Total Vibrational Energy Research Articles

Transmission characteristics of train-induced vibration in buildings based on wave propagation analysis

Various studies have focused on predicting, evaluating, and controlling train-induced building vibrations and radiated noise. This study aimed to clarify the theory of building vibration transmission by investigating the transmission characteristics of vibrations in buildings using wave propagation analysis. First, the building was modelled as a periodic structure, as each floor was similar in layout. Based on the wave propagation method, a periodic structure model was established in which the dynamic stiffness matrix of the cell structure could be derived using the spectral element method. Second, a response transfer function (RTF) database of 140 simplified typical residential buildings was established by wave analysis method. Finally, the transmission laws of train-induced vibration were studied. The results indicated that the vibration transmission laws were related to the mode shapes of structures and the participation of modes, which was affected by the spectral characteristics of the input excitation. With an increase in building height, the natural frequency decreased, which influenced the participation of each mode, and this would cause the transmission characteristics of the total vibration energy to change.

Rotational inertia-based tuned-mass-damper for controlling force transmission

Nowadays, the inerter device has become one of most popular mechanical devices in the vibration absorption field for both stationary and non-stationary mechanical structures. One of the problems commonly reported in the literature is the force transmission control in the foundations that support the machines, which is generally addressed by using either isolators or classic dynamic vibration absorbers (DVAs). However, the mechanical energy dissipation capability of these two solutions is still limited. This work focuses on improving the control performance for the conventional absorber using the inerter’s inertial mass amplification and negative stiffness effects. In order to fairly evaluate the control performance of the DVA based on grounded inerter, the and optimization criteria are proposed. When the dimensionless frequency response function (FRF) of the transmissibility is minimized at the resonant peaks, the criterion reveals an improvement of 29.74% in mitigating harmonic vibration. Finally, the total vibration energy transmitted to the foundation is minimized via criterion that provides an improvement of 33.03%.

A novel active tendon pendulum tuned mass damper and its application in transient vibration control

Enhancing the performance characteristics of Tuned Mass Dampers (TMDs), in particular extending their narrow frequency band of operation, has been the subject of many researches. In the adaptive type of TMDs, the device's properties can be adjusted gradually in response to a slight alteration in the excitation characteristics and physical properties of the main structure. A novel vibration absorbing system, namely Active Tendon Pendulum TMD (AT-PTMD), is proposed in the present study. The device consists of a simple pendulum whose horizontal movement is restricted by a tendon with an adjustable tensile force which is attached to the pendulum’s rod. The device is designed and formulated, and its efficiency is assessed numerically and experimentally. For this purpose, a 3-degree of freedom structure is considered. Scrutinizing the responses of the uncontrolled, passively controlled and actively controlled structure shows the appropriate performance of the AT-PTMD in comparison with the passive TMD system in transient vibration reduction, particularly in reducing the total vibrational energy of the structure's response. Considering the achieved results, the proposed AT-PTMD system is capable of reducing the maximum displacement and acceleration of the main structure up to 43% and 37%, respectively, which substantiates its excellence over the common passive vibration absorbing devices. The case study also proves that the utilized mechanism for adjusting the equivalent stiffness of AT-PTMD increases its operating frequency range by 105% compared to common TMDs. Unlike active structural control systems, the suggested approach will not induce structural instability in any operating mode.

Analytical solutions of the energy harvesting potential from vehicle vertical vibration based on statistical energy conservation

Two kinds of approaches have been proposed to harvest the vibrational energy from a running vehicle, namely using a regenerative damper to replace a traditional hydraulic suspension damper, or adding one or more dynamic vibration absorbers (DVAs). Extensive studies have been conducted by simulation or experiment on the first approach, whereas the studies on the second approach are very limited and even the energy harvesting potential is not clear. This paper tries to present an analytical solution, to uniformly reveal the energy harvesting potential from vehicle vertical vibration by both approaches, with a focus on approaches with DVAs. A generic quarter car model is proposed to represent various vibration energy harvesting configurations. With a newly enunciated statistical energy conservation property for linear vibration systems, the analytical solution of the energy harvesting potential is derived for the proposed model subjected to random excitation. It is illustrated from these analytical expressions that the total vehicle vertical vibration energy is not directly related to DVA configurations, and the vibration energy dissipated in the tire can be transferred to the absorbers. Literature results and newly implemented statistical analyses are presented to validate and demonstrate the derived solutions. Sensitivity analysis is then performed to reveal the effect of various vehicle parameters on the energy harvesting potential.

