the generalization of equal peak method for delay coupled nonlinear system abstract the equal peak property based extension method to a delay coupled nonlinear system is studied in this paper a time delayed vibration absorber is proposed to realize the equal peak property for a nonlinear primary system firstly the mechanical model of the nonlinear primary system coupled with the time delayed vibration absorber is established and the optimization objective is proposed then four conditions to figure out the optimum delay coupled parameters for the equal peak property with the minimum resonance peak are carried out finally several case studies with different nonlinear terms are given the results show that the equal peak property can be realized by appropriate delay coupled parameters obtained by the optimization procedure besides by selecting the optimum delay coupled parameters the two resonance peaks can be suppressed to the minimum level the design for the time delayed vibration absorber by the proposed extension method can solve the bottleneck techniques for equal peak property in nonlinear primary systems under a wide range of excitation amplitude which are concerned in manufacturing and aerospace

the dynamics of repeated impacts with a sinusoidally vibrating table a deceptively simple difference equation is derived which approximately describes the motion of a small ball bouncing vertically on a massive sinusoidally vibrating plate in the case of perfect elastic impacts the equation reduces to the standard mapping which has been extensively studied by physicists in connection with the motions of particles constrained in potential wells it is shown that for sufficiently large excitation velocities and a coefficient of restitution close to one this deterministic dynamical system exhibits large families of irregular non periodic solutions in addition to the expected harmonic and subharmonic motions the physical significance of these and other chaotic motions which appear to occur frequently in non linear oscillations is discussed

effect of nonlinear impact damping on the frequency response of a torsional system with clearance in this article we examine a particular nonlinear impact damping model that has been well accepted by the scientific community first we consider the damping element with a linear spring and examine the nonlinear frequency response characteristics of a torsional system second the impact damping is examined along with the clearance nonlinearity including the backlash problem three semi analytical methods namely the describing function method multi term harmonic balance method and stochastic linearization method are utilized to investigate the effect of impact damping feasibility of such methods is confirmed by comparing predictions with results yielded by a numerical method the differences between impact damping and linear viscous damping mechanism are studied in terms of frequency responses time histories and the minimum number of harmonics required to simulate the behavior given sinusoidal excitations furthermore the effect of impact damping on sub and super harmonic responses and quasi periodic regimes are examined

finiteness of r equivalence groups of some adjoint classical groups of type d32 abstract let f be a field of characteristic different from 2 we construct families of adjoint groups g of type d 3 2 defined over f but not over k such that g f r is finite for various fields f which are finitely generated over their prime subfield we also construct families of examples of such groups g for which g f r z 2 z when f k t and k is almost arbitrary this gives the first examples of adjoint groups g which are not quasi split nor defined over a global field such that g f r is a non trivial finite group

cohomological invariants and r triviality of adjoint classical groups using a cohomological obstruction we construct examples of absolutely simple adjoint classical groups of type 2a n with n equivalent to 3 mod 4 c n or 1d n with n equivalent to 0 mod 4 which are not r trivial hence not stably rational

analysis and design of nonlinear resonances via singularity theory abstract bifurcation theory and continuation methods are well established tools for the analysis of nonlinear mechanical systems subject to periodic forcing we illustrate the added value and the complementary information provided by singularity theory with one distinguished parameter while tracking bifurcations reveals the qualitative changes in the behaviour tracking singularities reveals how structural changes are themselves organised in parameter space the complementarity of that information is demonstrated in the analysis of detached resonance curves in a two degree of freedom system

a going down principle for ample groupoids and the baum connes conjecture abstract we study a going down or restriction principle for ample groupoids and its applications the going down principle for locally compact groups was developed by chabert echterhoff and oyono oyono and allows to study certain functors that arise in the context of the topological k theory of a locally compact group in terms of their restrictions to compact subgroups we extend this principle to the class of ample hausdorff groupoids using le gall s groupoid equivariant version of kasparov s bivariant kk theory moreover we provide an application to the baum connes conjecture for ample groupoids which are strongly amenable at infinity this result in turn is then used to relate the baum connes conjecture for an ample groupoid group bundle which is strongly amenable at infinity to the baum connes conjecture for the fibres

