Journal of Nonlinear Dynamics The latest articles from Hindawi © 2017 , Hindawi Limited . All rights reserved. Complex Dynamics and Synchronization in a System of Magnetically Coupled Colpitts Oscillators Mon, 10 Apr 2017 00:00:00 +0000 We propose the use of a simple, cheap, and easy technique for the study of dynamic and synchronization of the coupled systems: effects of the magnetic coupling on the dynamics and of synchronization of two Colpitts oscillators (wireless interaction). We derive a smooth mathematical model to describe the dynamic system. The stability of the equilibrium states is investigated. The coupled system exhibits spectral characteristics such as chaos and hyperchaos in some parameter ranges of the coupling. The numerical exploration of the dynamics system reveals various bifurcations scenarios including period-doubling and interior crisis transitions to chaos. Moreover, various interesting dynamical phenomena such as transient chaos, coexistence of solution, and multistability (hysteresis) are observed when the magnetic coupling factor varies. Theoretical reasons for such phenomena are provided and experimentally confirmed with practical measurements in a wireless transfer. L. K. Kana, A. Fomethe, H. B. Fotsin, E. T. Wembe, and A. I. Moukengue Copyright © 2017 L. K. Kana et al. All rights reserved. System Performance of an Inertially Stabilized Gimbal Platform with Friction, Resonance, and Vibration Effects Tue, 28 Mar 2017 00:00:00 +0000 The research work evaluates the quality of the sensor to perform measurements and documents its effects on the performance of the system. It also evaluates if this performance changes due to the environments and other system parameters. These environments and parameters include vibration, system friction, structural resonance, and dynamic system input. The analysis is done by modeling a gimbal camera system that requires angular measurements from inertial sensors and gyros for stabilization. Overall, modeling includes models for four different types of gyros, the gimbal camera system, the drive motor, the motor rate control system, and the angle position control system. Models for friction, structural resonance, and vibration are analyzed, respectively. The system is simulated, for an ideal system, and then includes the more realistic environmental and system parameters. These simulations are run with each of the four types of gyros. The performance analysis depicts that for the ideal system; increasing gyro quality provides better system performance. However, when environmental and system parameters are introduced, this is no longer the case. There are even cases when lower quality sensors provide better performance than higher quality sensors. Ruting Jia, Vidya K. Nandikolla, Gary Haggart, Charles Volk, and Daniel Tazartes Copyright © 2017 Ruting Jia et al. All rights reserved. Two-Dimensional Kinetic Shape Dynamics: Verification and Application Mon, 31 Oct 2016 13:14:44 +0000 A kinetic shape (KS) is a smooth two- or three-dimensional shape that is defined by its predicted ground reaction forces as it is pressed onto a flat surface. A KS can be applied in any mechanical situation where position-dependent force redirection is required. Although previous work on KSs can predict static force reaction behavior, it does not describe the kinematic behavior of these shapes. In this article, we derive the equations of motion for a rolling two-dimensional KS (or any other smooth curve) and validate the model with physical experiments. The results of the physical experiments showed good agreement with the predicted dynamic KS model. In addition, we have modified these equations of motion to develop and verify the theory of a novel transportation device, the kinetic board, that is powered by an individual shifting their weight on top of a set of KSs. Ismet Handzic, Haris Muratagic, and Kyle B. Reed Copyright © 2016 Ismet Handzic et al. All rights reserved. Chaos in Essentially Singular 3D Dynamical Systems with Two Quadratic Nonlinearities Tue, 20 Sep 2016 16:38:52 +0000 A new class of 3D autonomous quadratic systems, the dynamics of which demonstrate a chaotic behavior, is found. This class is a generalization of the well-known class of Lorenz-like systems. The existence conditions of limit cycles in systems of the mentioned class are found. In addition, it is shown that, with the change of the appropriate parameters of systems of the indicated class, chaotic attractors different from the Lorenz attractor can be generated (these attractors are the result of the cascade of limit cycles bifurcations). Examples are given. Vasiliy Belozyorov Copyright © 2016 Vasiliy Belozyorov. All rights reserved. Finite-Time Synchronization for Uncertain Master-Slave Chaotic System via Adaptive Super Twisting Algorithm Sun, 03 Jul 2016 11:18:30 +0000 A second-order sliding mode control for chaotic synchronization with bounded disturbance is studied. A robust finite-time controller is designed based on super twisting algorithm which is a popular second-order sliding mode control technique. The