Radiative cooling rates of substituted PAH ions.

The unimolecular dissociation and infrared radiative cooling rates of cationic 1-hydroxypyrene (OHPyr+, C16H10O+) and 1-bromopyrene (BrPyr+, C16H9Br+) are measured using a cryogenic electrostatic ion beam storage ring. A novel numerical approach is developed to analyze the time dependence of the dissociation rate and to determine the absolute scaling of the radiative cooling rate coefficient. The model results show that radiative cooling competes with dissociation below the critical total vibrational energies Ec = 5.39(1)eV for OHPyr+ and 5.90(1) eV for BrPyr+. These critical energies and implications for radiative cooling dynamics are important for astrochemical models concerned with energy dissipation and molecular lifecycles. The methods presented extend the utility of storage ring experiments on astrophysically relevant ions.

Tracking control of moving flexible system by incorporation of feedback-based vibrational energy sink in model predictive control algorithm

This paper proposes a new approach towards the nonlinear problem of tracking control for mobile multivariable vibrational structure featuring an Euler-Bernoulli vibrational beam. The control scheme involves obtaining interactions between flexural and rigid motions of the multivariable continuum mechanics system with actuator force limitation both regarding domain and frequency bandwidth. To this end, the boundary control inputs are selected prioritizing two tasks, satisfying actuator limitations and obtaining minimum possible tracking error. The former is employed as hard constraint in model predictive control (MPC) scheme while the latter is considered as soft constraint. The control scheme is adjusted such that when actuator limits are exceeded, the soft constraints are relaxed to maintain stability. In order to provide smooth tracking, Euler-Bernoulli transverse vibration is attenuated by incorporating Feedback Vibrational Energy Sink (FVES) method in obtaining control law. Hence, actuators are manipulated such that total vibrational energy of flexible beam is damped without using passive or conventional active dampers. The accuracy of the proposed method has been verified via FEA-based simulations.

Hilbert spectrum analysis method of blast vibration signal based on HHT instantaneous phase optimization

Compared with wavelet analysis method of signal data, HHT (Hilbert-Huang Transform) method is widely used for the local signal data analysis in the time–frequency domain associated with adaptable capacity, which has been recognized as one of the most efficient method to address the non-stationary signals. In this study, Matlab software was used as the calculation code and field millisecond delay blasting data was collected as the research objects, the Hilbert time–frequency spectrum, marginal spectrum, instantaneous energy spectrum and Hilbert energy spectrum scatter were obtained for the signal IMF components under the standard instfreq.m function (as shown in Section 3.3) frequency modulation with the identified bandwidth of 1 Hz. The reasons of negative frequency for digital signals were discussed based on the theoretical analysis and the digitial signals were then summarized as two types of negative frequency according to the instantaneous phase characteristics. The field collected blasting vibration signals were used to illustrate the features of the negative frequency points such as large number, correlated relation between the signal amplitude extent and frequency band, and non-negligible of the total vibration energy. In addition, a theoretical equation was proposed for the instantaneous phase optimization function based on the HHT method, and a triple identification approach of millisecond time was proposed based on instantaneous phase optimization method. The process of Hilbert spectrum analysis based on HHT instantaneous phase optimization was implemented using Matlab, which was used to analyze Hilbert spectrum characteristics. Further, a theoretical comparison and analysis between the standard instfreq.m time–frequency modulation and the proposed phase optimized HHT spectrum were performed, and the results shows that the optimized HHT spectrum analysis improves the accuracy of time–frequency spectrum and Hilbert spectrum calculation, besides, the frequency domain recognition width is about 2∙r times of that from the standard solution. Finally, the phase optimization was used to analyze the amplitude spectrum, instantaneous velocity energy spectrum and 3D time–frequency seismic velocity energy spectrum features, application of HHT-based instantaneous phase optimization method is given for the accurate recognition application of multi-segment detonation millisecond time in underground blasting.

