•A novel demodulation method with a reference signal is developed.•A finite element model is developed for validating the demodulation method.•Undamped mode shapes of a beam under random excitation ...were estimated.•A baseline-free damage detection method is used for processing estimated mode shapes.•The location of a damage in the beam was accurately estimated.
A novel demodulation method with a reference signal is developed for operational modal analysis and damage detection of a beam structure under random excitation. The novel demodulation method can process measurements of the beam by a continuously scanning laser Doppler vibrometer (CSLDV) system and measurements of a reference point on the beam by a single-point laser Doppler vibrometer to estimate its modal parameters, such as damped natural frequencies and undamped mode shapes. Damped natural frequencies of the beam are estimated from fast Fourier transforms of measurements of the CSLDV system. A cross-correlation function between a measurement of the CSLDV system and a measurement of a single-point laser Doppler vibrometer is calculated, and the cross-correlation function is multiplied by a sinusoidal signal whose frequency is an estimated damped natural frequency of the beam. The processed cross-correlation function is filtered by a low-pass filter to obtain the undamped mode shape of the beam that corresponds to the estimated damped natural frequency of the beam. Smooth polynomials are used to fit estimated undamped mode shapes, which can be considered as undamped mode shapes of an undamaged beam. Curvatures of estimated undamped mode shapes and polynomials are compared by curvature damage indices to determine the location of a damage in the beam. The novel demodulation method with a reference signal is investigated for baseline-free damage detection from both finite element simulation and experiment. Modal parameters of a finite element model of the damaged beam and a damaged beam specimen, which are under random excitation, are successfully estimated, and locations of damages in the beam model and beam specimen are accurately determined.
•A Ramanujan subspace projection (RSP) method is proposed for harmonic removal.•The RSP method can extract weak harmonic components and is robust to noise.•The RSP method is computationally ...efficient.•Combining RSP and SSI achieves modal identification under harmonic excitation.•Experimental and field test data confirm the effectiveness of the proposed method.
The presence of deterministic harmonic excitation, such as that induced by rotating machinery, violates the classical operational modal analysis (OMA) assumption that the system output is strictly ergodic. This paper proves that the presence of harmonic excitation has no effect on the identification of structural modes except in the case where some of the harmonic excitation frequencies are close to the structural frequencies. Therefore, the harmonic component must be removed from the mixed random and harmonic system output before further processing. This paper proposes a Ramanujan subspace projection (RSP) method for harmonic removal, which is realized by projecting the raw system output onto the complex conjugate division (CCD) of the Ramanujan subspace. The novelty of this study is that it reveals the relationship between the frequencies defined in the period and frequency domains, allowing the RSP method to directly extract the harmonic component from the specific CCD without any frequency domain analysis. In addition, an energy indicator is proposed to select the underlying CCDs with the most robust harmonic feature. Using the indicator, one only needs to project the raw system output onto a subset of the CCDs rather than all of them, thereby significantly reducing the computational effort. After removing the harmonic components from the raw output, the remainder can be fed into the covariance-driven stochastic subspace identification (Cov-SSI) method for OMA. The numerical, experimental and field test results show that the proposed RSP method is not only resistant to random noise but also capable of precisely extracting the weak harmonic component from the raw output with less computation. Furthermore, the modal parameters of the structures subjected to mixed random and harmonic excitation can be accurately identified by combining the Cov-SSI and RSP methods.
The frequent use of bridges in high-speed railway lines greatly increases the probability that trains are running on bridges when earthquakes occur. This paper investigates the random vibrations of a ...high-speed train traversing a slab track on a continuous girder bridge subjected to track irregularities and traveling seismic waves by the pseudo-excitation method (PEM). To derive the equations of motion of the train–slab track–bridge interaction system, the multibody dynamics and finite element method models are used for the train and the track and bridge, respectively. By assuming track irregularities to be fully coherent random excitations with time lags between different wheels and seismic accelerations to be uniformly modulated, non-stationary random excitations with time lags between different foundations, the random load vectors of the equations of motion are transformed into a series of deterministic pseudo-excitations based on PEM and the wheel–rail contact relationship. A computer code is developed to obtain the time-dependent random responses of the entire system. As a case study, the random vibration characteristics of an ICE-3 high-speed train traversing a seven-span continuous girder bridge simultaneously excited by track irregularities and traveling seismic waves are analyzed. The influence of train speed and seismic wave propagation velocity on the random vibration characteristics of the bridge and train are discussed.
The actions of wind and wave have a great influence on the ship rolling motion, which may cause chaotic situation even capsizing. Stochastic bifurcation and chaos for a class of ships rolling motion ...in longitudinal waves under non-smooth perturbation and random excitation, i.e., the effects of wind and wave, is studied by analytical and numerical methods. The stationary probability density function (SPDF) for rolling motion is obtained through the stochastic averaging method as well as stochastic phenomenological (P) bifurcation is analysed by the qualitative change of it. The parameter conditions for chaos are strictly derived through Melnikov method and random Melnikov method, respectively. Chaotic regions and characteristics of systems parameters are illustrated and discussed in detail. In addition, taking the maritime patrol ship as an example, the analytical results as well as the effects of parameter excitation and noise on chaos are verified and analysed by relevant numerical simulations. These results demonstrate that changing parameter excitation amplitude or noise intensity can induce or suppress chaos.
•Dynamical system for a class of ships rolling motion in longitudinal waves is constructed by the realistic environment of ship navigation.•Stochastic bifurcation and chaos of this new system are studied under non-smooth perturbation and random excitation.•Stochastic phenomenological (P) bifurcation is analysed by stochastic averaging method.•Chaotic dynamics with or without random excitation is investigated by classic Melnikov method and random Melnikov method.
