In this study, vibration analysis of a cantilever pipe conveying fluid under distributed random excitation was performed using stochastic approach. The equation of motion was first discretized by ...means of the Galerkin method. Next, the classic flutter analysis of the pipe conveying fluid was performed in absence of random excitation. Then, the random load was taken into account as a white noise excitation. Spectral density of response and response variance were calculated versus the velocity of internal flow in the pipe. The velocity of the maximum of the response variance in case of white noise excitation was regarded as flutter speed. The effects of viscoelastic dissipation, mass ratio and damping ratio of surrounding environment were investigated for the pipe under random excitation and results showed a good agreement with other studies. The spectral density of response was used to obtain the flutter frequency. Random time history and probability density function were exploited to study the pipe’s random behavior near the flutter speed. This novel approach for pipe conveying fluid was also used to investigate all possible flutter speeds. The results provided a better understanding of dynamical behavior of pipes conveying fluid under random excitation.
When a bistable energy harvester (BEH) is driven by weak random excitation, its harvesting efficiency will decrease due to the seldom occurrence of interwell motion. To overcome this defect, we ...developed an improved bistable energy harvester (IBEH) from BEH by adding a small magnet at the middle of two fixed magnets. It is proved that the attractive force originated from the additional magnet can pull down the potential barrier and shallow the potential well, but still keep the middle position of beam unstable. This can make jumping between potential wells easier. Thus IBEH can realize snap-through even at fairly weak excitation. The magnetic potential energy is given and the electromechanical equations are derived. Then the harvesting performance of IBEH under random excitation is studied. Validation experiments are designed and carried out. Comparisons prove that IBEH is preferable to BEH in harvesting random energy and can give out a high output voltage even at weak excitation. The size of additional magnet can be optimized to reach the best performance of IBEH.
•An improved BEH is developed by adding an additional magnet to reduce the barrier.•High efficiency of harvesting weak random vibration energy are realized by IBEH.•The additional magnet can be optimized to maximum the power for a certain intensity.
In this paper the optimal parameters of a dynamic vibration absorber (DVA) with negative stiffness is analytically studied. The analytical solution is obtained by Laplace transform method when the ...primary system is subjected to harmonic excitation. The research shows there are still two fixed points independent of the absorber damping in the amplitude-frequency curve of the primary system when the system contains negative stiffness. Then the optimum frequency ratio and optimum damping ratio are respectively obtained based on the fixed-point theory. A new strategy is proposed to obtain the optimum negative stiffness ratio and make the system remain stable at the same time. At last the control performance of the presented DVA is compared with those of three existing typical DVAs, which were presented by Den Hartog, Ren and Sims respectively. The comparison results in harmonic and random excitation show that the presented DVA in this paper could not only reduce the peak value of the amplitude-frequency curve of the primary system significantly, but also broaden the efficient frequency range of vibration mitigation.
•A DVA with negative stiffness is presented.•The optimal parameters of the DVA are analytically obtained.•The design method for the negative stiffness is determined.•The excellent performances of the DVA are illustrated.
•Node-based meshless model for stochastic thermal vibration of plates is developed.•Accurate prediction of the stochastic dynamics of the laminated quadrilateral plates is achieved.•Remarkable effect ...of laminated parameters and thermal factor on the vibration behaviors is revealed.
This paper presents a node-based meshless model for investigating the stationary/non-stationary stochastic thermal response characteristics of laminated arbitrary quadrilateral plates excited by various random loads. The thermo-elastic theory is incorporated into Hamilton's principle for deriving the dynamic governing formulas of the arbitrary quadrilateral plate. The displacement variables of plate structure are approximated by two-dimensional Chebyshev meshless shape functions, which is combined with multipoint mapping theory to discretize the system equations. After that, the stochastic dynamic response solutions of quadrilateral plates considering different boundary cases are generated by introducing a pseudo excitation methodology (PEM). The applicability and predictive accuracy of the present formulation to thermal vibration behaviors of quadrilateral plates are elucidated by means of carrying out convergence clarification and sufficient comparative studies between the calculated results as well as reference solutions from available literature. Also, the effects of several main factors including laminated parameters, thermal effects, excitation loads, etc. on free vibration and stationary/non-stationary response properties of laminated quadrilateral plates are revealed, which may serve as benchmark solutions for evaluating the correctness of other analytical or numerical methods.
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•A unified framework of static/dynamic reliability analysis is established based on direct probability integral method (DPIM).•New formula to determine smoothing parameter of Dirac function is ...suggested.•Two DPIM-based approaches for dynamic reliability analysis are proposed.•Example of nonlinear dynamic structure indicates superiority of unified framework.