proposed controller is designed by combining an adaptive law with super twisting algorithm. New results based on adaptive super twisting control for the synchronization of identical Qi three-dimensional four-wing chaotic system are presented. The finite-time convergence of synchronization is ensured by using Lyapunov stability theory. The simulations results show the usefulness of the developed control method. P. Siricharuanun and C. Pukdeboon Copyright © 2016 P. Siricharuanun and C. Pukdeboon. All rights reserved. Nonlinear Dynamics and Analysis of Intracranial Saccular Aneurysms with Growth and Remodeling Thu, 16 Jun 2016 09:39:08 +0000 A new mathematical model for the interaction of blood flow with the arterial wall surrounded by cerebral spinal fluid is developed with applications to intracranial saccular aneurysms. The blood pressure acting on the inner arterial wall is modeled via a Fourier series, the arterial wall is modeled as a spring-mass system incorporating growth and remodeling, and the surrounding cerebral spinal fluid is modeled via a simplified one-dimensional compressible Euler equation with inviscid flow and negligible nonlinear effects. The resulting nonlinear coupled fluid-structure interaction problem is analyzed and a perturbation technique is employed to derive the first-order approximation solution to the system. An analytical solution is also derived for the linearized version of the problem using Laplace transforms. The solutions are validated against related work from the literature and the results suggest the biological significance of the inclusion of the growth and remodeling effects on the rupture of intracranial aneurysms. Manal Badgaish, Jeng-Eng Lin, and Padmanabhan Seshaiyer Copyright © 2016 Manal Badgaish et al. All rights reserved. Dynamic Analysis of the High Speed Train and Slab Track Nonlinear Coupling System with the Cross Iteration Algorithm Thu, 25 Feb 2016 12:18:34 +0000 A model for dynamic analysis of the vehicle-track nonlinear coupling system is established by the finite element method. The whole system is divided into two subsystems: the vehicle subsystem and the track subsystem. Coupling of the two subsystems is achieved by equilibrium conditions for wheel-to-rail nonlinear contact forces and geometrical compatibility conditions. To solve the nonlinear dynamics equations for the vehicle-track coupling system, a cross iteration algorithm and a relaxation technique are presented. Examples of vibration analysis of the vehicle and slab track coupling system induced by China’s high speed train CRH3 are given. In the computation, the influences of linear and nonlinear wheel-to-rail contact models and different train speeds are considered. It is found that the cross iteration algorithm and the relaxation technique have the following advantages: simple programming; fast convergence; shorter computation time; and greater accuracy. The analyzed dynamic responses for the vehicle and the track with the wheel-to-rail linear contact model are greater than those with the wheel-to-rail nonlinear contact model, where the increasing range of the displacement and the acceleration is about 10%, and the increasing range of the wheel-to-rail contact force is less than 5%. Xiaoyan Lei, Shenhua Wu, and Bin Zhang Copyright © 2016 Xiaoyan Lei et al. All rights reserved. Prey-Predator Model with Two-Stage Infection in Prey: Concerning Pest Control Mon, 30 Nov 2015 14:09:15 +0000 A prey-predator model system is developed; specifically the disease is considered into the prey population. Here the prey population is taken as pest and the predators consume the selected pest. Moreover, we assume that the prey species is infected with a viral disease forming into susceptible and two-stage infected classes, and the early stage of infected prey is more vulnerable to predation by the predator. Also, it is assumed that the later stage of infected pests is not eaten by the predator. Different equilibria of the system are investigated and their stability analysis and Hopf bifurcation of the system around the interior equilibriums are discussed. A modified model has been constructed by considering some alternative source of food for the predator population and the dynamical behavior of the modified model has been investigated. We have demonstrated the analytical results by numerical analysis by taking some simulated set of parameter values. Swapan Kumar Nandi, Prasanta Kumar Mondal, Soovoojeet Jana, Palash Haldar, and T. K. Kar Copyright © 2015 Swapan Kumar Nandi et al. All rights reserved. On the Complex Dynamics of Continued and Discrete Cauchy’s Method Thu, 08 Oct 2015 07:08:41 +0000 Let be a complex polynomial of fixed degree . In this paper we show that Cauchy’s method may fail to find all zeros of for any initial guess lying in the complex plane and we propose several ways to find all zeros of a given polynomial using scaled Cauchy’s methods. Mohamed Lamine Sahari Copyright © 2015 Mohamed Lamine Sahari. All rights reserved. The Dynamics of a Cubic Nonlinear System with No Equilibrium Point Wed, 02 