scholarly journals Numerical Investigation of the Dynamic Response of Symmetric Laminated Composite Beams to Harmonic Excitations

2009 ◽  
Vol 18 (5) ◽  
pp. 096369350901800 ◽  
Author(s):  
Zeki Kıral
Keyword(s):  
Dynamic Response ◽  
Frequency Response ◽  
Flexural Rigidity ◽  
Plate Theory ◽  
Damping Ratio ◽  
Excitation Frequency ◽  
Laminated Composite ◽  
Harmonic Excitation ◽  
Numerical Results ◽  
Harmonic Response

The aim of this study is to investigate the dynamic response of a laminated composite beam subjected to a harmonic excitation by a numerical time integration method known as Newmark method. The finite element method based on the classical laminated plate theory is used in order to obtain structural stiffness. The structural damping is modelled as proportional damping which is referred to as Rayleigh damping and two different damping ratios are used. The effect of damping on the frequency response of the beam is investigated for a broad range of excitation frequency. The effect of excitation point on the harmonic response is also considered. Four different lay-up configurations namely [0]2s, [0/90]s, [45/-45]s and [90]2s are considered in order to show the effect of the stacking sequence on the frequency response of the beam. The numerical results presented in this study show that, the magnitude of the harmonic response of the beam reduces considerably as the damping ratio increases and [90]2s lay-up produces largest dynamic response due to the reducing flexural rigidity. Numerical results also show that the location and frequency of the harmonic excitation has important role on the dynamic response of the beam.

Nonlinear Dynamics of a Dielectric Elastomer Membrane Under Compressive Loading

2020 ◽  
Author(s):  
Robert L. Lowe ◽  
Christopher G. Cooley
Keyword(s):  
Nonlinear Dynamics ◽  
Dynamic Response ◽  
Frequency Response ◽  
Compressive Loading ◽  
Excitation Frequency ◽  
Harmonic Excitation ◽  
Dielectric Elastomer ◽  
Large Strains ◽  
Membrane Stretch ◽  
Wide Range

Abstract This paper investigates the nonlinear dynamics of square dielectric elastomer membranes under time-dependent, through-thickness compressive loading. The dielectric elastomer is modeled as an isotropic ideal dielectric, with mechanical stiffening at large strains captured using the Gent hyperelastic constitutive model. The equation of motion for the in-plane membrane stretch is derived using Hamilton’s principle. The static response of the membrane is first investigated, with equilibrium stretches calculated numerically for a wide range of compressive pre-loads and applied voltages. Snap-through instabilities are observed, with the critical snap-through voltage decreasing with increasing compressive pre-load. The dynamic response of the membrane is then investigated under forced harmonic excitation. Frequency response plots characterizing the steady-state vibration reveal primary, subharmonic, and superharmonic resonances. Near these resonances, two stable vibration states are possible, corresponding to upper and lower branches in the frequency response. Significant and practically meaningful differences in the dynamic response are observed when the system vibrates at a fixed frequency about the upper and lower branches, a feature not discussed in previous research.

Bifurcation Modes of Periodic Solution in a Duffing System Under Constant Force as Well as Harmonic Excitation

2019 ◽  
Vol 29 (13) ◽  
pp. 1950173 ◽  
Author(s):  
Lei Hou ◽  
Xiaochao Su ◽  
Yushu Chen
Keyword(s):  
Frequency Response ◽  
Damping Ratio ◽  
Excitation Frequency ◽  
Harmonic Balance Method ◽  
Harmonic Excitation ◽  
Nonlinearity Parameter ◽  
Constant Force ◽  
Response Curves ◽  
Duffing System ◽  
Singularity Method

This paper focuses on the classification of the bifurcation modes of a Duffing system under the combined excitations of constant force and harmonic excitation. The Harmonic Balance method combined with the arc-length continuation is used to obtain the periodic solutions of the system, and the Floquet theory is employed to analyze the stability of the corresponding solutions. Accordingly, the frequency-response curves affected respectively by the constant force and the magnitude of the harmonic excitation are analyzed to show the basic dynamical properties of the system. Afterwards, the bifurcation investigations are carried out with the aid of the two-state variable singularity method. It is derived that there are a total of six different types of bifurcation modes due to the effects of the constant force and the magnitude of the harmonic excitation. At last, the effects of the nonlinearity parameter and the damping ratio on the bifurcation modes of the system are also discussed. The results obtained in this paper extend the findings in reference that the system can have markedly three types of frequency-response curves: with only one solution, or with maximum three or five solutions for a certain excitation frequency, and contribute to a better understanding of the significant influence of the constant force.