Generally, the static and dynamic reliabilities of structures are addressed separately in the existing methods except the computationally expensive stochastic sampling-based approaches. This study establishes a unified framework of reliability analysis for static and dynamic structures based on the direct probability integral method (DPIM). Firstly, the probability density integral equations (PDIEs) of performance functions for static and dynamic structures are presented based on the principle of probability conservation. The DPIM decouples the physical mapping (i.e., performance function) of structure and PDIE, and involves the partition of probability space and the smoothing of Dirac delta function. This study proposes a new adaptive formula of smoothing parameter based on kernel density estimation. Then, the improved DPIM is utilized to obtain the probability density function (PDF) of performance functions by solving the corresponding representative values and the PDIE successively. Furthermore, the reliability of static structure is calculated by integrating the PDF of performance function within safety domain. To overcome the difficulty of evaluating first passage dynamic reliability, the two approaches, namely the DPIM-based absorbing condition (DPIM-AC) and the DPIM-based extreme value distribution (DPIM-EVD), are also proposed. Finally, three engineering examples with stochastic parameters and random excitation indicate the desired efficiency and accuracy of the established framework for unified reliability analysis. Specifically, the challenging issue of dynamic reliability assessment for nonlinear structural system is attacked based on DPIM rather than Monte Carlo simulation or other sampling-based method. The proposed method is beneficial for propagation analysis of aleatory or/and epistemic uncertainties, as well as for stochastic model updating.
•Energy-based optimal design and performance evaluation of TMDI-equipped BIS.•Quantification of seismic energy dissipation trade-off between BIS and TMDI.•Optimal TMDI design charts on the inertial ...plane for performance-based BIS design.•Assessment of colored frequency content excitation on the performance of TMDI.•Wavelet-based interpretation performance assessment of TMDI subject to GMs.
In this paper, the concept of an ideal grounded linear inerter, endowing supplemental inertia to passive linear tuned mass-dampers (TMDs) through its inertance property without increasing the TMD mass, is considered to reduce lateral displacement demands in base isolated structural systems (BISs). Optimal tuned mass-damper-inerter (TMDI) design parameters are numerically determined to maximize energy dissipation by the TMDI under stationary white noise support excitation. Performance of these optimally designed TMDI-equipped BISs is assessed for stationary white and colored noise excitations as well as for four recorded earthquake acceleration ground motions (GMs) with different non-stationary frequency content. It is found that for fixed mass ratio the inclusion of the grounded inerter reduces significantly secondary mass displacement and stroke for all considered excitations while it improves appreciably BIS displacement demands except for the particular case of a near-fault accelerogram characterized by early arrival of a high-energy low-frequency pulse as captured in its wavelet spectrogram. More importantly, it leads further to reductions to BIS acceleration demands with the exception of colored noise excitation for which an insignificant increase is noted. The positive effects of the inerter saturate with increasing inertance and BIS damping ratio demonstrating that small inertance values are more effective in vibration suppression of BISs with low inherent damping. Overall, it is recommended to combine low damping isolation layers with large inertance and low secondary mass TMDIs.
This paper investigates the energy-efficiency design of adaptive control for active suspension systems with a bioinspired nonlinearity approach. To this aim, a bioinspired dynamics-based adaptive ...tracking control is proposed for nonlinear suspension systems. In many existing techniques, one important effort is used for canceling vibration energy transmitted by suspension inherent nonlinearity to improve ride comfort. Unlike existing methods, the proposed approach takes full advantage of beneficial nonlinear stiffness and damping characteristics inspired by the limb motion dynamics of biological systems to achieve advantageous nonlinear suspension properties with potentially less energy consumption. The stability analysis of the desired bioinspired nonlinear dynamics is conducted within the Lyapunov framework. Theoretical analysis and simulation results reveal that the proposed bioinspired nonlinear dynamics-based adaptive controller has a significant impact on the amount of energy consumption, considering the same basic control method and random excitation of road irregularity for a similar ride comfort performance.
•A novel compact rotary MR damper with variable stiffness and variable damping characteristics was designed and prototyped for the seat suspension.•The nonlinear stiffness control scheme can avoid ...the end-stop impact and dissipate vibration energy.•The no-jerk skyhook damping control scheme can reduce the vibration amplitude.•The vibration attenuation performance of the seat suspension was largely improved by the VSVD rotary MR damper.
Long-term vibration poses a threat to drivers’ health and affects their ride performance. Furthermore, large-magnitude vibration and sudden shocks may even result in end-stop impacts, raising the drivers’ injury risk. To reduce the vibration and avoid end-top impacts, this paper presents an innovative seat suspension installed with variable stiffness and variable damping (VSVD) rotary magnetorheological (MR) dampers. At first, a novel compact VSVD rotary MR damper was designed and prototyped for the suspension, making the suspension’s stiffness and damping controllable. Then, with two identical VSVD MR dampers were installed, the prototyped seat suspension was characterised by an MTS test frame to verify its capabilities of variable stiffness and damping. A control strategy consisting of a nonlinear stiffness control and a no-jerk skyhook damping control was also designed. Finally, the vibration attenuation performance of the seat suspension was numerically and experimentally evaluated under three vibration excitations, i.e., harmonic excitation, bump excitation, and random excitation. Both numerical and experimental results indicate that the vibration control performance of the seat suspension can be significantly improved by the VSVD rotary MR dampers.
•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 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.
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