isolated sub harmonic resonance branch in the frequency response of an oscillator with slight asymmetry in the clearance a family of isolated sub harmonic branches in nonlinear frequency response of piecewise linear system is examined in this paper given their peculiarity they could be easily overlooked in frequency response studies in numerical integration or laboratory experiments when the quasi static frequency sweeping technique is employed an increase in the viscous damping ratio could shrink the isolated branches and ultimately the sub harmonic resonance may vanish asymmetry does not appear to be the key factor that generates the isolated branches rather the relationship between the linear mean operating and transition point seems to dictate their occurrence

deformation of operator algebras by borel cocycles abstract assume that we are given a coaction of a locally compact group g on a c algebra a and a t valued borel 2 cocycle on g motivated by the approach of kasprzak to rieffel s deformation we define a deformation a of a among other properties of a we show that a k l 2 g is canonically isomorphic to a g g this together with a slight extension of a result of echterhoff et al implies that for groups satisfying the baum connes conjecture the k theory of a remains invariant under homotopies of

when is the cuntz krieger algebra of a higher rank graph approximately finite dimensional evans d g and sims a when is the cuntz krieger algebra of a higher rank graph approximately finite dimensional preprint arxiv 1112 4549v1

z stability of crossed products by strongly outer actions ii we consider a crossed product of a unital simple separable nuclear stably finite z stable c algebra a by a strongly outer cocycle action of a discrete countable amenable group under the assumption that a has finitely many extremal tracial states and is elementary amenable we show that the twisted crossed product c algebra is z stable as an application we also prove that all strongly outer cocycle actions of the klein bottle group on z are cocycle conjugate to each other this is the first classification result for actions of non abelian infinite groups on stably finite c algebras

the harmonic balance method with arc length continuation in rotor stator contact problems there are a variety of abnormal running conditions in rotating machinery which lead to rotor stator interaction dynamics which in turn can cause a rich mixture of effects associated with rub related phenomena these effects manifest themselves in the occurrence of multiple solutions for steady state vibration response scenarios including amplitude jumps during rotor acceleration and vibration responses at different multiple frequencies of excitation forces such as unbalance this paper describes a numerical algorithm based on the harmonic balance method to calculate the periodic response of a non linear system under periodic excitation the algorithm also calculates the stability of the periodic solutions found marks turning and bifurcation points and follows a solution branch over varying system parameters via arc length continuation

cyclic cohomology and chern connes pairing of some crossed product algebras abstract we compute the cyclic and hochschild cohomology groups for the algebras a a l g z 3 a a l g z 4 and a a l g z 6 we also compute the partial chern connes index table for each of these algebras

periodic solution finder for an impact oscillator with a drift in this paper an efficient semi analytical method is developed to compute periodic solutions for a new model of an impact oscillator with a drift which explains the progression mechanism in vibro impact systems and can be used to optimize their performance the method constructs a periodic response assuming that each period is comprised of a sequence of distinct phases for which analytical solutions are known for example a period may consist of the following sequential phases i contact with progression ii contact without progression iii no contact and iv contact without progression using this information a system of four piecewise linear first order differential equations is transformed to a system of non linear algebraic equations the method allows one to accurately predict a range of control parameters for which the best progression rates are obtained

low dimensional maps for piecewise smooth oscillators abstract dynamics of the piecewise smooth nonlinear oscillators is considered for which general methodology of reducing multidimensional flows to low dimensional maps is proposed this includes a definition of piecewise smooth oscillator and creation of a global iterative map providing an exact solution the global map is comprised of local maps which are constructed in the smooth sub regions of phase space to construct this low dimensional map it is proposed to monitor the points of intersections of a chosen boundary between smooth subspaces by a trajectory the dimension reduction is directly related to the dimension of the chosen boundary and the lower its dimension is the larger dimension reduction can be achieved full details are given for a drifting impact oscillator where the five dimensional flow is reduced to one dimensional 1d approximate analytical map first an exact two dimensional map has been formulated and analysed a further reduction to 1d approximate map is introduced and discussed standard nonlinear dynamic analysis reveals a complex behaviour ranging from periodic oscillations to chaos and co existence of multiple attractors accuracy of the constructed maps is examined by comparing with the exact solutions for a wide range of the system parameters

finite groups acting on higher dimensional noncommutative tori abstract for the canonical action of sl 2 z on 2 dimensional simple rotation algebras a it is known that if f is a finite subgroup of sl 2 z the crossed products a f are all af algebras in this paper we show that this is not the case for higher dimensional noncommutative tori more precisely we show that for each n 3 there exist noncommutative simple n dimensional tori a which admit canonical action of z n and for each odd n 7 with 2 n n 5 their crossed products a z n are not af with nonzero k 1 groups it is also shown that the only possible canonical action by a finite group on a 3 dimensional simple torus is the flip action by z 2 besides we discuss the canonical actions by finite groups z 5 z 8 z 10 and z 12 on the 4 dimensional torus of the form a a