scholarly journals Vibrational Analysis of Composite Beam Embedded with Nitinol Shape Memory Alloy Wires

2018 ◽  
Vol 7 (3.4) ◽  
pp. 143
Author(s):  
Omer Muwafaq Mohmmed Ali ◽  
Rawaa Hamid Mohammed Al-Kalali ◽  
Ethar Mohamed Mahdi Mubarak
Keyword(s):  
Shape Memory Alloy ◽  
Shape Memory ◽  
Frequency Response ◽  
Response Curve ◽  
Natural Frequencies ◽  
Damping Ratio ◽  
Vibrational Analysis ◽  
Laminated Composite ◽  
Vibration Modes ◽  
Frequency Response Curve

In this paper, laminated composite materials were hybridized with fibers (E-glass) and shape memory alloy wires which considered a smart material. The effect of changing frequency on the (acceleration- frequency) response curve, the damping ratio of the vibration modes, the natural frequencies of the vibration mode, the effect of shape memory alloy wires number on the damping characteristics were studied. Hand lay-up technique was used to prepare the specimens, epoxy resin type was used as a matrix reinforced by fiber, E-glass. The specimens were manufactured by stacking 2 layers of fibers. Shape memory alloy, type Nitinol (nickel-titanium) having a diameter (1 and 2mm), was used to manufacture the specimens by embedding (1,2 and 3) wires into epoxy. Experimentally, the acceleration- frequency response curve was plotted for the vibration modes, this curve was used to measure the natural frequencies of the vibration modes and calculate the damping ratio of the vibration modes. ANSYS 15- APDL was used to determine the mode shape and find the natural frequencies of the vibration modes then compared with the experimental results. The results illustrated that, for all specimens increasing the natural frequency leads to decreasing the damping ratio. Increasing the number of shape memory alloy wires leads to increase the values of the damping ratio of the vibration modes and the natural frequencies of the vibration modes at room temperature. 

Nonlinear vibration of pile groups under lateral loading

1992 ◽  
Vol 29 (4) ◽  
pp. 702-710 ◽  
Author(s):  
Hans H. Vaziri ◽  
Yingcai Han
Keyword(s):  
Dynamic Response ◽  
Nonlinear Vibration ◽  
Damping Ratio ◽  
Pile Group ◽  
Harmonic Excitation ◽  
Pile Groups ◽  
Plane Normal ◽  
Interaction Factors ◽  
Full Scale Tests ◽  
Measured Response

Dynamic response of a pile group, comprising six full-size cast-in-place reinforced concrete piles, is investigated under varying levels of lateral harmonic excitation in two directions: along a plane composed of three piles (X-direction) and along a plane normal to it composed of two piles (Y-direction). The measured response is compared with the theoretical predictions using the dynamic interaction factors approach. To account for the nonlinear response of the pile group using the theoretical model, provisions are made for yielding of soil around the piles by introducing the boundary-zone concept. It is shown that the proposed theory adequately captures the measured response of the pile group under both linear (weak excitation) and nonlinear (strong excitation) conditions. The study performed indicates that although the rocking stiffness of the pile group is strongly influenced by the number of piles along the direction of excitation, the horizontal stiffness remains virtually unaffected. The results obtained show that the stiffness and damping ratio of the pile group reduce as the excitation intensity increases. It is also found that the pile–soil–pile interaction plays a major role in the overall dynamic response of the pile group; this effect is manifested by a reduction in the stiffness and an increase in the damping of the pile group. Key words : dynamics, vibration, piles, pile group, nonlinear vibration, full-scale tests, modelling, resonance, soil separation, soil yielding.