Sep 2015 13:07:16 +0000 We study the dynamics of a three-dimensional nonlinear system with cubic nonlinearity and no equilibrium points with the use of Poincaré maps, Lyapunov Exponents, and bifurcations diagrams. The system has rich dynamics: chaotic behavior, regular orbits, and 3-tori periodicity. Finally, the proposed system is also reported to verify electronic circuit modeling feasibility. J. O. Maaita, Ch. K. Volos, I. M. Kyprianidis, and I. N. Stouboulos Copyright © 2015 J. O. Maaita et al. All rights reserved. Complete Coefficient Criteria for Five-Dimensional Hopf Bifurcations, with an Application to Economic Dynamics Mon, 03 Aug 2015 08:51:57 +0000 Paper presents a complete mathematical characterization of coefficient criteria for five-dimensional Hopf bifurcations and an example of the application of these criteria to a model of economic dynamics. The application illustrates that the proposed criteria are practical and useful in determining the existence or nonexistence of Hopf bifurcations of five-dimensional dynamical systems in entire ranges of the system’s parameters. Christos Douskos and Panagiotis Markellos Copyright © 2015 Christos Douskos and Panagiotis Markellos. All rights reserved. Investigation of Chaotic and Strange Nonchaotic Phenomena in Nonautonomous Wien-Bridge Oscillator with Diode Nonlinearity Sun, 15 Feb 2015 13:12:19 +0000 We have studied the chaotic and strange nonchaotic phenomena of a simple quasiperiodically forced Wien bridge oscillator circuit with diode as the only nonlinearity in this electronic oscillator system responsible for various nonlinear behaviors. Both the experimental results and the numerical simulation results for their confirmation are provided to show the bifurcation process. Various measures used for the numerical confirmation of SNA are power spectrum, maximal Lyapunov exponent, path of translational variables, mean square displacement, projection of poincaré section, log-log plot, and autocorrelation function. Based upon the numerical results, the birth of SNAs has been identified in the band merging route, intermittency route, and blowout bifurcation route. In addition, the birth of SNAs has been analyzed with peculiar mechanism, namely, “0-1 Test” employing the one state dynamical variable. R. Rizwana and I. Raja Mohamed Copyright © 2015 R. Rizwana and I. Raja Mohamed. All rights reserved. A Magnetic Coupling Based Strategy for Synchronization of a System Consisting of Chaotic Modified Van der Pol Duffing Oscillators Sun, 28 Dec 2014 00:10:14 +0000 We propose a new paradigm for the synchronization of two unconnected magnetic core coils based modified Van der Pol Duffing (MVDPD) oscillators circuits. The method is such that only magnetic field based coupling is sufficient to drive two identical chaotic circuits to a synchronized state as well as achieving the global stabilization of the system to its regular dynamics. The dynamics of the coupled system is investigated and Lyapunov stability theory is applied to prove that under some conditions the drive-response system can achieve practical synchronization. Numerical and PSpice simulations are given to demonstrate the effectiveness of the controller. L. K. Kana, A. Fomethe, H. B. Fotsin, and P. H. Louodop Fotso Copyright © 2014 L. K. Kana et al. All rights reserved. Influence of Opening Locations on the Structural Response of Shear Wall Tue, 25 Nov 2014 11:10:39 +0000 Shear walls have been conferred as a major lateral load resisting element in a building in any seismic prone zone. It is essential to determine behavior of shear wall in the preelastic and postelastic stage. Shear walls may be provided with openings due to functional requirement of the building. The size and location of opening may play a significant role in the response of shear walls. Though it is a well known fact that size of openings affects the structural response of shear walls significantly, there is no clear consensus on the behavior of shear walls under different opening locations. The present study aims to study the dynamic behavior of shear walls under various opening locations using nonlinear finite element analysis using degenerated shell element with assumed strain approach. Only material nonlinearity has been considered using plasticity approach. A five-parameter Willam-Warnke failure criterion is considered to define the yielding/crushing of the concrete with tensile cutoff. The time history responses have been plotted for all opening cases with and without ductile detailing. The analysis has been done for different damping ratios. It has been observed that the large number of small openings resulted in better displacement response. G. Muthukumar and Manoj Kumar Copyright © 2014 G. Muthukumar and Manoj Kumar. All rights reserved. Hyers-Ulam Stability of Third Order Euler’s Differential Equations Tue, 04 Nov 2014 00:00:00 +0000 We investigate the Hyers-Ulam stability of third order Euler's differential equations of the form on any open interval , or , where , and are complex constants. A. K. Tripathy and A. Satapathy Copyright © 2014 A. K. Tripathy and A. Satapathy. All rights reserved. Experiment on Bifurcation and Chaos in Coupled Anisochronous Self-Excited Systems: Case of Two Coupled van der Pol-Duffing Oscillators Wed, 29 Oct 2014 12:23:48 +0000 The analog circuit implementation and the experimental bifurcation analysis of coupled anisochronous self-driven systems modelled by two mutually coupled van der Pol-Duffing oscillators are considered. The coupling between the two oscillators is set in a symmetrical way that linearly depends on the difference of their velocities (i.e., dissipative coupling). Interest in this problem does not decrease because of its significance and possible application in the analysis of different, biological, chemical, and electrical systems (e.g., coupled van der Pol-Duffing electrical system). Regions of quenching behavior as well as conditions for the appearance of Hopf bifurcations are analytically defined. The scenarios/routes to chaos are studied with particular emphasis on the effects of cubic nonlinearity (that is responsible for anisochronism of small oscillations). When monitoring the control parameter, various striking dynamic behaviors are found including period-doubling, symmetry-breaking, multistability, and chaos. An appropriate electronic circuit describing the coupled oscillator is designed and used for the investigations. Experimental results that are consistent with results from theoretical analyses are presented and convincingly show quenching phenomenon as well as bifurcation and chaos. J. Kengne, F. Kenmogne, and V. Kamdoum Tamba Copyright © 2014 J. Kengne et al. All rights reserved. On Full-State Hybrid Projective Synchronization of General Discrete Chaotic Systems Tue, 14 Oct 2014 12:59:19 +0000 The problems of full-state hybrid projective synchronization (FSHPS) and inverse full-state hybrid projective synchronization (IFSHPS) for general discrete chaotic systems are investigated in 2D. Based on nonlinear control method and Lyapunov stability theory, new controllers are designed to study FSHPS and IFSHPS, respectively, for 2D arbitrary chaotic systems in discrete-time. Numerical example and simulations are used to validate the main results of this paper. Adel Ouannas Copyright © 2014 Adel Ouannas. All rights reserved. Catastrophe and Hysteresis by the Emerging of Soliton-Like Solutions in a Nerve Model Tue, 07 Oct 2014 13:56:34 +0000 The nonlinear problem of traveling nerve pulses showing the unexpected process of hysteresis and catastrophe is studied. The analysis was done for the case of one-dimensional nerve pulse propagation. Of particular interest is the distinctive tendency of the pulse nerve model to conserve its behavior in the absence of the stimulus that generated it. The hysteresis and catastrophe appear in certain parametric region determined by the evolution of bubble and pedestal like solitons. By reformulating the governing equations with a standard boundary conditions method, we derive a system of nonlinear algebraic equations for critical points. Our approach provides opportunities to explore the nonlinear features of wave patterns with hysteresis. Fernando Ongay Larios, Nikolay P. Tretyakov, and Maximo A. Agüero Copyright © 2014 Fernando Ongay Larios et al. All rights reserved. Multimode Analysis of the Dynamics and Integrity of Electrically Actuated MEMS Resonators Thu, 25 Sep 2014 06:22:35 +0000 We present a theoretical investigation of the dynamic behavior of a microelectromechanical system (in brief, MEMS) device modelled as a clamped-clamped microbeam subjected to electrostatic and electrodynamic actuation. We use the Galerkin projection technique to reduce the partial integro-differential equation governing the dynamics of the microbeam to a system of coupled ordinary differential equations which describe the interactions of the linear mode shapes of the microbeam. Analytical solutions are derived and their stability is studied for the simplest reduced-order model which takes into account only the first linear mode in the Galerkin procedure. We further investigate the influence of the first few higher modes on the Galerkin procedure, and hence its convergence, by analysing the boundaries between pull-in and pull-in-free vibrations domains in the space of actuation parameters. These are determined for the various multimode combinations using direct numerical time integration. Our results show that unsafe domains form V-like shapes for actuation frequencies close to the superharmonic, fundamental, and subharmonic resonances. They also reveal that the single first-mode reduced model usually considered underestimates the left branches and overestimates the right branches of these boundaries. Serge Bruno Yamgoué and Alain Juvenal Tchiegang Copyright © 2014 Serge Bruno Yamgoué and Alain Juvenal Tchiegang. All rights reserved. The Effect of Slow Invariant Manifold and Slow Flow Dynamics on the Energy Transfer and Dissipation of a Singular Damped System with an Essential Nonlinear Attachment Mon, 01 Sep 2014 05:38:54 +0000 We study the effect of slow flow dynamics and