Improvement of the semi-analytical method, based on Hamilton's principle and spectral analysis, for determination of the geometrically non-linear response of thin straight structures. Part III: steady state periodic forced response of rectangular plates

In Parts I and II of this series of papers, a practical simple “multi-mode theory”, based on the linearization of the non-linear algebraic equations, written on the modal basis, in the neighbourhood of each resonance, has been developed for beams and fully clamped rectangular plates.¹ Simple explicit formulae have been derived, which allowed, via the so-called first formulation, direct calculation of the basic function contributions to the first three non-linear mode shapes of clamped-clamped and clamped-simply supported beams, and the two first non-linear mode shapes of FCRP. Also, in Part I of this series of papers, this approach has been successively extended, in order to determine the amplitude-dependent deflection shapes associated with the non-linear steady state periodic forced response² of clamped-clamped beams, excited by a concentrated or a distributed harmonic force in the neighbourhood of the first resonance.This new approach has been applied in the present work to obtain the NLSSPFR formulation for FCRP, SSRP, and CCCSSRP, leading in each case to a non-linear system of coupled differential equations, which may be considered as a multi-dimensional form of the well-known Duffing equation. The single-mode assumption, and the harmonic balance method, have been used for both harmonic concentrated and distributed excitation forces, leading to one-dimensional non-linear frequency response functions of the plates considered. Comparisons have been made between the curves based on these functions, and the results available in the literature, showing a reasonable agreement, for finite but relatively small vibration amplitudes. A more accurate estimation of the FCRP non-linear frequency response functions has been obtained by the extension of the improved version of the semi-analytical model developed in Part I for the NLSSPFR of beams, to the case of FCRP, leading to explicit analytical expressions for the “multi-dimensional non-linear frequency response function”, depending on the forcing level, and the amplitude of the response induced in the range considered for the excitation frequency.     

VIBRATION-BASED DAMAGE IDENTIFICATION USING RECONSTRUCTED FRFS IN COMPOSITE STRUCTURES

This work aims to establish a vibration-based damage identification method for fiber-reinforced laminated composites and their sandwich construction. This new on-line structural damage identification technique uses the structural dynamic system reconstruction method exploiting the frequency response functions (FRFs) of a damaged structure. To verify the effectiveness of this damage identification method, the frequency responses obtained by vibration testing of fatigue-damaged laminated composites and honeycomb sandwich beams with debonding are examined according to the extent of the damage via the fatigue-damage load cycle for laminated composites, and via the debonding extent for honeycomb sandwich beams. The changes of the peaks and valley of the FRFs according to the debonding extent and the fatigue load cycles are examined, and the area changes in the FRFs are also discussed as the damage index. The residual FRFs or the difference between intact and damaged FRFs are newly defined for application of the on-line damage identification method. Finally, the delamination extent for the sandwich beams and the fatigue damage level for the laminated composites can be easily identified in terms of the changes in natural frequencies and damping ratios of the reconstructed FRFs for these damaged composite structures.     

Structural damage assessment in a cantilever beam with a breathing crack using higher order frequency response functions

Vibration measurements offer an effective, inexpensive and fast means of non-destructive testing of structures and various engineering components. There are mainly two approaches to crack detection through vibration testing; open crack model with emphasis on changes in modal parameters and secondly, the breathing crack model focusing on nonlinear response characteristics. The open crack model based on linear response characteristics can identify the crack only at an advanced stage. Researchers have shown that a structure with a breathing crack behaves more like a nonlinear system, similar to that of a bilinear oscillator and the nonlinear response characteristics can very well be investigated to identify the presence of the crack. In the present study, the bilinear restoring force is approximated by a polynomial series and a nonlinear dynamic model of the cracked structure is developed using higher order frequency response functions. The effect of crack severity on the response harmonic amplitudes are investigated and a new procedure is suggested whereby the crack severity can be estimated through measurement of the first and second harmonic amplitudes.     

FRF-based structural damage detection of controlled buildings with podium structures: Experimental investigation

How to use control devices to enhance system identification and damage detection in relation to a structure that requires both vibration control and structural health monitoring is an interesting yet practical topic. In this study, the possibility of using the added stiffness provided by control devices and frequency response functions (FRFs) to detect damage in a building complex was explored experimentally. Scale models of a 12-storey main building and a 3-storey podium structure were built to represent a building complex. Given that the connection between the main building and the podium structure is most susceptible to damage, damage to the building complex was experimentally simulated by changing the connection stiffness. To simulate the added stiffness provided by a semi-active friction damper, a steel circular ring was designed and used to add the related stiffness to the building complex. By varying the connection stiffness using an eccentric wheel excitation system and by adding or not adding the circular ring, eight cases were investigated and eight sets of FRFs were measured. The experimental results were used to detect damage (changes in connection stiffness) using a recently proposed FRF-based damage detection method. The experimental results showed that the FRF-based damage detection method could satisfactorily locate and quantify damage.     

