Lateral Excitation Research Articles

Energy-Trapping Characteristics of Lateral Field Excited GdCOB Crystal Bulk Acoustic Wave Devices Based on Stepped Electrodes.

In this work, high-frequency forced vibrations of lateral field excitation (LFE) devices with stepped electrodes based on monoclinic crystals GdCOB are modeled, and the influence laws of the device parameters (the step number, size, and thickness of the stepped electrodes) on the energy-trapping effects of the device are revealed. The results show that the step number has a significant effect on the energy-trapping effect of the device: with the increase in the step number, the stronger energy-trapping effect of the device can be obtained; with the increase in the thickness difference of two layers of electrodes, the energy-trapping effect of the device becomes stronger; with the increase in the difference of the electrode radius, the energy-trapping effect of the device is enhanced gradually. The results of this work can provide an important theoretical basis for the design of stepped-electrode LFE resonators and sensors with high-quality factors based on monoclinic crystals.

Calibration of inverted pendulum pedestrian model for laterally oscillating bridges based on stepping behaviour

Despite the problem of lateral excitation of bridges by walking pedestrians being intensively studied for over two decades, there is currently no model which could quantitatively explain pedestrian-generated lateral forces. The most promising of the models proposed thus far, that is the rigid-leg inverted pendulum model (IPM) confined to the frontal plane, has been previously shown to qualitatively capture the main features of pedestrian behaviour on laterally oscillating ground, including kinematics and kinetics. However, to make the model suitable for engineering applications, it needs be reconciled with observations. To this end, a dataset collected from pedestrians walking on a laterally-oscillating instrumented treadmill is used to derive fundamental properties of pedestrian walking gait. Informed by these findings, a foot placement control law is proposed ensuring good match between the outputs of the IPM and empirical data in terms of the main components of pedestrian-generated lateral forces. That control law is then parametrised based on pedestrian anatomical and gait characteristics, thus generalising the calibrated IPM and making it suitable for use in a predictive manner. Simulations of the lateral bridge response to the lateral loading from a crowd of pedestrians with random parameters and interacting with a bridge are also conducted. It is shown that the calibrated IPM can generate self-excited forces in close agreement with those measured and that the generalised IPM, producing slightly conservative loading predictions on average, can serve in the assessment of lateral structural stability.

High-Throughput, Low Background, and Wide-Field Microscopy by Flat-Field Photobleaching Imprinting Microscopy.

Wide-field photobleaching imprinting microscopy (PIM) can improve fluorescence image contrast by cleverly exploiting the fluorophores' photobleaching properties. However, as conventional wide-field PIM commonly adopts Gaussian illumination with a nonuniform lateral fluence distribution, the field-of-view (FOV) and sampling density are largely reduced. In addition, the slow axial fluence gradient of Gaussian illumination limits the signal-to-background ratio (SBR) improvement and optical sectioning capability of PIM. Here, we present flat-field photobleaching imprinting microscopy (ffPIM) with a uniform lateral excitation fluence and sharp axial intensity gradient at the focal plane. ffPIM demonstrates low background, large FOV, and thin optical section. More importantly, compared to either conventional wide-field PIM or light-sheet microscopy, ffPIM shows much better balance for FOV, sampling density, SBR, and optical sectioning capability. The performance of ffPIM is characterized by simulation and resolving multiple cellular structures. Finally, ffPIM can be easily implemented to a standard commercial wide-field microscope and, thereby, allow general laboratories to benefit from this technique.

Road friction coefficient estimation under low longitudinal, lateral and combined excitation

On the way to autonomous driving more and more advanced driver assistance systems (ADASs) are developed to increase safety and comfort. These functions require additional quantified information about the environment, for example information about the current road condition, which a human driver would perceive intuitively. In this paper, a road condition estimation, described by a road friction coefficient, is developed using a second order divided differences filter in combination with estimates of the time varying parameters, namely the dynamic wheel radius and the tire stiffness. Using real measurement data of commercial vehicles, the estimation algorithm is compared to a static and less complex longitudinal friction coefficient estimator. The comparison shows good results for both estimators with differences at low excitation and during cornering maneuvers.