examples of non rational varieties of adjoint groups let k be a field of characteristic 2 and k a separable closure of k s we say that an algebraic variety xrk is stably k rational if there exist two m n m n w x affine spaces a a and a k rational map a x f a merkurjev 9 k k gave a criterion of stable k rationality for the adjoint classical groups with absolute rank f 3 which covers the case of the variety pso q for any quadratic form qrk of rank f 6 this criterion gives examples of field k and quadratic form q of rank 6 with non trivial signed discriminant such that the variety pso q is not stably k rational the main result of this paper is the following

period one motions of a mechanical oscillator with periodically time varying piecewise nonlinear stiffness the dynamic behavior of a piecewise nonlinear mechanical oscillator with parametric and external excitations is investigated the viscously damped single degree of freedom oscillator is subjected to a periodically time varying piecewise nonlinear restoring function defined by a clearance surrounded by continuously nonlinear quadratic and cubic regions typical applications represented by this oscillator are highlighted a multi term harmonic balance formulation is used in conjunction with discrete fourier transforms and a parametric continuation scheme to determine steady state period 1 motions of the system due to both parametric and external excitations the accuracy of the analytical solutions is demonstrated by comparing them to direct numerical integration solutions floquet theory is applied to determine the stability of the steady state harmonic balance solutions at the end detailed parametric studies are presented to quantify the combined influence of clearance quadratic and cubic nonlinearities within reasonable ranges of all other system parameters a comparison between time varying and time invariant systems is also provided to demonstrate the influence of the parametric and external excitations on a piecewise nonlinear system

non commutative spheres iii irrational rotations leta be the irrational rotation algebra i e thec algebra generated by two unitariesu v satisfyingvu e 2 i uv with irrational and consider the fixed point subalgebrab under the flip automorphismu u 1 v v 1 we prove thatb is an af algebra

dynamics of a piecewise non linear system subject to dual harmonic excitation using parametric continuation abstract the dynamic behavior of piecewise linear and or non linear vibratory systems subject to a single harmonic excitation has been recently analyzed by using a one or multi term harmonic balance or galerkin s method piecewise linear techniques analog simulation and direct numerical integration digital simulation instead this paper proposes to utilize the technique of parametriccontinuationto study the steady state response and global dynamics of a two degree of freedom piecewise non linear system with backlash or multi valued springs and impact damping the physical system is under the influence of a mean load and is subject to a dual harmonic external excitation where the second frequency is either twice or three times the fundamental excitation frequency the effects of various parameters such as impact damping mean and alternating loads the piecewise stiffness ratios and the relative phase between the excitation harmonics on the system response are thoroughly examined system or excitation parameter regimes that exhibit sub harmonic super harmonic quasi periodic and chaotic solutions are obtained efficiently and systematically by using the proposed scheme this investigation also clarifies the differences between viscous and non linear impact damping models which have been proposed earlier in the literature for studying clearance non linearities limited experimental data validate our modelling strategy finally selected predictions from this technique match very well with a multi term harmonic balance method and with direct numerical integration wherever applicable

the harmonic balance method for bifurcation analysis of large scale nonlinear mechanical systems abstract the harmonic balance hb method is widely used in the literature for analyzing the periodic solutions of nonlinear mechanical systems the objective of this paper is to exploit the method for bifurcation analysis i e for the detection and tracking of bifurcations of nonlinear systems to this end an algorithm that combines the computation of the floquet exponents with bordering techniques is developed a new procedure for the tracking of neimark sacker bifurcations that exploits the properties of eigenvalue derivatives is also proposed the hb method is demonstrated using numerical experiments of a spacecraft structure that possesses a nonlinear vibration isolation device

