Investigation on Nonlinear Trends of Composite Laminated Plate

2012 ◽  
Author(s):  
Wei Zhang ◽  
Jianen Chen ◽  
Qian Wang ◽  
Min Sun
Keyword(s):  
Multiple Scales ◽  
Plate Theory ◽  
Equations Of Motion ◽  
Primary Resonance ◽  
Laminated Plates ◽  
Laminated Plate ◽  
Response Curves ◽  
Composite Laminated Plate ◽  
Nonlinear Trend ◽  
Nonlinear Trends

The nonlinear trends of composite laminated plates are investigated. The governing equations of motion for the plate are derived with the von Karman strain-displacement relations for the geometric nonlinearity and the Reddy’s third-order shear deformation plate theory. The four dimensional nonlinear averaged equations with the case of 1/2-subharmonic resonance and principal parametric resonance for the first mode and primary resonance for the second mode are obtained by applying the method of multiple scales. The frequency-response curves are analyzed under consideration of strongly coupled of two modes. The influences of the coefficients in dynamic equations and the detuning parameters on the nonlinear trend are studied, and the results indicate that the composite laminated plate may have different trends of nonlinearity under aforementioned resonance conditions. The sweep experiment is conducted to find the softening and hardening nonlinearity. The different trends are obtained when the excitation amplitude is 1.2g. The spectrums of the different stages of the test show that the change of the nonlinear trend may be caused from the sub-harmonic resonance in this test.

Nonlinear Vibrations of Two-Span Composite Laminated Plates with Equal and Unequal Subspan Lengths

2017 ◽  
Vol 9 (6) ◽  
pp. 1485-1505
Author(s):  
Lingchang Meng ◽  
Fengming Li
Keyword(s):  
Multiple Scales ◽  
Equations Of Motion ◽  
Primary Resonance ◽  
Laminated Plates ◽  
Laminated Plate ◽  
Composite Laminated Plate ◽  
Vibration Localization ◽  
Composite Laminated Plates ◽  
Localization Phenomenon ◽  
Harmonic Resonance

AbstractThe nonlinear transverse vibrations of ordered and disordered two-dimensional (2D) two-span composite laminated plates are studied. Based on the von Karman's large deformation theory, the equations of motion of each-span composite laminated plate are formulated using Hamilton's principle, and the partial differential equations are discretized into nonlinear ordinary ones through the Galerkin's method. The primary resonance and 1/3 sub-harmonic resonance are investigated by using the method of multiple scales. The amplitude-frequency relations of the steady-state responses and their stability analyses in each kind of resonance are carried out. The effects of the disorder ratio and ply angle on the two different resonances are analyzed. From the numerical results, it can be concluded that disorder in the length of the two-span 2D composite laminated plate will cause the nonlinear vibration localization phenomenon, and with the increase of the disorder ratio, the vibration localization phenomenon will become more obvious. Moreover, the amplitude-frequency curves for both primary resonance and 1/3 sub-harmonic resonance obtained by the present analytical method are compared with those by the numerical integration, and satisfactory precision can be obtained for engineering applications and the results certify the correctness of the present approximately analytical solutions.

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.

scholarly journals Nonlinear Dynamic Response of Ropeway Roller Batteries via an Asymptotic Approach

2021 ◽  
Vol 11 (20) ◽  
pp. 9486
Author(s):  
Andrea Arena
Keyword(s):  
Nonlinear Dynamic ◽  
Multiple Scales ◽  
Equations Of Motion ◽  
Primary Resonance ◽  
Resonance Excitation ◽  
Dynamic Features ◽  
Response Curves ◽  
Internal Resonances ◽  
The Third ◽  
Fold Bifurcation

The nonlinear dynamic features of compression roller batteries were investigated together with their nonlinear response to primary resonance excitation and to internal interactions between modes. Starting from a parametric nonlinear model based on a previously developed Lagrangian formulation, asymptotic treatment of the equations of motion was first performed to characterize the nonlinearity of the lowest nonlinear normal modes of the system. They were found to be characterized by a softening nonlinearity associated with the stiffness terms. Subsequently, a direct time integration of the equations of motion was performed to compute the frequency response curves (FRCs) when the system is subjected to direct harmonic excitations causing the primary resonance of the lowest skew-symmetric mode shape. The method of multiple scales was then employed to study the bifurcation behavior and deliver closed-form expressions of the FRCs and of the loci of the fold bifurcation points, which provide the stability regions of the system. Furthermore, conditions for the onset of internal resonances between the lowest roller battery modes were found, and a 2:1 resonance between the third and first modes of the system was investigated in the case of harmonic excitation having a frequency close to the first mode and the third mode, respectively.