Effect of near-fault vertical seismic excitation on running safety of trains on high-speed railway bridges

The vertical component of near-fault earthquake motion is significant and may result in the derailment of trains that are running on bridges. In this study, a shaking table test of a train running on a high-speed railway bridge is performed based on a four-array shaking table and a 1:10 scale model of the train-track-bridge, and the corresponding numerical model is established. The reliability of the numerical model is first verified by test results. Then, with safety and comfort indexes as evaluation criteria, the test and numerical data are analyzed to reveal the near-fault vertical seismic effects on the running safety of trains on bridges. Finally, with the wheel-rail relative displacement of the test and derailment evaluation indexes of the numerical simulation, the near-fault vertical seismic effects on the derailment of trains running on bridges are analyzed to explore the derailment mechanism. The results show that near-fault vertical seismic excitation generally has a negative impact on the running safety of trains on bridges, with a maximum impact of 27% under selected seismic excitations. Furthermore, the negative impact increases with the vertical-to-horizontal peak acceleration ratio. The safety threshold of peak ground acceleration is often reduced due to vertical seismic effects, and the maximum reduction reaches 14.3% under Northridge-01 seismic excitation. In the case of a given lateral seismic excitation, vertical seismic excitation increases the maximum distance that the wheel-rail contact point moves laterally towards the wheel flange and further promotes flange climb derailment. Moreover, vertical seismic excitation reduces the minimum value of the wheel-rail vertical force and increases the possibility of jumping derailment.

Numerical and experimental studies on a new metallic-yielding pistonic damper based on pure-bending flexural yielding mechanism

In this study, the numerical and experimental investigations of a new passive control system recently introduced by the authors are discussed. This system is a metallic-yielding pistonic damper (MYP) in which the lateral excitation is transferred to a set of rectangular metallic-yielding plates under pure-bending loading conditions. The dissipator plates are placed into a steel surrounding rigid box which has only one sliding translational degree of freedom along its longitudinal axis. Based on this configuration, the damper performs as a piston-like axial element under cyclic motions. In this study first, the conceptual design and theoretical basis of the proposed system are presented and then, the details of the MYP numerical and experimental program are discussed. For this purpose, the MYP stability and performance are examined by conducting displacement-control cyclic tests on 12 physical specimens as well as finite element analyses on the corresponding numerical models. According to obtained results, the specimens experiencing ductility values from 15 to 38 during the tests, exhibit a broad range of ultimate capacity from 23 to 245 kN. Overall, the damper is found to have nonlinear behavior with consistent strain hardening and preserve its stability and performance during a large number of consecutive cyclic motions. Moreover, it was found that the MYP control system supplies high levels of damping ratios at low values of the lateral story drift due to its fuse-like performance.

Effect of Direction and Frequency of Skull Motion on Mechanical Vulnerability of the Human Brain.

Strain energy and kinetic energy in the human brain were estimated by magnetic resonance elastography (MRE) during harmonic excitation of the head, and compared to characterize the effect of loading direction and frequency on brain deformation. In brain MRE, shear waves are induced by external vibration of the skull and imaged by a modified MR imaging sequence; the resulting harmonic displacement fields are typically "inverted" to estimate mechanical properties, like stiffness or damping. However, measurements of tissue motion from MRE also illuminate key features of the response of the brain to skull loading. In this study, harmonic excitation was applied in two different directions and at five different frequencies from 20 to 90 Hz. Lateral loading induced primarily left-right head motion and rotation in the axial plane; occipital loading induced anterior-posterior head motion and rotation in the sagittal plane. The ratio of strain energy to kinetic energy (SE/KE) depended strongly on both direction and frequency. The ratio of SE/KE was approximately four times larger for lateral excitation than for occipital excitation and was largest at the lowest excitation frequencies studied. These results are consistent with clinical observations that suggest lateral impacts are more likely to cause injury than occipital or frontal impacts, and also with observations that the brain has low-frequency (∼10 Hz) natural modes of oscillation. The SE/KE ratio from brain MRE is potentially a simple and powerful dimensionless metric of brain vulnerability to deformation and injury.