Performance-Based Compositive Passive Control Analysis of Multi-Tower Building with Chassis: Optimization of Kelvin-Voigt Dampers

The compositive passive control (CPC) method of “interlayer seismic isolation “plus “shock absorption between adjacent towers” was applied to a multi-tower building (MTB) with a large podium. The interaction between adjacent towers was used to reduce the structural response under seismic action. Based on the Clough–Penzien spectral seismic model, the extended state equation of random response of MTB was derived with the minimum total energy of structural vibration as the optimization control objective. By comparing the seismic scheme and interlayer seismic isolation scheme, the relationship between the control parameters of the connecting control device and the random response of the structure was discussed and analyzed, and the control effect of the composite passive control system under different control schemes was also studied from the perspective of seismic response time history and vibration cumulative energy time history. Through numerical analysis, it was proved that the damping coefficient of the Kelvin-Voigt model has a great influence on the mean square error of total vibration energy while the stiffness coefficient has a poor sensitivity to it. Under the optimization control objective, the connection control device was better arranged at the top of the structure. The control effect can reach 84.64% under the condition of random ground motion as input. The CPC method maintains the advantages of the interlayer seismic isolation scheme and reduces the defect of the response amplification caused by the interlayer isolation, which provides a reference for the follow-up study of the CPC method of MTB.

Hybrid Isolation Strategy for Seismically Isolated Multi-Tower Building with a Large Podium

The Compositive Passive Control method (CPC method) of “interlayer seismic isolation” + “shock absorption between adjacent towers” is applied to Multi-Tower Building (MTB) with a large podium. Taking the total vibration energy of the structure as the optimal control objective, the response expressions of a multi-DOF layer shear model and an equivalent single-DOF layer shear model are derived. The rationality of the equivalent model is demonstrated from the perspective of mode characteristics and time history response. Based on the Kanai–Tajimi spectral seismic motion model, the control effect and the optimal control parameters of the CPC method are studied. Compared with the conventional seismic scheme and the interlayer seismic isolation scheme, the influence of the CPC method on the structure natural vibration characteristics and dynamic response under different parameters of the connecting control device is discussed and analyzed. The numerical analysis proves that the CPC method provides a significant damping effect compared with the interlayer seismic isolation scheme. It maintains the advantages of the interlayer seismic isolation scheme and reduces the defect of the response amplification caused by the interlayer isolation. This analysis constitutes a good reference for the follow-up study of the CPC method of MTB.

The system loss factor in sound and vibration

In 1930, Kimball wrote a paper entitled "The damping factor in vibrations" that appeared in the journal Product Engineering. That paper proposed a damping factor based on the decrement of a vibrating system with exponential decay. Kimball showed that the proposed damping factor was proportional to the ratio of the energy dissipated per cycle to the total vibrational energy. The total vibrational energy was defined as the maximum potential energy over a cycle. Since that time, the definition of total vibrational energy has been more thoroughly examined because the total vibrational energy varies within a cycle due to damping. In this presentation, a new definition is proposed that defines the total vibrational energy as the temporal average of the total vibrational energy over a cycle. This definition has the advantage of reducing the system loss factor to the modal loss factor under certain limits. Since 1930, Kimball's damping factor has appeared in various forms under various names, the most common of which is the system loss factor. This presentation discusses these appearances in order to understand energy losses in dynamic systems caused by a wide array of physical mechanisms. The presentation concludes with a discussion of the system loss factor in present-day numerical simulations, highlighting its independence from eigenvalue information. [Work supported by ONR under Grant N00014-19-1-2100.]