Structural damage detection of controlled building structures using frequency response functions

If a building structure requires both a vibration control system and a health monitoring system, the integration of the two systems will be cost-effective and beneficial. One of the key problems of this integrated system is how to use control devices to enhance system identification and damage detection. This paper presents a new method for system identification and damage detection of controlled building structures equipped with semi-active friction dampers through model updating based on frequency response functions. The two states of the building are first created by adding a known stiffness using semi-active friction dampers. A scheme based on the frequency response functions of the two states of the building is then presented to identify stiffness parameters of structural members in consideration of structural connectivity and transformation information. By applying the proposed model updating scheme to the damaged building, a damage detection scheme is proposed based on the identified stiffness parameters of structural members of both the original and damaged buildings. The feasibility of the proposed schemes is finally demonstrated through a detailed numerical investigation in terms of an example building, in which the effects of measurement noise and excitation conditions are discussed. The numerical results clearly show that the proposed method can locate and quantify damage satisfactorily even though measurement noise is taken into consideration.     

Experiments and numerical results on non-linear vibrations of an impacting Hertzian contact. Part 1: harmonic excitation

The purpose of this paper is to investigate experimental and numerical dynamic responses of a preloaded vibro-impacting Hertzian contact under sinusoidal excitation. Dynamic response under random excitation is analyzed in the second part of this paper. A test rig is built corresponding to a double sphere-plane contact preloaded by the weight of a moving cylinder. Typical response curves are obtained for several input levels. Time traces and spectral contents are explored. Both amplitude and phase of harmonics of the dynamic response are investigated.Linearized resonance frequency and damping ratio are identified from the almost linear behaviour under very small input amplitude. Increasing the external input amplitude, the softening behaviour induced by Hertzian non-linear stiffness is clearly demonstrated. The resonance peak is confined to a narrow frequency range. Jump discontinuities are identified for both amplitude and phase responses. The forced response spectrum exhibits several harmonics because of a non-linear Hertzian restoring force. Numerical simulations show a very good agreement with experimental results.For higher input amplitudes, the system exhibits vibro-impacts. Loss of contact non-linearity clearly dominates the dynamic behaviour of the vibro-impacting contact and leads to a wide frequency range softening resonance. The spectral content of the response is dominated by both the first and the second harmonics. Evolution of the experimental downward jump frequency vs. input amplitude allows the identification of the non-linear damping law during intermittent contact. Simulations of the vibro-impacting Hertzian contact are performed using a shooting method and show a very good agreement with experimental results.     

Generalised modal stability of inclined cables subjected to support excitations

Parametric excitation is of concern for cables such as on cable-stayed bridges, whereby small amplitude end motion can lead to large, potentially damaging, cable vibrations. Previous identification of the stability boundaries for the onset of such vibrations has considered only a single mode of the cable, ignoring non-linear coupling between modes, or has been limited to special cases. Here multiple cable modes in both planes are included, with support excitation close to any natural frequency. Cable inclination, sag, parametric and direct excitation and nonlinearities, including modal coupling, are included. The only significant limitation is that the sag is small. The method of scaling and averaging is used to find the steady-state amplitude of the directly excited mode and, in the presence of this response, to define stability boundaries of other modes excited parametrically or through nonlinear modal coupling. It is found that the directly excited response significantly modifies the stability boundaries compared to previous simplified solutions. The analysis is validated by a series of experimental tests, which also identified another nonlinear mechanism which caused significant cable vibrations at twice the excitation frequency in certain conditions. This new mechanism is explained through a refinement of the analysis.     

A simplified quasi-Gaussian random process model based on non-linearity

The non-Gaussian response of a simple polynomial non-linear element to Gaussian excitation is investigated, and correlation functions and spectral densities up to the fourth order are established in terms of the second order correlation function and spectral density of the excitation. Suitable choice of excitation and non-linearity parameters then permits the response to be used, either in analysis as a well-described near-Gaussian random process, or as a good approximate model of any given near-Gaussian random process.     