Nonlinear Oscillations of a Composite Laminated Plate with Parametrically and Externally Excitations

2013 ◽  
Vol 699 ◽  
pp. 641-644
Author(s):  
Xiao Li Bian ◽  
Shuang Bao Li
Keyword(s):  
Thin Plate ◽  
Nonlinear Oscillations ◽  
Plate Theory ◽  
Laminated Plate ◽  
Rectangular Thin Plate ◽  
Third Order ◽  
Composite Laminated Plate ◽  
Strain Relationship ◽  
Relationship Of ◽  
Equations Of Motions

Nonlinear oscillations of a simply-supported symmetric cross-ply composite laminated rectangular thin plate are investigated in this paper. The rectangular thin plate is subjected to the transversal and in-plane excitations. Based on the Reddy’s third-order shear deformation plate theory and the stress-strain relationship of the composite laminated plate, a two-degree-of-freedom non-autonomous nonlinear system governing equations of motions for the composite laminated rectangular thin plate is derived by using the Galerkin’s method. Numerical simulations illustrate that there exist complex nonlinear oscillations for composite laminated rectangular thin plate.

Nonlinear Forced Vibration Analysis of Smart Curved CNTs Conveying Fluid

2021 ◽  
Author(s):  
Vahid Mohamadhashemi ◽  
Amir Jalali ◽  
Habib Ahmadi
Keyword(s):  
Carbon Nanotube ◽  
Velocity Vector ◽  
Multiple Scales ◽  
Fluid Velocity ◽  
Equations Of Motion ◽  
Primary Resonance ◽  
Maximum Amplitude ◽  
Beam Theory ◽  
Physical Parameters ◽  
Conveying Fluid

In this study, the nonlinear vibration of a curved carbon nanotube conveying fluid is analyzed. The nanotube is assumed to be covered by a piezoelectric layer and the Euler–Bernoulli beam theory is employed to establish the governing equations of motion. The influence of carbon nanotube curvature on structural modeling and fluid velocity vector is considered and the slip boundary conditions of CNT conveying fluid are included. The mathematical modeling of the structure is developed using Hamilton’s principle and then, the Galerkin procedure is employed to discretize the equation of motion. Furthermore, the frequency response of the system is extracted by applying the multiple scales method of perturbation. Finally, a comprehensive study is carried out on the primary resonance and piezoelectric-based parametric resonance of the system. It is shown that consideration of nanotube curvature may lead to an increase in nonlinearity. Implementing the fluid velocity vector in which nanotube curvature is included highly affects the maximum amplitude of the response and should not be ignored. Furthermore, different system parameters have evident impacts on the behavior of the system and therefore, selecting the reasonable geometrical and physical parameters of the system can be very useful to achieve a favorable response.

Nonlinear Vibration Behaviors of Composite Laminated Plates with Time-Dependent Base Excitation and Boundary Conditions

2017 ◽  
Vol 18 (2) ◽  
Author(s):  
Yu-Yang Chai ◽  
Feng-Ming Li ◽  
Zhi-Guang Song
Keyword(s):  
Boundary Conditions ◽  
Theoretical Method ◽  
Laminated Plates ◽  
Time Dependent ◽  
Laminated Plate ◽  
Base Excitation ◽  
Analysis And Design ◽  
Composite Laminated Plate ◽  
Composite Laminated Plates ◽  
Frequency Relationship

AbstractThe nonlinear vibrations of composite laminated plates with time-dependent base excitation and boundary conditions are investigated. According to the von Kármán nonlinear plate theory, the dynamic equations of motion of the laminated plates are established. The nonlinear partial differential equations are transformed to the nonlinear ordinary differential ones using the Bubnov-Galerkin’s  method. The primary resonance and the primary parametric resonance of the laminated plate with time-dependent boundary conditions are investigated by means of the method of multiple scales. The validity of the present theoretical method is verified by comparing the amplitude–frequency relationship curves acquired from the present theoretical method with those calculated from the numerical simulation. The amplitude–frequency characteristic curves and the displacement time histories for different ply angles of the composite laminated plate are analyzed. The effects of the viscous damping factor and the transverse displacement excitation on the amplitude–frequency relationship curves are also studied. The present results are helpful for the nonlinear dynamical analysis and design of the composite laminated plate with time-dependent boundary conditions.