slow invariant manifolds on the energy transfer and dissipation of a dissipative system of two linear oscillators coupled with an essential nonlinear oscillator with a mass much smaller than the masses of the linear oscillators. We calculate the slow flow of the system, the slow invariant manifold, the total energy of the system, and the energy that is stored in the nonlinear oscillator for different sets of the parameters and show that the bifurcations of the SIM and the dynamics of the slow flow play an important role in the energy transfer from the linear to the nonlinear oscillator and the rate of dissipation of the total energy of the initial system. Jamal-Odysseas Maaita and Efthymia Meletlidou Copyright © 2014 Jamal-Odysseas Maaita and Efthymia Meletlidou. All rights reserved. Exact Solitary Wave Solution in the ZK-BBM Equation Sun, 31 Aug 2014 06:52:07 +0000 The traveling wave solution for the ZK-BBM equation is considered, which is governed by a nonlinear ODE system. The bifurcation structure of fixed points and bifurcation phase portraits with respect to the wave speed c are analyzed by using the dynamical system theory. Furthermore, the exact solutions of the homoclinic orbits for the nonlinear ODE system are obtained which corresponds to the solitary wave solution curve of the ZK-BBM equation. Juan Zhao and Wei Li Copyright © 2014 Juan Zhao and Wei Li. All rights reserved. Optimal Control of a Delayed HIV Infection Model via Fourier Series Tue, 26 Aug 2014 05:34:05 +0000 We present a delayed optimal control which describes the interaction of the immune system with the human immunodeficiency virus (HIV) and CD4+ T-cells. In order to improve the therapies, treatment and the intracellular delays are incorporated into the model. The optimal control in this model represents the efficiency of drug treatment in preventing viral production and new infections. The optimal pair of control and trajectories of this nonlinear delay system with quadratic cost functional is obtained by Fourier series approximation. The method is based on expanding time varying functions in the nonlinear delay system into their Fourier series with unknown coefficients. Using operational matrices for integration, product, and delay, the problem is reduced to a set of nonlinear algebraic equations. Gh. Ghanbari and M. H. Farahi Copyright © 2014 Gh. Ghanbari and M. H. Farahi. All rights reserved. Increase in Equilibrium Price by Fast Oscillations Tue, 20 May 2014 08:28:24 +0000 The dynamics of a market can be described by a differential equation. Using the concept of fast oscillation, the system (typical market) can also oscillate around a new equilibrium price, with an increase. Previously that increase was established by applying harmonic force. In present work, harmonic force is replaced by an arbitrary periodic force with zero mean. Hence the increase in equilibrium price can be controlled by varying the external arbitrary periodic force. Babar Ahmad and Khalid Iqbal Mahr Copyright © 2014 Babar Ahmad and Khalid Iqbal Mahr. All rights reserved. Control and Synchronization of Chaotic and Hyperchaotic Lorenz Systems via Extended Backstepping Techniques Tue, 06 May 2014 08:17:19 +0000 We propose novel controllers for stabilization and tracking of chaotic and hyperchaotic Lorenz systems using extended backstepping techniques. Based on the proposed approach, generalized weighted controllers were designed to control chaotic behaviour as well as to achieve synchronization in chaotic and hyperchaotic Lorenz systems. The effectiveness and feasibility of the proposed weighted controllers were verified numerically and showed their robustness against noise. O. S. Onma, O. I. Olusola, and A. N. Njah Copyright © 2014 O. S. Onma et al. All rights reserved. Parameter Estimation and Hybrid Lag Synchronization in Hyperchaotic Lü Systems Sun, 30 Mar 2014 09:21:22 +0000 The antiphase and complete lag synchronization of hyperchaotic Lü systems with unknown parameters is investigated. Based on the Lyapunov stability theory, the sufficient conditions for achieving hybrid lag synchronization are derived. The optimized parameter observers are approached analytically via adaptive control approach. Numerical simulation results are presented to verify the effectiveness of the proposed scheme. Qing Wei and Zuolei Wang Copyright © 2014 Qing Wei and Zuolei Wang. All rights reserved. Dynamics from Multivariable Longitudinal Data Wed, 19 Mar 2014 13:30:27 +0000 We introduce a method of analysing longitudinal data in variables and a population of observations. Longitudinal data of each observation is exactly coded to an orbit in a two-dimensional state space . At each time, information of each observation is coded to a point , where is the physical condition of the observation and is an ordering of variables. Orbit of each observation in is described by a map that dynamically rearranges order of variables at each time step, eventually placing the most stable, least frequently changing variable to the left and the most frequently changing variable to the right. By this