frequency response characteristics of a multi degree of freedom system with clearances abstract in an earlier study the frequency response characteristics of a single degree of freedom system with a clearance non linearity were studied the current study an extension of the earlier work is concerned with the frequency response characteristics of a multi degree of freedom system with clearances the method of harmonic balance is used to develop approximate analytical solutions of the undamped equations of motion of a multi degree of freedom system composed of three coupled non linear oscillators for primary resonances and a harmonic excitation general formulations are presented which can be used to study both the existence and the stability of the solutions these general formulations are used to discuss a number of modal spacing and modal coupling issues an analysis methodology for multi degree of freedom systems is introduced and illustrated by two special but practical cases a strongly non linear system and a weakly non linear system the results of the analysis of the special cases are validated by using analog simulation it is shown that an analysis of the special cases of the general multi degree of freedom non linear formulation can provide not only an improved understanding of the dynamic behavior of non linear systems but also can be used as the basis for the development of simplified approximate solutions the limitations of the current study and areas for further research are discussed

crossed products byc0 x actions abstract suppose thatghas a representation grouph thatgab g g g is compactly generated and thatais ac algebra for which the complete regularization of prim a is a locally compact hausdorff spacex in a previous article we showed that there is a bijection z f between the collection of exterior equivalence classes of locally inner actions g aut a and the collection of principalgab bundlesz together with continuous functionsf x h2 g t in this paper we compute the crossed productsa gin terms of the dataz f andc h

k theory of equivariant quantization abstract using an equivariant version of connes thom isomorphism we prove that equivariant k theory is invariant under strict deformation quantization for a compact lie group action

degree three unramified cohomology of adjoint semisimple groups we compute degree 3 unramified cohomology of adjoint semisimple group new classes of non rational adjoint semisimple groups are found

near elastic vibro impact analysis by discontinuous transformations and averaging we show how near elastic vibro impact problems linear or nonlinear in between impacts can be conveniently analyzed by a discontinuity reducing transformation of variables combined with an extended averaging procedure a general technique for this is presented and illustrated by calculating transient or stationary motions for different harmonic oscillators with stops or clearances and self excited friction oscillators with stops or clearances first and second order analytical predictions are derived and shown to agree to estimated accuracy with results of numerical simulation

two dimensional map for impact oscillator with drift an impact oscillator with a drift is considered using a simple co ordinates transformation the bounded oscillations are separated from the drift in general the dynamic state of the system is fully described by four variables time relative displacement p and velocity y of the mass and relative displacement of the slider top q however this number can be reduced by two if the beginning of the progression phase is monitored in this paper a new two dimensional numerical map is developed and its dynamics is discussed

hochschild and cyclic homology of the crossed product of algebraic irrational rotational algebra by finite subgroups of sl 2 z abstract let sl 2 z be a finite subgroup acting on the irrational rotational algebra a via the restriction of the canonical action of sl 2 z consider the crossed product algebra a alg obtained by the restriction of the action on the algebraic irrational rotational algebra in this paper we prove many results on the homology group of the crossed product algebra a alg we also analyse the case of the smooth crossed product algebra a and calculate some of its homology groups

uncovering inner detached resonance curves in coupled oscillators with nonlinearity abstract detached resonance curves have been predicted in multi degree of freedom nonlinear oscillators when subject to harmonic excitation they appear as isolated loops of solutions in the main continuous frequency response curve and their detection may thus be hidden by numerical or experimental analysis in this paper an analytical approach is adopted to predict their appearance expressions for the amplitude frequency equations and bifurcation curves are derived for a two degree of freedom system with cubic stiffness nonlinearity and the effect of the system parameters is investigated the interest is specifically towards the occurrence of closed detached curves appearing inside the main continuous frequency response curve which may lead to a dramatic reduction of the amplitude of the system response both cases of hardening and softening stiffness characteristics are considered the analytical findings are validated by numerical analysis

an algorithm for response and stability of large order non linear systems application to rotor systems abstract a numerical algorithm to calculate the periodic response stability and bifurcations of a periodically excited non conservative multi degree of freedom mdof system with strong local non linearities is presented first the given large order system is reduced using a fixed interface component mode synthesis procedure cms in which the degrees of freedom associated with non linear elements are retained in the physical co ordinates while all others whose number far exceeds the number of non linear dof are transformed to modal co ordinates and reduced using real mode cms a shooting and continuation method is then applied to the reduced system to solve for the periodic response floquet stability theory is used to calculate stability and bifurcations of the periodic response the algorithm is applied to study the response to imbalance stability and bifurcations of a 24 dof flexible rotor supported on journal bearings the results indicate that the proposed algorithm though approximate can yield very accurate information about dynamic behavior of large order non linear systems even with few numbers of retained component modes the algorithm which imposes less demand on computer time and memory is believed to be of considerable potential in analyzing a variety of practical problems