Estimation of tensile force in tie-rods using a frequency-based identification method

A technique is developed to identify in-situ the tensile force in tie-rods which are used in ancient monumental masonry buildings to eliminate the lateral load exercised by the vaults and arcs. The technique is based on a frequency-based identification method that allows to minimize the measurement error and that is of simple execution. In particular, the first natural frequencies of the tie-rods are experimentally identified by measuring the frequency response functions (FRFs) with instrumented hammer excitation; four to six natural frequencies can be easily identified with a simple test. Then, a numerical model, based on the Rayleigh-Ritz method, is developed for the axially loaded tie-rod by using the Timoshenko beam theory retaining shear deformation and rotary inertia. Non-uniform section of the rod is considered since this is often the case for hand-made tie-rods in old buildings. The part of the tie-rod inserted inside the masonry wall is also modeled and a simple support is assumed at the extremities inside the walls. The constraints given to the part of the tie-rod inserted inside the masonry structure are assumed to be elastic foundations. The tensile force and the stiffness of the foundation are the unknowns. In some cases, the length of the rod inside the masonry wall can be also assumed as unknown. The numerical model is used to calculate the natural frequencies for a given set of unknowns. Then, a weighted difference between the calculated and identified natural frequencies is calculated and this difference is minimized in order to identify the unknowns, and in particular the tensile force. An estimation of the error in the identification of the force is given. The technique has been tested on five tie-rods at the ground floor of the famous castle of Fontanellato, Italy.     

Linearization of non-linear stochastically excited dynamic systems

A “second order” linearization method for non-linear stochastically excited dynamic systems is described. Second order probabilistic functions are used to evaluate the linearized stiffness or damping coefficients of the non-linear elements. The values of these coefficients are frequency dependent, in contrast to the nowadays generally used “first order” linearization methods. Principles of both “first order” and “second order” methods are discussed. So-called “linearization functions” of typical non-linearities greatly simplifying practical computations are introduced. The actual linearization procedure is discussed. A simple approximate criterion for the validity of the linearization is established.     

Estimation of the dynamical properties of polyurethane foam through use of Prony series

A system identification procedure is formulated for estimation of parameters associated with a dynamic model of a single-degree-of-freedom foam-mass system. The foam is modelled as a linear viscoelastic material, whose constitutive law is expressed by an exponential hereditary relaxation kernel. The identification procedure is based on modelling the free response of the system as a Prony series (sum of exponentials terms) and fitting this Prony series to the data. This estimated response model is then utilized to estimate the parameters in the system model based on an explicit solution of the model. The procedure is analyzed for its reliability under different sources of error and uncertainties, such as the presence of weak components and experimental noise, and some modifications are evaluated to improve the robustness of the procedure. Finally, the procedure is applied to experimental data to obtain relevant stiffness, viscous and viscoelastic parameters associated with the system. Variations in values of these parameters as a function of static compression are also investigated.     

USING THE CROSS-CORRELATION TECHNIQUE TO EXTRACT MODAL PARAMETERS ON RESPONSE-ONLY DATA

Modal parameter identification is used to identify those parameters of the model which describe the dynamic properties of a vibration system. Classical modal parameter extractions usually require measurements of both the input force and the resulting response in laboratory conditions. However, when large-scale operational structures are subjected to random and unmeasured forces such as wind, waves, or aerodynamics, modal parameters estimation must base itself on response-only data. Over the past years, many time-domain modal parameter identification techniques from output-only have been proposed. Among them, the natural excitation technique (NExT) has been a very powerful tool for the modal analysis of structures excited in operating environment. This issue reviews the theoretical development of natural excitation technique (NExT), which uses the cross-correlation functions of measured responses coupling with conventional time-domain parameter extraction under the assumption of white-noise random inputs. Then a frequency-domain poly reference modal identification scheme by coupling the cross-correlation technique with conventional frequency-domain poly reference modal parameter extraction is presented. It uses cross-power spectral density functions instead of frequency response functions and auto- and cross-correlation functions instead of impulse response functions to estimate modal parameters from response-only data. An experiment using an airplane model is performed to investigate the effectiveness of the cross-correlation technique coupled with frequency-domain poly reference modal identification scheme.     