A Composite Plate Theory for Arbitrary Laminate Configurations

1987 ◽  
Vol 54 (1) ◽  
pp. 181-189 ◽  
Author(s):  
A. Toledano ◽  
H. Murakami
Keyword(s):  
Composite Plate ◽  
Plate Theory ◽  
Piecewise Linear ◽  
Present Theory ◽  
Laminated Plates ◽  
Stress Distributions ◽  
Laminated Plate ◽  
Individual Layer ◽  
Mixed Variational Principle ◽  
Shear Deformable

In order to improve the accuracy of in-plane responses of shear deformable composite plate theories, a new laminated plate theory was developed for arbitrary laminate configurations based upon Reissner’s (1984) new mixed variational principle. To this end, across each individual layer, piecewise linear continuous displacements and quadratic transverse shear stress distributions were assumed. The accuracy of the present theory was examined by applying it to the cylindrical bending problem of laminated plates which had been solved exactly by Pagano (1969). A comparison with the exact solutions obtained for symmetric, antisymmetric, and arbitrary laminates indicates that the present theory accurately estimates in-plane responses, even for small span-to-thickness ratios.

scholarly journals Performance Analysis of an Electromagnetically Coupled Piezoelectric Energy Scavenger

Energies ◽  
2020 ◽  
Vol 13 (4) ◽  
pp. 845 ◽  
Author(s):  
Abdolreza Pasharavesh ◽  
Reza Moheimani ◽  
Hamid Dalir
Keyword(s):  
Energy Harvesting ◽  
Multiple Scales ◽  
Nonlinear Partial Differential Equations ◽  
Low Frequency ◽  
Primary Resonance ◽  
Excitation Amplitude ◽  
Load Resistance ◽  
Response Curves ◽  
Piezoelectric Energy ◽  
Resonance Frequencies

The deliberate introduction of nonlinearities is widely used as an effective technique for the bandwidth broadening of conventional linear energy harvesting devices. This approach not only results in a more uniform behavior of the output power within a wider frequency band through bending the resonance response, but also contributes to energy harvesting from low-frequency excitations by activation of superharmonic resonances. This article investigates the nonlinear dynamics of a monostable piezoelectric harvester under a self-powered electromagnetic actuation. To this end, the governing nonlinear partial differential equations of the proposed harvester are order-reduced and solved by means of the perturbation method of multiple scales. The results indicate that, according to the excitation amplitude and load resistance, different responses can be distinguished at the primary resonance. The system behavior may involve the traditional bending of response curves, Hopf bifurcations, and instability regions. Furthermore, an order-two superharmonic resonance is observed, which is activated at lower excitations in comparison to order-three conventional resonances of the Duffing-type resonator. This secondary resonance makes it possible to extract considerable amounts of power at fractions of natural frequency, which is very beneficial in micro-electro-mechanical systems (MEMS)-based harvesters with generally high resonance frequencies. The extracted power in both primary and superharmonic resonances are analytically calculated, then verified by a numerical solution where a good agreement is observed between the results.

Free Vibration of Buckled Laminated Plates by Finite Element Method

1997 ◽  
Vol 119 (4) ◽  
pp. 635-640 ◽  
Author(s):  
Le-Chung Shiau ◽  
Teng-Yuan Wu
Keyword(s):  
Free Vibration ◽  
Plate Theory ◽  
Equations Of Motion ◽  
Composite Plates ◽  
Laminated Plates ◽  
Squeezing Effect ◽  
Governing Equations ◽  
Amplitude Vibration ◽  
Equilibrium Profile ◽  
Sudden Jump

Free vibration behavior of buckled composite plates are studied by using a high precision triangular plate element. This element is developed based on a simplified high order plate theory and von Ka´rma´n large deformation assumptions. The nonlinear governing equations of motion for the plates is linearized into two sets of equations by assuming small amplitude vibration of the laminates about its buckled static equilibrium profile. Results show that, in the postbuckling regime, the fundamental mode may be shifted from the first mode to the second due to squeezing effect of the in-plane force on the plate. For plate with certain boundary conditions, the natural frequency may have a sudden jump due to buckle pattern change of the plate in the postbuckling regime.

Vibration Analysis of Rectangular Functionally Graded Plate Bonded With PZT5 Sensor/Actuator

2010 ◽  
Author(s):  
M. H. Kargarnovin ◽  
N. S. Viliani
Keyword(s):  
Volume Fraction ◽  
Plate Theory ◽  
Equations Of Motion ◽  
Equation Of Motion ◽  
Functionally Graded ◽  
Bottom Surface ◽  
Feedback Gain ◽  
Laminated Plate ◽  
Functionally Graded Plate ◽  
Sensor Actuator

The vibration of FG plate embedded with PZT5 rectangular patches on the top and/or the bottom surface(s) as actuators/sensors is investigated. Based on the classical laminated plate theory, the governing differential equations of motion are derived under a variable electric charge. The equation of motion for PZT5 patch is obtained and solved. The effect of feedback gain and FGM volume fraction exponent on the plate frequency and its deflection are studied. It is noticed that increasing the feedback gain leads to the reduction of frequency and displacement. Moreover, by increasing the value of the FGM volume fraction exponent the resonant frequency decreases.

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