super and sub harmonic response calculations for a torsional system with clearance nonlinearity using the harmonic balance method abstract this article presents a new multi term harmonic balance method hbm for nonlinear frequency response calculations of a torsional sub system containing a clearance type nonlinearity the ability of the simplified subsystem to capture the salient behavior of the larger system is verified by the comparison of results to experimental data unlike previous analytical and numerical methods the proposed hbm includes adaptive arc length continuation and stability calculation capabilities to find periodic solutions in multi valued nonlinear frequency response regimes as well as to improve convergence essential steps of the proposed hbm calculations are introduced and it is validated by comparing time and frequency domain predictions with those yielded by numerical solutions experimental studies or analog simulations for several examples then nonlinear frequency response characteristics of an oscillator with clearance nonlinearity are examined with focus on super and sub harmonics we also explore some issues that are not fully resolved in the literature for instance the effect of mean operating point is examined for 0 and 0 18 0 25 cases where is the stiffness ratio of the piecewise linear elastic function in addition the number of harmonic terms that must be included in the hbm response calculations given sinusoidal excitation has been investigated finally some simple analytical predictions for super and sub harmonic resonances are presented

global view on a nonlinear oscillator subject to time delayed feedback control we apply time delayed feedback control to stabilise unstable periodic orbits of an amplitude phase oscillator the control acts on both the amplitude and the frequency of the oscillator and we show how the phase of the control signal influences the dynamics of the oscillator a comprehensive bifurcation analysis in terms of the control phase and the control strength reveals large stability regions of the target periodic orbit as well as an increasing number of unstable periodic orbits caused by the time delay of the feedback loop our results provide insight into the global features of time delayed control schemes

quantum hall effect on the hyperbolic plane in this paper we study both the continuous model and the discrete model of the quantum hall effect qhe on the hyperbolic plane the hall conductivity is identified as a geometric invariant associated to an imprimitivity algebra of observables we define a twisted analogue of the kasparov map which enables us to use the pairing between k theory and cyclic cohomology theory to identify this geometric invariant with a topological index thereby proving the integrality of the hall conductivity in this case

isomorphism and morita equivalence classes for crossed products of irrational rotation algebras by cyclic subgroups of sl2 z abstract let be irrational numbers and a b be matrices in s l 2 z of infinite order we compute the k theory of the crossed product a a z and show that a a z and a b z are isomorphic if and only if mod z and i a 1 is matrix equivalent to i b 1 combining this result and an explicit construction of equivariant bimodules we show that a a z and a b z are morita equivalent if and only if and are in the same g l 2 z orbit and i a 1 is matrix equivalent to i b 1 finally we determine the morita equivalence class of a f for any finite subgroup f of s l 2 z

an equivariant brauer group and actions of groups onc algebras suppose that g t is a second countable locally compact trans formation group given by a homomorphism l g homeo t and that a is a separable continuous trace c algebra with spectrum t an action g aut a is said to cover l if the induced action of g on t coincides with the original one we prove that the set brg t of morita equivalence classes of such systems forms a group with multiplication given by the balanced tensor product a b a c0 t b and we refer to brg t as the equivariant brauer group we give a detailed analysis of the structure of brg t in terms of the moore cohomology of the group g and the integral cohomology of the space t using this we can characterize the stable continuous trace c algebras with spectrum t which admit actions covering l in particular we prove that if g r then every stable continuous trace c algebra admits an essentially unique action covering l thereby substantially improving results of raeburn and rosenberg

crossed products by finite group actions with the rokhlin property we prove that a number of classes of separable unital c algebras are closed under crossed products by finite group actions with the rokhlin property including a ai algebras at algebras and related classes characterized by direct limit decompositions using semiprojective building blocks b simple unital ah algebras with slow dimension growth and real rank zero c c algebras with real rank zero or stable rank one d simple c algebras for which the order on projections is determined by traces e c algebras whose quotients all satisfy the universal coefficient theorem f c algebras with a unique tracial state along the way we give a systematic treatment of the derivation of direct limit decompositions from local approximation conditions by homomorphic images which are not necessarily injective