This work addresses the influence of nonlinearities in energy harvesting from a piezomagnetoelastic structure subjected to random vibrations. Nonlinear equations of motion that describe the ...electromechanical system are given along with theoretical simulations. The numerical analysis presents a comparison between the voltage provided from a linear, nonlinear bistable and nonlinear monostable systems due to random vibration. Experimental performance of the generator exhibits qualitative agreement with the theory, showing an enhancement of piezoelectric power generation in a bistable system when it vibrates around both stable equilibrium points. A relationship between variations in the excitation and a bistable system response is established from numerical simulations, defining a region of enhanced power generation when compared to the linear and nonlinear monostable cases.
•Bistable piezomagnetoelastic generator subjected to random excitations is analyzed.•Performance is enhanced when system oscillates around all stable equilibrium points.•Numerical and experimental approaches show good qualitative agreement.•A relationship between the variance of excitation and potential energy is defined.•A desired region, where the performance of bistable system is enhanced, is defined.
This paper provides a novel approach for identifying the process damping directly from chatter-free milling tests. First, power spectrum density matrix of cutter's deflections is theoretically ...derived by introducing transfer function and random excitation force, and the spectral decomposition of the power spectrum density matrix is formulated as an explicit function of modal parameters. Then, exponential attenuation method is adopted to extract the damping ratios from the inverse Fourier transformation result of the decomposed form. Finally, tangential and radial ploughing force coefficients, which are utilized to characterize process damping, are simultaneously calculated based on energy balance principle. Besides, experimental setup consisting of displacement sensors is specially designed to measure the cutter's deflections, which are further used to calculate the power spectrum density required in the above identification procedure. It is experimentally proven that the accuracy of chatter stability limits in milling process is improved when the proposed process damping model is considered.
•Process damping is directly identified from chatter-free milling tests based on operational modal analysis.•Power spectrum density matrix of cutter's deflections is analytically derived as an explicit function of modal parameters.•Experimental setup suitable for measuring the cutter's deflections is designed.•Effectiveness of the proposed process damping model is verified by chatter experiments.
•The damper optimized is the rotational inertia double tuned mass damper (RIDTMD).•The RIDTMD contains a physical mass and a rotational mass provided by an inerter.•For each main mass ratio, there is ...a particular optimum RIDTMD rotational mass ratio.•The RIDTMD provides more effective control than a TMD with the same main mass ratio.
The rotational inertial double tuned mass damper (RIDTMD) is a type of passive mass damper which includes a physical mass as well as a rotational mass. This rotational mass is produced by an inerter which is capable of providing large effective mass utilizing very little physical mass. By selecting the proper design parameters, the RIDTMD show promise at more effective response reduction of underlying primary systems in comparison to conventional tuned mass dampers (TMDs). However, when the primary system is subjected to random loads, the previously considered optimum design values for harmonic excitation are not effective. This motivates an investigation to determine the exact analytical optimum solution for selecting the stiffness and damping design values of RIDTMD when the primary structure is subjected to random force and base excitation. In this paper, an exact optimization solution procedure is presented with the goal of finding the optimum design values of the RIDTMD when mitigating the response of a structure subjected to random force and base excitation. Utilizing the obtained optimum design values, the effectiveness of the RIDTMD is also studied in comparison to conventional TMDs. The results of this study show that the RIDTMD with optimized stiffness and damping values outperforms the optimized conventional TMD; however, the degree of its increased effectiveness in reducing the main mass response is reliant upon the selection of appropriate pairs of secondary and rotational mass.
•A mathematical model of an ice-accreted rod vibrating in an air flow is presented.•A combined deterministic periodic and random excitation is supposed.•The stationary response PDF is investigated ...and its stochastic stability is assessed.
The paper presents a mathematical Single-Degree-of-Freedom model of a cable with ice accretion vibrating in an air flow. It follows an experimental investigation of several aeroelastic models in a wind tunnel. The analysis of the experimental data is very complicated because a number of structural and stream characteristics mutually interact. Distinction between deterministic and random response components is only possible using a theoretical solution. The vibrational movement of the models used can be expressed by van der Pol-Duffing type equations. The aeroelastic excitation that is due to the air flow is modeled as an additive process consisting of a deterministic periodic part and random components. The paper investigates several particular configuration parameter settings for a non-white Gaussian random part of an excitation process and characterizes corresponding response properties. The Fokker-Planck equation is constructed for the random part of the response, and its semi-analytical solution in exponential form is expressed using a probability potential. Partial amplitudes of a harmonic approximation of the response are determined using the stochastic averaging strategy. The existence of a stationary probability distribution of the response is investigated, and its stochastic stability is assessed. Open problems and further research steps are outlined.
•A novel and efficient RBDO method is proposed for structures under random excitation.•The mapping between the operator norm and reliability index is introduced.•Probability constraints can be ...transformed into deterministic constraints through a mapping function.•The proposed method demonstrates good accuracy and efficiency.
Reliability-based design optimization (RBDO) can fulfill both reliability and economic requirements by considering the stochastic properties of structure and excitation. However, the computational efficiency of this optimization is hindered by the nested loops involved in reliability analysis and optimization processes. In order to overcome this limitation, a novel method is proposed for structures subjected to random excitation, which is based on the mapping between operator norm and reliability index. This approach necessitates effectuating the transformation of the optimization objective from reliability indexes to operator norms with a small number of samples, thereby eliminating the laborious process of nested loops. It can effectively solve design optimization problems with reliability constraints, particularly for structures with explicit structural response under random excitation. Four examples are presented to demonstrate the effectiveness and applicability of the proposed method.
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