Nonlinear Combination Resonances in Cantilever Composite Plates

1995 ◽  
Author(s):  
Kyoyul Oh ◽  
Ali H. Nayfeh
Keyword(s):  
Natural Frequencies ◽  
Excitation Frequency ◽  
Power Spectra ◽  
Low Frequency ◽  
Composite Plates ◽  
High Amplitude ◽  
Mode Shapes ◽  
Laser Vibrometer ◽  
Combination Resonance ◽  
Response Curves

Abstract We experimentally investigated nonlinear combination resonances in a graphite-epoxy cantilever plate having the configuration (–75/75/75/ – 75/75/ – 75)s. As a first step, we compared the natural frequencies and mode shapes obtained from the finite-element and experimental modal analyses. The largest difference in the obtained frequencies was 2.6%. Then, we transversely excited the plate and obtained force-response and frequency-response curves, which were used to characterize the plate dynamics. We acquired time-domain data for specific input conditions using an A/D card and used them to generate time traces, power spectra, pseudo-state portraits, and Poincaré maps. The data were obtained with an accelerometer monitoring the excitation and a laser vibrometer monitoring the plate response. We observed the external combination resonance Ω≈12(ω2+ω5) and the internal combination resonance Ω≈ω8≈12(ω2+ω13), where the ωi are the natural frequencies of the plate and Ω is the excitation frequency. The results show that a low-amplitude high-frequency excitation can produce a high-amplitude low-frequency motion.

High- to Low-Frequency Modal Interactions in a Cantilever Composite Plate

1998 ◽  
Vol 120 (2) ◽  
pp. 579-587 ◽  
Author(s):  
K. Oh ◽  
A. H. Nayfeh
Keyword(s):  
Natural Frequencies ◽  
Power Spectra ◽  
Low Frequency ◽  
Time History ◽  
Laser Vibrometer ◽  
Modal Interactions ◽  
Flexible Beams ◽  
Torsional Mode ◽  
Bending Mode ◽  
Simultaneous Activation

We have shown through experiment a complicated dynamic behavior of a cantilever (90/30/–30/–30/30/90)s graphite-epoxy plate. The plate was base excited using a 2000-lb table shaker near its seventh (third torsional) mode. We monitored the input excitation condition using a base mounted accelerometer and the plate response using a laser vibrometer. For some excitation amplitudes and frequencies, we observed the activation of a low-frequency (first bending) mode accompanied by amplitude and phase modulations of the seventh mode. The energy transfer from the high- to low-frequency modes observed in the plate configuration is similar to those observed in flexible beams by Anderson, Balachandran, and Nayfeh (1994) and Nayfeh and Nayfeh (1994) and in frames by Popovic, Nayfeh, Oh, and Nayfeh (1995). Therefore, we conclude that this type of modal interactions is possible for all ranges of structural stiffnesses and configurations whenever there exist modes whose natural frequencies are much lower than the natural frequencies of the directly excited modes. In addition, we also observed simultaneous activation of a two-to-one internal resonance along with the high- to low-frequency modal interactions for some excitation amplitudes and frequencies. We used time-history and power-spectra plots to characterize the experimental data and force-response plots to characterize the dynamics of the plate.

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.

Effect of Delamination on Natural Frequencies of E-glass and S-glass Epoxy Composite Plates

2021 ◽  
Author(s):  
P. K. Karsh ◽  
Bindi Thakkar ◽  
R. R. Kumar ◽  
Abhijeet Kumar ◽  
Sudip Dey
Keyword(s):  
Natural Frequencies ◽  
Epoxy Composite ◽  
Orientation Angle ◽  
Laminated Composite ◽  
Composite Plates ◽  
Mode Shapes ◽  
Transverse Shear Deformation ◽  
The Finite Element Method ◽  
Modes Of Failure ◽  
Ply Orientation

The delamination is one of the major modes of failure occurring in the laminated composite due to insufficient bonding between the layers. In this paper, the natural frequencies of delaminated S-glass and E-glass epoxy cantilever composite plates are presented by employing the finite element method (FEM) approach. The rotary inertia and transverse shear deformation are considered in the present study. The effect of parameters such as the location of delamination along the length, across the thickness, the percentage of delamination, and ply-orientation angle on first three natural frequencies of the cantilever plates are presented for S-glass and E-glass epoxy composites. The standard eigenvalue problem is solved to obtain the natural frequencies and corresponding mode shapes. First three mode shape of S-Glass and E-Glass epoxy laminated composites are portrayed corresponding to different ply angle of lamina.

