensional mode. This mode is thought to be applicable when the plates are excited by a uniformly distributed pressure as may occur with a dynamic pressure wave. The natural frequencies corresponding to this mode increase fairly rapidly with the curvature of the plate.The natural frequency of vibration of the plates when the mode is the fundamental inextensional mode is also considered. The frequency of this mode is higher than that of the extensional mode for small curvatures, but the inextensional mode frequency falls slowly with increase in curvature of the plate. Thus, if the curvature of the plate is sufficiently large, the frequency of the fundamental inextensional mode is lower than that of the extensional mode.

Investigation of Rocking Semicircular and Parabolic Disk Equilibria, Stability, and Natural Frequencies

2014 ◽  
Author(s):  
Michael J. Mazzoleni ◽  
Michael B. Krone ◽  
Brian P. Mann
Keyword(s):  
Natural Frequency ◽  
Cross Sections ◽  
Natural Frequencies ◽  
Stable Equilibrium ◽  
Pitchfork Bifurcation ◽  
Equation Of Motion ◽  
Bistable Behavior ◽  
Wide Range ◽  
Stable Equilibrium Position ◽  
Good Agreement

This paper performs a theoretical and experimental investigation of the natural frequency and stability of rocking semicircular and parabolic disks. Horace Lamb’s method for deriving the natural frequency of an arbitrary rocking disk is applied to two shapes with semicircular and parabolic cross sections, respectively. For the case of the semicircular disk, the system’s equation of motion is derived to verify Lamb’s method. Additionally, the rocking semicircular disk is found to always have one stable equilibrium position. For the case of the parabolic disk, this investigation unveils a super-critical pitchfork bifurcation for changes in a single geometric parameter which reveals that the system can exhibit bistable behavior. Rapid prototyping technology was used to manufacture sample disks across a wide range of parameters, and a laser tachometer was used to experimentally determine the natural frequency of each disk. Comparisons between experiment and theory show good agreement.

Multi-Pulse Chaotic Dynamics of a Composite Laminated Plate with Strong Coupling

2014 ◽  
Vol 548-549 ◽  
pp. 431-437
Author(s):  
Y. Zhao ◽  
W. Xu ◽  
J.H. Zhang
Keyword(s):  
Strong Coupling ◽  
Chaotic Dynamics ◽  
Nonlinear Dynamical System ◽  
Melnikov Method ◽  
Laminated Plate ◽  
Chaotic Motions ◽  
Nonlinear Dynamical ◽  
Simply Supported ◽  
Composite Laminated Plate ◽  
Two Degree Of Freedom

In this paper, the multi-pulse chaotic dynamics of a simply-supported symmetric cross-ply composite laminated rectangular plate with the parametric and forcing excitations is investigated by using the extended Melnikov method. The two-degree-of-freedom non-autonomous nonlinear dynamical system of the plate with strong coupling is considered. The results obtained here indicate that multi-pulse chaotic motions can occur in the plate. Numerical simulation is also employed to find the multi-pulse chaotic motions of the plate based on the theoretical analysis.

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