Rethinking the description of water product in polyatomic OH/OD + XH (X ≡ D, Br, NH2 and GeH3) reactions: theory/experimental comparison

Davis’ group and Setser’s group using different experimental techniques measured water vibrational distribution for OH/OD + XH → H2O/HOD + X hydrogen abstraction reactions (X ≡ D, Br, NH2, GeH3). Theoretically, this issue has been studied by several groups: different potential energy surfaces (PESs) have been developed for each system, and quasi-classical trajectory (QCT) and quantum mechanics (QM) calculations have been performed. However, important experimental/theoretical controversies still exist. In the present work, we have revisited and performed new kinetics and dynamics calculations, comparing the theoretical and experimental results on the same footing. In general, theoretical results reproduce reasonably well experimental rate constants and total vibrational energy released to water, ~ 50–60%, although they underestimate water bending excitation. In the present work, we analyse different causes of this theory/experiment discrepancy and propose different mechanisms to explain the water bending excitation for diatom–diatom and polyatomic systems. Finally, we reflect on the ability of QCT and QM calculations to provide reasonable (although not quantitative) predictions for polyatomic reactions and observe that even using full-dimensional QM calculations on very accurate PESs, agreement with the experiment is far from that reached in the case of triatomic systems.

Design, construction and experimental performance of a nonlinear energy sink in mitigating multi-modal vibrations

To passively reduce the vibration energy in mechanical systems under shock load, nonlinear energy sinks (NES) can be locally attached, serving as vibration absorbers. The NES is an alternative to the standard tuned-mass-damper (TMD). While the TMD has a linear connecting spring, the NES has a nonlinear one. As a consequence, the NES has an energy dependent natural frequency. Because of this property, the NES is able to mitigate multi-modal transient vibrations sequentially from high to low frequency through a resonance capture cascade (RCC). This is a major advantage over the TMD, which is tuned only to reduce vibrations in a narrow frequency band, typically a single mode. Recently, three performance measures for the NES were derived, 1) The energy dissipation, the amount of total vibration energy dissipated by the NES. 2) The pumping time that estimates the time required for the NES to absorb a single frequency and 3) the cascading time, estimating the time the NES engages in RCC, absorbing all the modal frequencies. The novelty of these measures is that they only require the knowledge of the system's parameters. In this research, a complete implementation of a NES is presented, from design and practical realization, to verifying the performance measures experimentally. The performance measures thus allow to predict experimental performance of the NES without simulations or experiments, opposite to what literature does. The NES is constructed with a novel design methodology. This methodology allows for tailor made purely nonlinear stiffness. The NES is placed on a frame representing a scale model single-story building, to validate the single-mode performance. To obtain resonance cascading, a second story is added to obtain a two-mode dominant vibrating structure. The cascading time is predicted and confirmed by the experiments. The experiments agree well with both simulations and predictions regarding performance. This work validates the ease of use of the performance measures and their ability to predict experimental performance of a NES mitigating multi-modal vibrations.

Calculation of ionized chemically nonequilibrium flow around a reentry module

A method for calculating a hypersonic ionized flow at the entrance of the reentry module into the Earth’s atmosphere has been developed. The mathematical modeling of such a flow was performed using a system of equations, which includes the equations of the continuity of components, the equation of momentum, the equations of total energy, vibrational energy, and electron energy. Chemical reactions and ionization reactions were taken into account. The vibrational temperatures of diatomic molecules and electrons were calculated. Calculations were made for various flight altitudes (60-85 km) at free-stream speeds from the first to the second cosmic velocity. The results of computations according to the proposed methodology are in satisfactory agreement with the experimental data and the computation results of other authors.