Numerical Study of a New Variable Friction TMD

2011 ◽  
Vol 243-249 ◽  
pp. 5450-5457 ◽  
Author(s):  
Li Qin ◽  
Wei Ming Yan ◽  
Sheng Bo Guo
Keyword(s):  
Frequency Response ◽  
Numerical Study ◽  
Damping Ratio ◽  
Harmonic Balance Method ◽  
Structural Response ◽  
Harmonic Excitation ◽  
Response Curves ◽  
Equivalent Damping ◽  
Response Characteristics ◽  
Variable Friction

The paper proposes a new variable friction system, of which the friction force can increase linearly with the displacement of system. This new system can be used in TMD to avoid the disadvantage of Coulomb friction TMD. Using first order harmonic balance method, the equivalent damping ratio and frequency of SDOF variable friction system is deduced and analyzed. The frequency response characteristics of SDOF variable friction system is discussed. The control effectiveness of variable friction TMD under harmonic excitation is analyzed theoretically. The results demonstrate that the frequency response curves of variable friction TMD and classically damped TMD are similar and both can effectively reduce structural response under harmonic excitation.

scholarly journals A New Method to Calculate Additional Damping Ratio considering the Effect of Excitation Frequency

2020 ◽  
Vol 2020 ◽  
pp. 1-15
Author(s):  
Weizhi Xu ◽  
Dongsheng Du ◽  
Shuguang Wang ◽  
Weiwei Li
Keyword(s):  
Dynamic Response ◽  
Ground Motion ◽  
Calculation Method ◽  
Response Spectrum ◽  
Damping Ratio ◽  
Excitation Frequency ◽  
Structural Dynamic ◽  
Important Indicator ◽  
Simplified Calculation ◽  
Simplified Calculation Method

The additional damping ratio (ADR) is an important indicator for evaluating the damping effect of structures with energy-dissipation devices. Most existing methods for determining the ADR require an analysis of the structural dynamic response and complex iterative calculations. An innovative simplified calculation method for determining the ADR of a structure supplemented by nonlinear viscous dampers is proposed. This method does not require the dynamic response of the structure to be calculated and only requires the structural characteristics, excitation frequency, and damper parameters. In this study, several typical calculation methods for the ADR were analysed. Then, a calculation formula for the ADR was derived with consideration of harmonic excitation under the condition where the excitation frequency is equal to the structural natural frequency, without calculation of the structural dynamic response or an iterative process. The effect of the excitation frequency on the calculated value of the ADR with different damping exponents was studied. Accordingly, the response spectrum average period (RSAP) was considered as the excitation period of ground motion to evaluate the excitation frequency, and a simplified calculation method for the ADR considering the effect of the excitation frequency characterised by the RSAP of the ground motion was established. Finally, the accuracy and effectiveness of the proposed method were verified by comparison with ADRs calculated using other methods.

Nonlinear Dynamic Responses of Elastic Structures With Two Rectangular Liquid Tanks Subjected to Horizontal Excitation

2010 ◽  
Vol 6 (2) ◽  
Author(s):  
Takashi Ikeda
Keyword(s):  
Frequency Response ◽  
Equations Of Motion ◽  
Excitation Frequency ◽  
Pitchfork Bifurcation ◽  
Harmonic Excitation ◽  
Dynamic Responses ◽  
Response Curves ◽  
Chaotic Vibrations ◽  
Tuned Liquid Dampers ◽  
Theoretical Results

Nonlinear vibrations of an elastic structure with two partially filled liquid tanks subjected to horizontal harmonic excitation are investigated. The natural frequencies of the structure and sloshing satisfy the tuning condition 1:1:1 when tuned liquid dampers are used. The equations of motion for the structure and the modal equations of motion for the first, second, and third sloshing modes are derived by using Galerkin’s method, taking into account the nonlinearity of the sloshing. Then, van der Pol’s method is employed to determine the frequency response curves. It is found in calculating the frequency response curves that pitchfork bifurcation can occur followed by “localization phenomenon” for a specific excitation frequency range. During this range, sloshing occurs at different amplitudes in the two tanks, even if the dimensions of both tanks are identical. Furthermore, Hopf bifurcation may occur followed by amplitude- and phase-modulated motions including chaotic vibrations. In addition, Lyapunov exponents are calculated to prove the occurrence of both amplitude-modulated motions and chaotic vibrations. Bifurcation sets are also calculated to show the influence of the system parameters on the frequency response. Experiments were conducted to confirm the validity of the theoretical results. It was found that the theoretical results were in good agreement with the experimental data.