Maximizing the Fundamental Natural Frequency of Triangular Composite Plates

1996 ◽  
Vol 118 (2) ◽  
pp. 141-146 ◽  
Author(s):  
S. Abrate
Keyword(s):  
Natural Frequency ◽  
Material Properties ◽  
Composite Structures ◽  
Natural Frequencies ◽  
Ritz Method ◽  
Laminated Composite ◽  
Composite Plates ◽  
Mode Shapes ◽  
Fundamental Natural Frequency ◽  
Wide Range

While many advances were made in the analysis of composite structures, it is generally recognized that the design of composite structures must be studied further in order to take full advantage of the mechanical properties of these materials. This study is concerned with maximizing the fundamental natural frequency of triangular, symmetrically laminated composite plates. The natural frequencies and mode shapes of composite plates of general triangular planform are determined using the Rayleigh-Ritz method. The plate constitutive equations are written in terms of stiffness invariants and nondimensional lamination parameters. Point supports are introduced in the formulation using the method of Lagrange multipliers. This formulation allows studying the free vibration of a wide range of triangular composite plates with any support condition along the edges and point supports. The boundary conditions are enforced at a number of points along the boundary. The effects of geometry, material properties and lamination on the natural frequencies of the plate are investigated. With this stiffness invariant formulation, the effects of lamination are described by a finite number of parameters regardless of the number of plies in the laminate. We then determine the lay-up that will maximize the fundamental natural frequency of the plate. It is shown that the optimum design is relatively insensitive to the material properties for the commonly used material systems. Results are presented for several cases.

Flexural Vibrations of a Multi-Material Microhydraulic Hose Subjected to External Excitation. Experimental Research and Theoretical Description

2021 ◽  
Author(s):  
Marek Lubecki ◽  
Michał Stosiak ◽  
Mirosław Bocian ◽  
Kamil Urbanowicz
Keyword(s):  
Experimental Research ◽  
Natural Frequencies ◽  
Excitation Frequency ◽  
Classical Equation ◽  
Analytical Description ◽  
Theoretical Description ◽  
Laser Vibrometer ◽  
Flexural Vibrations ◽  
Stiffness And Damping ◽  
Mathematica Software

Abstract The paper presents experimental research and mathematical modeling of flexural vibrations of a composite hydraulic microhose. The tested object was a Polyflex 2020N-013V30 hydraulic microhose, consisting of a braided aramid layer placed in a thermoplastic matrix. The vibrations were induced with an external electromagnetic exciter in the range from 0 Hz to 100 Hz using the sweep function. Using a laser vibrometer, the exciter’s displacement was measured in the above-mentioned range. Long exposure photographs were taken to identify the form of microhose’s vibrations as well as to measure it’s amplitude. The existence of considerable non-linearity in subsequent natural frequencies was shown. At the same time, mathematical simulations were carried out using the Mathematica software. For the analytical description of the object’s vibrations partial differential equations based on the string equation were used. A part responsible for damping in the material was added to the classical equation of the string. The dependence of the values of the stiffness and damping coefficients a on the excitation frequency made it possible to model nonlinearities manifested by the upward shift of higher natural frequencies and the suppression of the amplitudes of successive modes. Further development of the proposed model will allow for modeling the internal pressure in the hose and its effect on transverse vibrations. It will also allow to design of vibrations of composite microhoses and avoid the coupling of these vibrations with external excitations.

Nonlinear Vibrations of a Beam-Spring-Large Mass System

2017 ◽  
Author(s):  
Mohammad A. Bukhari ◽  
Oumar R. Barry
Keyword(s):  
Natural Frequencies ◽  
Multiple Scales ◽  
Equations Of Motion ◽  
Primary Resonance ◽  
Large Mass ◽  
Mode Shapes ◽  
Resonance Excitation ◽  
Response Curves ◽  
Mass System ◽  
Spring System

This paper presents the nonlinear vibration of a simply supported Euler-Bernoulli beam with a mass-spring system subjected to a primary resonance excitation. The nonlinearity is due to the mid-plane stretching and cubic spring stiffness. The equations of motion and the boundary conditions are derived using Hamiltons principle. The nonlinear system of equations are solved using the method of multiple scales. Explicit expressions are obtained for the mode shapes, natural frequencies, nonlinear frequencies, and frequency response curves. The validity of the results is demonstrated via comparison with results in the literature. Exact natural frequencies are obtained for different locations, rotational inertias, and masses.