operation, we are able to extract dynamics from data and visualise the orbit of each observation. In addition, clustering of data in the stable variables is revealed. All possible paths that any observation can take in are given by a subshift of finite type (SFT). We discuss mathematical properties of the transition matrix associated to this SFT. Dynamics of the population is a nonautonomous multivalued map equivalent to a nonstationary SFT. We illustrate the method using a longitudinal data of a population of households from Agincourt, South Africa. Maria Vivien Visaya and David Sherwell Copyright © 2014 Maria Vivien Visaya and David Sherwell. All rights reserved. Markov Chain Model to Explain the Dynamics of Human Depression Tue, 18 Mar 2014 08:48:59 +0000 Depression is one of the major concerns of the present generation. A Markov chain model has been used to portray and investigate this curse. Long-term behaviour of the model has been discussed. Different types of treatment strategies have been considered in this paper to identify the most powerful measure of keeping this disease from its spread in the society. This paper also focuses on the usefulness of the drugs available at present for the treatment of this disease. Souvik Bhattacharya Copyright © 2014 Souvik Bhattacharya. All rights reserved. Dynamic Analyses of Urban Expressway Network with Mesoscopic Traffic Flow Model Integrated Variable Speed Limits Tue, 18 Mar 2014 07:04:52 +0000 Urban congestion is a major and costly problem in many cities both in China and other countries. The purpose of building urban expressway is to alleviate the growing traffic pressure. In this paper, the mesoscopic traffic flow models are improved by variable speed limits strategy for the dynamic of vehicles on urban expressway network. The models include static queuing model, the velocity model, and the movement model of the vehicle. Moreover the method of the simulation is also proposed. So that we can get the corresponding variable speed limits values and aid traffic managers in making decisions to develop a network traffic flow control strategy. In the end, the elevated expressway of Jinan city is used as a simulation example. We investigated the performance of the transport system with averaged density, speed, and flow on link. We also analysed the dynamic of the traffic system on expressway network at different demand levels. The simulation results show that the models are feasible and effective and the variable speed limits strategy can successfully alleviate the traffic congestion in some extent. The operational efficiency of the transportation system is greatly improved. Shu-Bin Li, Bai-Bai Fu, and Wen-Xiu Dang Copyright © 2014 Shu-Bin Li et al. All rights reserved. Bifurcation Analysis of a Delayed Predator-Prey Model with Holling Type III Functional Response and Predator Harvesting Mon, 03 Mar 2014 12:15:26 +0000 This paper tries to highlight a delayed prey-predator model with Holling type III functional response and harvesting to predator species. In this context, we have discussed local stability of the equilibria, and the occurrence of Hopf bifurcation of the system is examined by considering the harvesting effort as bifurcation parameter along with the influences of harvesting effort of the system when time delay is zero. Direction of Hopf bifurcation and the stability of bifurcating periodic solutions are also studied by applying the normal form theory and the center manifold theorem. Lastly some numerical simulations are carried out to draw for the validity of the theoretical results. Uttam Das and T. K. Kar Copyright © 2014 Uttam Das and T. K. Kar. All rights reserved. Frequency Response of an Impacting Lap Joint Thu, 27 Feb 2014 10:05:21 +0000 Damage or failure of a relatively small component can precipitate the failure of a larger part of a structure. The behavior of damaged or worn joints is of particular concern. To address contact/impact in structural systems, this work models a structural lap joint from first principles. A beam with four stops and gaps is used to simulate a loose or damaged lap joint, which also represents designed manufacturing clearances in mechanical systems. The goal is to generate frequency responses to identify the local shock effect due to impact. Spatial and temporal solutions are presented for an example case. Converged time histories were used to generate the impulse as a metric of frequency response. Facilitating mode contribution calculations, the metric of impulse proves to be an excellent indicator of complexities in the beam's motion due to excitation frequency. Noncontact regions, sticking motions, local extrema, grazing impacts, and aperiodicities are identifiable for specific operating parameters. These conditions indicate when harmful impact may occur that can ultimately cause local damage within a structure. Knowledge of dangerous operating conditions can better focus on inspection before propagation occurs. Amir M. Rahmani and Elizabeth K. Ervin Copyright © 2014 Amir M. Rahmani and Elizabeth K. Ervin. All rights reserved.