Stable and unstable nonlinear resonant response of hanging chains: theory and experiment

1993 ◽  
Vol 440 (1909) ◽  
pp. 345-364 ◽  
Keyword(s):  
Excitation Frequency ◽  
Three Dimensional ◽  
Harmonic Excitation ◽  
Numerical Results ◽  
Experimental Results ◽  
Distinct Region ◽  
Asymptotic Results ◽  
Sensitive Dependence ◽  
Theoretical Predictions ◽  
Hanging Chain

The three-dimensional nonlinear dynamics of a hanging chain, driven by harmonic excitation at the top, are studied first analytically and numerically, and then experimentally. Asymptotic results demonstrate a sensitive dependence on excitation frequency and amplitude. For moderately large excitation amplitudes there are distinct regions of stable two-dimensional and stable three-dimensional response as function of frequency, as well as a distinct region in which all steady-state solutions are unstable. Numerical results were obtained to verify the asymptotic solutions and investigate the dynamics within the irregular response region. Numerical results for even larger excitation amplitudes showed that large impulse-like tension forces cause the chain to lose tension over a region adjacent to its freely hanging end, and then collapse. Following the collapse, the chain configuration intersects itself. Experimental results confirm qualitatively and quantitatively the theoretical predictions. The experimental results also demonstrate the loss of tension and subsequent collapse of the chain at the predicted excitation amplitudes, as well as the intersection of the chain with itself.

Intrinsic Localized Modes of Principal Parametric Resonances in Pendulum Arrays Subjected to Vertical Excitation

2015 ◽  
Vol 10 (5) ◽  
Author(s):  
Takashi Ikeda ◽  
Yuji Harata ◽  
Chongyue Shi ◽  
Keisuke Nishimura
Keyword(s):  
Experimental Data ◽  
Theoretical Analysis ◽  
Frequency Response ◽  
Excitation Frequency ◽  
Harmonic Excitation ◽  
Localized Modes ◽  
Response Curves ◽  
Chaotic Motions ◽  
Intrinsic Localized Modes ◽  
Spring Constants

Intrinsic localized modes (ILMs) are investigated in an N-pendulum array subjected to vertical harmonic excitation. The pendula behave nonlinearly and are coupled with each other because they are connected by torsional, weak, linear springs. In the theoretical analysis, van der Pol's method is employed to determine the expressions for frequency response curves for the principal parametric resonance, considering the nonlinear restoring moment of the pendula. In the numerical results, frequency response curves for N = 2 and 3 are shown to examine the patterns of ILMs, and demonstrate the influences of the connecting spring constants and the imperfections of the pendula. Bifurcation sets are also calculated to show the excitation frequency range and the conditions for the occurrence of ILMs. Increasing the connecting spring constants results in the appearance of Hopf bifurcations. The numerical simulations reveal the occurrence of ILMs with amplitude modulated motions (AMMs), including chaotic motions. ILMs were observed in experiments, and the experimental data were compared with the theoretical results. The validity of the theoretical analysis was confirmed by the experimental data.

Localization Phenomena in Pendulum Arrays Subjected to Vertical Excitation

2014 ◽  
Author(s):  
Takashi Ikeda ◽  
Yuji Harata ◽  
Chongyue Shi ◽  
Keisuke Nishimura
Keyword(s):  
Experimental Data ◽  
Theoretical Analysis ◽  
Frequency Response ◽  
Excitation Frequency ◽  
Harmonic Excitation ◽  
Response Curves ◽  
Chaotic Motions ◽  
Vertical Excitation ◽  
Parametric Resonances ◽  
Spring Constants

Localization phenomena, also referred to as intrinsic localized modes (ILMs), are investigated in an N-pendulum array subjected to vertical harmonic excitation. The pendula behave nonlinearly and are connected with each other by weak linear springs. In the theoretical analysis, van der Pol’s method is employed to determine the expressions for frequency response curves for the principal parametric resonances, considering the nonlinear restoring moment of the pendula. In the numerical results, frequency response curves for N=2 and 3 are shown to examine the patterns of ILMs, and the influences of the connecting spring constants and the imperfections of the pendula. Bifurcation sets are also calculated to show the excitation frequency range and the conditions for the occurrence of ILMs. Increasing the connecting spring constant results in the appearance of Hopf bifurcation. The numerical simulations reveal the occurrence of ILMs with amplitude modulated motions (AMMs) including chaotic motions. ILMs were observed in experiments, and the experimental data were compared with the theoretical results. The validity of the theoretical analysis was confirmed by the experimental data.

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