Comparative Study of Tunnel Blast-Induced Vibration on Tunnel Surfaces and Inside Surrounding Rock

In tunnel blast applications, vibration monitors are typically placed on tunnel surfaces to measure the responses of rock to explosion loads for statutory compliance. Few publications in the open literature have focused on the differences between the blasting vibration on tunnel surfaces and inside the surrounding rock. During blasting excavation of the experimental tunnels in the China Jinping Underground Laboratory, velocity sensors were arranged both on the tunnel walls and inside the surrounding rock to monitor far-field vibrations. In this paper, the vibration characteristics on the tunnel surfaces and inside the surrounding rock are presented based on the recorded field data. Corresponding empirical formulae for peak particle velocity (PPV) attenuation and dominant frequency variation are derived from these data. A three-dimensional dynamic finite-element model is used to verify the site survey results. The field and numerical studies show that compared with the inside vibration, the tunnel surface vibration has a higher, more readily attenuated PPV and a lower frequency with a slower rate of decline in the dominant frequency. The mechanisms that cause the differences between the surface and inside vibration are discussed in detail. The tunnel surface vibration in the far field is dominated by surface waves, which occupy more than 75% of the total vibrational energy. For this reason, the results presented in this paper do not apply to vibration in the near field, where body waves are expected to be dominant.

Thermochemical Nonequilibrium Processes in Weakly Ionized Air Using Three-Temperature Models

Two three-temperature thermochemical nonequilibrium models were used to simulate the relaxation processes in weakly ionized air in compression and expansion regions. The three energy equations were the total energy, vibrational energy, and electron energy. The partition of electronic energy was investigated by considering it to be in equilibrium with the vibrational energy (free-electron model) or electron energy (electron–electronic model). Several zero-dimensional simulations were completed that demonstrated the potential of a three-temperature model to capture additional physics of the nonequilibrium processes above that of the legacy two-temperature model. The electron–electronic model consistently predicted, as expected, the electron temperature to be the last to equilibrate and for there to be significant electron nonequilibrium in all cases considered. However, the utility of the free-electron model to increase the fidelity of a simulation above that predicted by the two-temperature model was shown to be limited. Additionally, two vibrational–electron energy exchange relaxation times for the molecule were investigated; the resulting nonequilibrium processes were relatively insensitive to the use of a particular model.

A theoretical explanation of RbBH4’s fractionally occupied ground-state phase and the reorientational motion of the [BH4]− group

In this work, a pseudo-structure model is adopted to describe the fractionally occupied phase of RbBH4 at low temperatures. The fractionally occupied cubic ground state with Fm3m symmetry can be explained as a superposition and average of three well-defined pseudo-structures with P43m, F43m and P42/nmc symmetries. First, both mechanical and dynamical stability of these pseudo-structures are supported by the calculated elastic constants and phonon spectra, respectively. By comparing the electronic structure, elastic properties and thermodynamic properties of these well-defined pseudo-structures, it can be found that all pseudo-structures exhibit a certain degree of similarity. Second, the system is stabilized by charge transfer. Bader charge analysis of the pseudo-structures shows that charge transfer in RbBH4 contributes a constant shift in formation energy. Coulomb interaction energy and total electronic energy variations with the unit cell volume have been obtained. The results show that the larger the volume of the unit cell, the lower the difference of Coulomb interaction energy between the pseudo-structures P43m, F43m and P42/nmc. Third, the barrier energies calculated for paths of transitions between these pseudo-structures vary significantly with the volume. As the cell volume decreases from 512 to 216 Å3, the B–H covalent bonds are compressed from 1.242 to 1.208 Å. Meanwhile, the rotational barrier of [BH4]− anion increases rapidly, from 0.04 to 0.97 eV. Last, considering the temperature effect, the free energy and entropy contributions are calculated based on the rigid rotor harmonic oscillator approximation. The Gibbs free energy shows that at low temperature the P42/nmc structure is the preferred structure, and with increasing temperature, the P43m structure becomes the preferred structure. We found that the fractionally occupied phase of RbBH4 can be explained by the size of the Rb+ cation and a subtle balance between the Coulomb interaction energy, electronic total energy and thermal vibration energy.