the tracial rokhlin property for actions of finite groups on c algebras we define tracial analogs of the rokhlin property for actions of finite groups approximate representability of actions of finite abelian groups and approximate innerness we prove the following four analogs of related nontracial results bullet the crossed product of an infinite dimensional simple separable unital c algebra with tracial rank zero by an action of a finite group with the tracial rokhlin property again has tracial rank zero bullet an outer action of a finite abelian group on an infinite dimensional simple separable unital c algebra has the tracial rokhlin property if and only if its dual is tracially approximately representable and is tracially approximately representable if and only if its dual has the tracial rokhlin property bullet if a strongly tracially approximately inner action of a finite cyclic group on an infinite dimensional simple separable unital c algebra has the tracial rokhlin property then it is tracially approximately representable bullet an automorphism of an infinite dimensional simple separable unital c algebra a with tracial rank zero is tracially approximately inner if and only if it is the identity on k 0 a mod infinitesimals

on the structure of twisted group c algebras we first give general structural results for the twisted group algebras c g of a locally compact group g with large abelian subgroups in particular we use a theorem of williams to realise c g as the sections of a c bundle whose fibres are twisted group algebras of smaller groups and then give criteria for the simplicity of these algebras next we use a device of rosenberg to show that when is a discrete subgroup of a solvable lie group g the k groups k c are isomorphic to certain twisted k groups k g of the homogeneous space g and we discuss how the twisting class h 3 g z depends on the cocycle

non periodic motion caused by grazing incidence in an impact oscillator the motion of a single degree of freedom periodically forced oscillator subjected to a rigid amplitude constraint is considered using analytical methods the singularities caused by grazing impact are studied it is shown that as a stable periodic orbit comes to grazing impact under the control of a single parameter a special type of bifurcation occurs the motion after the bifurcation may be non periodic and a criterion for this based on orientation and eigenvalues is given

the cancellation theorem for projective modules over irrational rotation c algebras on montre que deux modules projectifs sur a qui sont isomorphes de facon stable sont en fait isomorphes

threshold control strategy for a non smooth filippov ecosystem with group defense abstract a non smooth filippov ecosystem with group defense is proposed to investigate the effects of threshold and intermittent control strategy for ipm the proposed model has been analyzed theoretically using the qualitative analysis techniques related to filippov non smooth systems in the first place in particular the existence and stability of equilibria are discussed for the sliding mode dynamics through which it can be shown that the real equilibrium and pseudo equilibrium can coexist after that some relevant topics such as sliding mode bifurcation boundary focus bifurcation grazing bifurcation crossing bifurcation and buckling bifurcation are investigated using numerical analysis these complex sliding bifurcations reveal that the proposed filippov system admits the coexistence of multi attractors including equilibrium and crossing cycles thus indicating that there exists a close relationship between the intermittent control strategy and the initial densities of both populations similarly the global stability properties of real equilibrium and pseudo equilibrium of subsystems show that the intermittent control strategy can effectively control the pests under the prescribed threshold which is the aim of the ipm strategy

e theory and kk theory for groups which act properly and isometrically on hilbert space a good deal of research in c algebra k theory in recent years has been devoted to the baum connes conjecture 3 which proposes a formula for the k theory of group c algebras that blends group homology with the representation theory of compact subgroups the conjecture has brought c algebra theory into close contact with manifold theory through its obvious similarity to the borel conjecture of surgery theory 9 31 and its links with the theory of positive scalar curvature 27 in addition there are points of contact with harmonic analysis particularly the tempered representation theory of semisimple groups although the proper relation between the baum connes conjecture and representation theory is not well understood the conjecture is most easily formulated for groups which are discrete and torsion free for such a group g there is a natural homomorphism

non linear frequency response characteristics of an impact pair abstract the method of harmonic balance is used to develop approximate analytical solutions to the equations of motion of a single impact pair including a general discussion of the existence and stability of these solutions non linear frequency response characteristics are obtained for a single frequency excitation and primary resonance no subharmonic or superharmonic response and the results are validated using an analog computer simulation it has been found that the use of digital simulation numerical integration may lead to inaccurate results over certain frequency ranges it is also shown that although the shapes of the force displacement relationship for clearance non linearity and the classic cubic non linearity are similar the resulting non linear frequency response curves can be quite different various issues related to the clearance non linearity problem are discussed

forced vibrations of a torsional oscillator with coulomb friction under a periodically varying normal load the forced vibration response of a single degree of freedom torsional system with coulomb friction under a periodically varying normal load is studied first an enhanced multi term harmonic balance method is developed to calculate nonlinear responses directly in frequency domain this should be in general applicable to periodically varying nonlinear systems second a pulse width modulated normal load is approximated by a truncated fourier series with a reasonable number of harmonic components and utilized for case studies finally the effects of duty ratio on nonlinear frequency responses are examined