White noise nonlinear system analysis in nuclear magnetic resonance spectroscopy

Nonlinear noise excitation in nuclear magnetic resonance is a form of nonlinear spectroscopy which exploits the nonlinear susceptibilities in a very direct way. The nonlinear susceptibilities are defined by perturbation theory in the frequency domain. In nonlinear system analysis, on the other hand, the system response is described by a Volterra series in the time domain. The kernels of the Volterra functionals carry the information about the system and are to be determined by experiment.The series expansion of a molecular, atomic or nuclear system response is derived in quantum mechanics by time dependent perturbation theory, leading to a Volterra series with time ordered, triangular kernels. The kernels are multi-dimensional products of decaying exponentials, which describe coherence decays of particular density matrix elements. The Fourier transforms of the triangular Volterra kernels are the susceptibilies, which are formally identical in NMR spectroscopy and nonlinear optical spectroscopy. The nonlinear susceptibilities are multi-dimensional spectra, which in NMR spectroscopy reveal the spin communication pathways. These are established by various forms of single quantum coherence connectivities, such as indirect coupling, chemical exchange, cross-relaxation, dipolar and quadrupolar coupling.If the functionals of the Volterra series are orthogonalized with respect to Gaussian white noise excitation, the Wiener series results. The Wiener kernels can be derived by multi-dimensional cross-correlation of the system response with different powers of the Gaussian white noise excitation.Cross-correlation of the transverse magnetization response to noise excitation in NMR leads to multi-dimensional time functions, the Fourier transforms of which closely resemble the nonlinear susceptibilities. The cross-correlation spectra differ from the susceptibilities in the governing Liouvillean and the dynamic density matrix, which are affected by saturation for continuous excitation. Cross-correlation spectra and susceptibilities converge for vanishing excitation power. Therefore the cross-correlation spectra are referred to as stochastic susceptibilities.In stochastic NMR spectroscopy only odd order susceptibilities exist for transverse magnetization. The first nonlinear order is the third, and the nonlinear spectral information is derived from the third order susceptibility. Higher order susceptibilities are not feasible to derive from experimental data. An important share of the nonlinear information is found on the six subdiagonal 2D cross-sections through the third order susceptibility. These cross-sections arise in three pairs, which carry distinct information, separated according to longitudinal magnetization and population effects, zero quantum coherences, and double quantum coherences.In practice a nonlinear 3D spectrum is computed from experimental data by an algorithm in the frequency domain, which yields access to selected regions in the 3D spectrum. This spectrum is the symmetrized stochastic third order susceptibility. All its sub-diagonal 2D cross-sections are equivalent. They are the average of the six different sub-diagonal 2D cross-sections through the asymmetric third order susceptibility.The stochastic excitation technique in NMR is characterized by several unique attributes. (1) There is no minimum time for a data acquisition cycle, so that, at the expense of signal-to-noise ratio, strong samples can be investigated faster with stochastic NMR than with pulsed FT NMR. (2) Stochastic excitation tests the sample extensively, and measures a maximum amount of information in a single experiment. This feature is of particular interest for investigation of short-lived samples and of samples with little a priori information. (3) An experiment with stochastic excitation is simple to perform, but the data processing is more complex than in FT spectroscopy. (4) The nonlinear information about spin communication pathways is derived for individual frequency regions only, which are identified in the stochastic ID spectrum. This information is located primarily on the sub-diagonal 2D cross-sections through the third order susceptibility. (5) Stochastic NMR spectra derived from random noise excitation are contaminated by systematic noise. In the sub-diagonal 2D cross-sections the noise is reduced by filtering and symmetrization during data processing. (6) Sub-diagonal 2D cross-sections are sensitive to experimental phase distortions in one direction only. They are readily adjusted in phase with the same parameters as the ID spectrum. (7) Stochastic multi-dimensional spectra can be computed at variable resolution from one and the same set of raw data.So far stochastic NMR spectroscopy is not applied routinely in analytical spectroscopy. More practical experience is needed to evaluate its merits in comparison with Fourier transform NMR.Stochastic excitation is distinguished from continuous wave and sparsely pulsed excitation by low input power in connection with large bandwidth. This important property cannot be exploited in high resolution NMR in liquids, because excitation power is not a restricting factor in this case. The situation is different in NMR imaging, where large field gradients require large bandwidths and the excitation power becomes a point of concern. For this reason stochastic RF excitation is being investigated in NMR imaging.The multi-dimensional cross-correlation functions obtained from random noise excitation generally are contaminated by systematic noise. The occurrence of systematic noise can be avoided if pseudo-random excitation is used in combination with a transformation of the system response to obtain the kernels. This technique is used successfully in Hadamard spectroscopy, where the linear Volterra kernel is the Hadamard transform of the linear response functional. Nonlinear transformations^(220,221) for retrieval of nonlinear kernels have not yet been realized in NMR spectroscopy.The cross-correlation technique underlying the data evaluation in stochastic nonlinear system analysis is equivalent to interferometry in optical spectroscopy. The Michelson interferometer is the most prominent optical correlator. The time resolution of the kernels derived by cross-correlation is determined by the inverse bandwidth of the excitation. With the Michelson interferometer a time resolution of 10⁻¹⁴ s is achieved in IR spectroscopy. Since the IR correlogramm is Fourier transformed for spectral analysis, the time resolution cannot be exploited otherwise. For analysis of fast time dependent processes a two-dimensional interferometer should be constructed, which performs a 2D cross-correlation of the system response to two in general different noise inputs. One input pumps the time dependent process, the other is used to investigate the time dependence spectroscopically. This technique is introduced by the name of ‘two-dimensional interferometry’. It uses low excitation power, but provides high time resolution at large response energy. Related work is pursued in nonlinear optical spectroscopy with incoherent excitation. In this area the use of broad band lasers is investigated for generation of echoes and for correlation based measurements of relaxation times.     