Energy Transfer and Bond Dissociation in the o‐chlorotoluene + H2/Cl2/HCl Collisions

Energy flow and C–H and C–Cl bond dissociations in o‐chlorotoluene (OCT) in collisions with H2, Cl2, and HCl are studied using classical trajectory methods. The energy loss by the excited OCT is small, but it increases with increasing total vibrational energy content ET of OCT between 5000 cm−1 and 30000 cm−1. The energy loss is larger in OCT + HCl collision than in OCT + H2 or OCT + Cl2. The difference is mainly due the near‐resonant conditions between the vibration of the incident molecule and the C–H or C–Cl vibrations. Intermolecular energy transfer occurs through vibration–translation (V–T) and vibration–vibration (V–V) pathways. The intramolecular energy flow between C–H and C–Cl in highly excited OCT (60000–60300 cm−1) leads to bond dissociation. The probabilities of C–H and C–Cl dissociation are 10−5–10−1 and increase exponentially with increasing vibrational excitation of OCT. The probabilities are found to increase when the incident molecule becomes heavier.

Vibroacoustics behavior of self-similarly loaded sandwich structures

The reduction of structural vibrations and acoustic radiation is increasingly challenging due to lightweight material use driven by mass reduction, particularly in the aerospace industry. Trim panels are well-known materials with high acoustic transmission and radiation. This study combines semi-analytical modeling, numerical simulations and experiments on the vibroacoustic behavior of sandwich constructions locally overloaded by a pre-fractal mass distribution. The research originality lies in the overload distribution (a self-similar pattern inspired by the Cantor set) which is directly slotted within the honeycomb core, so that the structure load-bearing capability is not altered. As the mass effect spatially localizes the vibrations, the pre-fractal pattern focuses the effect of localization on some specific frequency band gaps, which reduces the total vibrational energy and thus the acoustic radiation. Before the extension to composite plates, simulations of a homogenized beam model have been computed to form a numerical modal database. Experiments have been conducted to compare and tune the mechanical model parameters. Satisfying agreement has been obtained between simulations and experiments. Finally, acoustic radiation simulations of self-similarly loaded structures have been conducted and radiation coefficients are expected to be weaker than for classical bending beams.

Analytically optimal parameters of fractional-order dynamic vibration absorber

In this paper the optimal parameters of the fractional-order Voigt type dynamic vibration absorber (DVA) are analytically studied for two cases, named as H∞ and H2 optimization criteria. At first the approximately analytical solution is obtained by the averaging method when the primary system is subjected to harmonic excitation. Then the optimal fractional coefficient and order are obtained based on H∞ optimization criterion, which is designed to minimize the maximum amplitude magnification factor of the primary system. Based on H2 optimization criterion, the optimal fractional parameters are obtained to reduce the total vibration energy of the primary system over the whole-frequency range. The comparisons of the approximate solutions with the numerical ones in the two cases are fulfilled, and the results verify that the approximately analytical solutions are correct and satisfactorily precise. At last the control performance of the fractional-order Voigt type DVA is compared with the classical integer-order counterpart, and it could be concluded that the fractional-order DVA has superiority in vibration engineering, and fractional-order element could replace the traditional damper and spring simultaneously in some cases.

Development of a control method for an electromagnetic semi-active suspension reclaiming energy with varying charge voltage in steps

A system of electromagnetic semi-active suspension reclaiming energy (ESASRE), with an novel control varying charge voltage in steps (CVCVIS) based optimal integrated controller, is newly proposed to improve ride comfort and energy reclaiming. The proposed CVCVIS is built by changing the number of battery packs. The dynamic model of the semiactive suspension reclaiming energy is established first, which fully accounts for the non-linear characteristics of the damping actuator reclaiming energy (DARE). The parameters of DARE are decided by a compromise between ride comfort and manufacturing cost, with consideration of installation convenience. A integrated control system for ESASRE includes a controller for calculating the real-time ideal control force based on optimal linear quadratic Gaussian (LQG) control and the other for calculating the number of charging batteries to obtain the real-time actual control force using the proposed quasilinear relation function. Performance comparisons are implemented using three suspension types: ESASRE, the passive suspension, and the ideal active suspension. The performance index of ESASRE is 19.8% lower than that of the passive suspension, and 3.82% higher than that of the active suspension. With ESASRE, the power flowing into the battery pack accounts for 77.72% of the total vibration energy absorbed by DARE.