Natural Frequencies and Mode Shapes of Laminated Composite Plates: Experiments and FEA

1996 ◽  
Vol 2 (4) ◽  
pp. 381-414 ◽  
Author(s):  
T.J. Anderson ◽  
A.H. Nayfeh
Keyword(s):  
Natural Frequencies ◽  
Laminated Composite ◽  
Composite Plates ◽  
Test Methods ◽  
Mode Shapes ◽  
Boundary Condi Tions ◽  
Element Analysis ◽  
Condi Tions ◽  
Theoretical Results ◽  
Good Agreement

The natural frequencies and mode shapes of several graphite-epoxy plates were determined using experimental modal analysis and finite-element analysis. The experimental and theoretical results are com pared. The samples tested included four types of layups: ±15°, ±30°, cross-ply, and quasi-isotropic plates. Each plate was tested in three configurations: free-hanging, cantilever, and fixed-fixed for a total of twelve test configurations. The material properties of the plates and the test methods used to obtain them are in cluded. There is a very good agreement between the experimental and theoretical results for the free-hanging and cantilever configurations. The agreement for the fixed-fixed results is poor. This indicates that the clamps for the fixed-fixed configuralion are not ideal and that they introduce some uncertainty in the boundary condi tions. The free-hanging results provide accurate experimental natural frequencies of several composite plates; they can be used to validate future theoretical developments. The fixed-fixed results are used to provide pos sible explanations for the discrepancies between the measured and calculated natural frequencies previously reported in the literature.

Comparison of Free Flexural Vibrations of Composite Plates or Panels Stiffened by a Central and a Non-Central Plate Strip

1999 ◽  
Author(s):  
U. Yuceoglu ◽  
V. Özerciyes
Keyword(s):  
Natural Frequencies ◽  
Plate Theory ◽  
Composite Plates ◽  
Mode Shapes ◽  
Mindlin Plate ◽  
Solution Technique ◽  
Orthotropic Plates ◽  
Bending Vibration ◽  
Central Plate ◽  
Plate Strip

Abstract The natural frequencies and the corresponding mode shapes of two classes of composite base plate or panel stiffened by a central or a non-central plate strip are analyzed and compared with each other. In each case, the base plates and the single, stiffening plate strips are assumed to be dissimilar orthotropic plates connected by a very thin, yet deformable adhesive layer. The free bending vibration problems for the two cases are formulated in terms of the Mindlin Plate Theory for orthotropic plates. The governing equations are reduced to a system of first order equations. The solution technique is the “Modified Version of the Transfer Matrix Method”. The effects of the bonded central and non-central stiffening strip on the mode shapes and the natural frequencies of the composite plate or panel system are investigated. Some important conclusions are drawn from the numerical and parametric studies presented.

An Experimental Investigation of Acoustic Black Hole Dynamics at Low, Mid, and High Frequencies

2016 ◽  
Vol 138 (6) ◽  
Author(s):  
Philip A. Feurtado ◽  
Stephen C. Conlon
Keyword(s):  
Black Hole ◽  
Performance Optimization ◽  
Low Frequency ◽  
Mode Shapes ◽  
Design Parameters ◽  
Laser Vibrometer ◽  
Beam Thickness ◽  
Added Benefit ◽  
Power Measurements ◽  
Bending Wave

The acoustic black hole (ABH) has been developed in recent years as an effective, passive, and lightweight method for attenuating bending wave vibrations in beams and plates and reducing the sound radiation and structural-acoustic response of structures. The ABH effect utilizes a local change in the plate or beam thickness to reduce the bending wave speed and increase the transverse vibration amplitude. Attaching a viscoelastic damping layer to the ABH results in effective energy dissipation and vibration reduction. Surface-averaged mobility and radiated sound power measurements were performed on an aluminum plate containing an array of 20 two-dimensional ABHs with damping layers and compared to a similar uniform plate. Detailed laser vibrometer scans of an ABH cell (including the ABH and surrounding homogeneous plate) were also performed to analyze the vibratory characteristics of individual ABH cells and compared with mode shapes calculated using finite elements. The results showed that the surface-averaged mobility was reduced by up to 14 dB for the fully damped ABH plate compared to a uniform reference plate while also reducing the mass of the plate. The results demonstrated that the dynamics of plates with embedded ABHs can be characterized by low, mid, and high frequency ranges, with low-order local ABH modes contributing significantly to low frequency ABH performance. The effects of damping layer thickness and diameter were also investigated to assess ABH performance optimization. It was shown that the damping layer can have the added benefit of mass loading the ABH and enhancing low frequency performance. The results will be useful for designing the low frequency performance of future ABH systems and describing ABH performance in terms of design parameters.

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