A SEMI-ANALYTICAL APPROACH TO THE NON-LINEAR DYNAMIC RESPONSE PROBLEM OF BEAMS AT LARGE VIBRATION AMPLITUDES, PART II: MULTIMODE APPROACH TO THE STEADY STATE FORCED PERIODIC RESPONSE

The semi-analytical approach to the non-linear dynamic response of beams based on multimode analysis has been presented in Part I of this series of papers (Azrar et al., 1999 Journal of Sound and Vibration224, 183-207 [1]). The mathematical formulation of the problem and single mode analysis have been studied. The objective of this paper is to take advantage of applying this semi-analytical approach to the large amplitude forced vibrations of beams. Various types of excitation forces such as harmonic distributed and concentrated loads are considered. The governing equation of motion is obtained and can be considered as a multi-dimensional form of the Duffing equation. Using the harmonic balance method, the equation of motion is converted into non-linear algebraic form. Techniques of solution based on iterative-incremental procedures are presented. The non-linear frequency and the non-linear modes are determined at large amplitudes of vibration. The basic function contribution coefficients to the displacement response for various beam boundary conditions are calculated. The percentage of participation for each mode in the response is presented in order to appraise the relation to higher modes contributing to the solution. Also, the percentage contributions of the higher modes to the bending moment near to the clamps are given, in order to determine accurately the error introduced in the non-linear bending stress estimated by different approximations. Solutions obtained in the jump phenomena region have been determined by a careful selection of the initial iteration at each frequency. The non-linear deflection shapes in various regions of the solution, the corresponding axial force ratios and the bending moments are presented in order to follow the behaviour of the beam at large vibration amplitudes. The numerical results obtained here for the non-linear forced response are compared with those from the linear theory, with available non-linear results, based on various approaches, and with the single mode analysis.     

FREQUENCY DOMAIN ARX MODEL AND MULTI-HARMONIC FRF ESTIMATORS FOR NON-LINEAR DYNAMIC SYSTEMS

Non-linear dynamic systems respond at frequencies other than the excitation frequency; however, standard frequency response function estimators for linear systems do not accommodate this harmonic distortion. A new multi-harmonic frequency response function estimator that utilizes discrete frequency models for non-linear systems is introduced here. The multi-harmonic estimator relates the frequency response at each frequency to the input and output spectra within a given frequency band in the same way that autoregressive exogenous input models relate inputs and outputs at particular samples in the time domain. Overdetermined, least-mean-squares calculations are used to minimize model error throughout a frequency band rather than at a single frequency as in the corresponding linear estimators. The resulting multi-harmonic frequency response function models are non-parametric (e.g., vary with amplitude) when linear functions are used and parametric when non-linear functions are used. A new sensitive indicator for experimentally characterizing non-linearity is introduced.     

Frequency domain analysis and identification of block-oriented nonlinear systems

Block-oriented nonlinear models including Wiener models, Hammerstein models and Wiener-Hammerstein models, etc. have been extensively applied in practice for system identification, signal processing and control. In this study, analytical frequency response functions including generalized frequency response functions (GFRFs) and nonlinear output spectrum of block-oriented nonlinear systems are developed, which can demonstrate clearly the relationship between frequency response functions and model parameters, and also the dependence of frequency response functions on the linear part of the model. The nonlinear part of these models can be a more general multivariate polynomial function. These fundamental results provide a significant insight into the analysis and design of block-oriented nonlinear systems. Effective algorithms are therefore proposed for the estimation of nonlinear output spectrum and for parametric or nonparametric identification of nonlinear systems. Compared with some existing frequency domain identification methods, the new estimation algorithms do not necessarily require model structure information, not need the invertibility of the nonlinearity and not restrict to harmonic inputs. Simulation examples are given to illustrate these new results.     

Damage localization in linear-form structures based on sensitivity investigation for principal component analysis

This paper addresses the problem of damage detection and localization in linear-form structures. Principal component analysis (PCA) is a popular technique for dynamic system investigation. The aim of the paper is to present a damage diagnosis method based on sensitivities of PCA results in the frequency domain. Starting from frequency response functions (FRFs) measured at different locations on the structure; PCA is performed to determine the main features of the signals. Sensitivities of principal directions obtained from PCA to structural parameters are then computed and inspected according to the location of sensors; their variation from the healthy state to the damaged state indicates damage locations. It is worth noting that damage localization is performed without the need of modal identification. Influences of some features as noise, choice of parameter and number of sensors are discussed. The efficiency and limitations of the proposed method are illustrated using numerical and real-world examples.     

Vibration based damage detection of a beam-type structure using noise suppression method

In this paper, a method is presented for the localisation of structural damage. The validation of the method is based on simulated data and experimental measurements. Due to measurement errors near resonances, the mode shapes extracted from the frequency response functions (FRFs) and hence the damage indices (DI) can contain many false peaks. The method presented in this paper uses this set of damage indices from each mode generated by the Gapped-Smoothing Method (GSM), and suppresses the noise by allowing only those peaks which show the location of the damage. This paper details the theory of the noise suppression method and the experimental results for a steel beam, damaged with two narrow slots at different locations. A noise addition process was applied to the simulated data in order to more realistically represent experimental measurements. The steel beam was modelled in ANSYS and harmonic analysis was used to obtain FRFs at different locations of the beam. The results were checked for different slot depths by adding 5–10% noise in the simulated results.     

MEASUREMENT AND ANALYSIS OF MODULATED DOUBLET MODE RESPONSE IN MOCK BLADED DISKS

The steady state response of spatially modulated doublet modes that occur in low count flexible bladed disks is investigated for the case in which the structure is driven by a harmonic travelling wave excitation source. Finite-element simulation and modal testing of prototypical bladed-disk structures demonstrate the presence of particular wavenumbers, beyond the base number of nodal diameters, which contaminate and distort the appearance of certain doublet modes. The manner in which the natural frequency and wavenumber content of such modes shift and split as functions of the number of blades and their span angle is discussed in the light of a companion perturbation analysis for rotationally periodic structures. Resonance conditions are established and verified through simultaneous measurements made with a spin test stand using sensors that are placed in the rotating (structure) and stationary (excitation) frames of reference. The travelling wave response components of a repeated frequency doublet mode are shown to propagate either in the same or opposite direction as the excitation source, depending on whether certain algebraic relationships between the excitation order, the base number of nodal diameters, and the contamination wavenumbers are satisfied. To the extent that such components can travel at different phase speeds and directions relative to one another, the placement of sensors on the structure can be optimized to best measure the response amplitude. Conversely, other placements can result in submaximal measurement of peak vibration amplitude over the structure.     

Broad band random excitation of a two-degree-of-freedom system with autoparametric coupling

The response of a two-degree-of-freedom system with autoparametric coupling under the action of broad band random excitation is investigated. The system corresponds to the autoparametric vibration absorber and is also typical of many common structural configurations. A method based upon the Markov vector approach, together with an approximate treatment of third and higher statistical moments, is used to derive a set of fourteen coupled non-linear equations for the first and second moments of the system responses. A numerical integration procedure is used to obtain quantitative results for the system mean and mean square responses over a range of system parameters.The results show that large random motions of the coupled system may occur when the internal detuning parameter is close to the principal internal resonance, and that these motions may give rise to a suppression effect on the random motions of the main system. A feature of the results is that under conditions of internal resonance the random motions are found to be quasi-stationary, with steady oscillatory terms in the response moments. This suggests the possibility of entrainment of regular harmonic responses by the system random motions.