Fundamental study on rapid detection of the insufficient lateral resistance of ballasted railway tracks by dynamic loading

To resume trains operation as soon as possible after disasters, it is necessary to quickly find out locations of ballasted railway with insufficient lateral ballast resistance. In this study, a new method was proposed to evaluate the lateral ballast resistance using dynamic lateral excitation. The dynamic method was performed on 1/9-scale ballasted railway models with ballast densities of 1.5 and 1.6 g/cm3. The simple harmonic excitation was generated from a pair of 20g flywheels, and the accelerations of the vibrator and the central sleeper were recorded by sensors attached on the central sleeper and the vibrator, respectively. Based on the obtained data sets, maximum accelerations as well as the maximum amplitudes of the lateral displacements of the vibrator and the central sleeper were analysed. It was found that the maximum accelerations of the vibrator were higher than those of the central sleepers. This was also true for the maximum amplitude of the lateral displacements. The ratio of the maximum amplitude of the lateral displacement of the central sleeper to that of the vibrator was evaluated. It was found that the amplitude ratio of the track model with the ballast density of 1.5 g/cm3 was higher than that with the ballast density of 1.6 g/cm3. This implies that the difference in the lateral ballast resistance owing to the difference in the ballast density may be detected based on the evaluation of the amplitude ratio.

A New Top-Mounted Shear-Hinge Structure Based on Modal Theory and Rubber-Pad Damping Theory

Steel-spring floating-slab tracks (SSFSTs) are widely used as efficient vibration-damping beds, and in China, they are mainly used in subways and municipal railroads. The shear hinge is an important component that improves the stability of the line, and field research has found that the top-mounted shear hinge (TMSH) undergoes varying degrees of damage, which indirectly affects the safety and stability of line operation. In this work, we studied the causes of damage to TMSHs, designed a new TMSH structure with a rubber-pad layer installed based on modal theory and rubber-pad vibration-damping theory, and proved that the new structure can reduce the occurrence of damage by comparing it with the original TMSH structure. The main aspects of this study are as follows: Firstly, the ultimate load capacity of the existing and new TMSH structures was checked by establishing a refined finite-element model. Then, modal analysis and frequency-response function analysis were carried out based on modal theory and frequency-response function theory to reveal the causes of TMSH damage and prove that the new structure can effectively delay damage. Finally, the modal and vibration patterns of the two structures were obtained via indoor hammering tests and compared with the simulation results. The results show that the two TMSH structures are in line with the strength requirements, and the existing TMSH damage mainly results from the resonance between its natural frequency and the high-excitation frequency of the floating slab under long-term cyclic train loading, causing high-frequency vibration fatigue damage. It is also demonstrated that the new structure can effectively reduce the natural frequency of the TMSH so that its value is located in the region of low vibration on the floating slab. The excitation vibration levels of the TMSH mounted on the curved section of the 4.8 m floating slab and the 3.6 m floating slab were reduced by 9 dB and at least 3 dB, respectively. After adding rubber pads located in the 400–3000 Hz floating-slab high-vibration-level region of the TMSH damage-prone parts, the amplitude reduction, including lateral excitation of damage-prone parts, resulted in a vibration amplitude reduction of more than 30 dB. However, the vertical excitation of the mid-end and rear-end bolts slightly increased their amplitudes, whereas the shear-rod amplitude was reduced by 48 dB, and the front-bolt amplitude was reduced by 5.28 dB. The natural frequency and vibration pattern obtained from the hammering test were consistent with the simulation results, and the reliability of our conclusions was verified from both experimental and simulation perspectives.

Analytical solution for the horizontal dynamic response of strength composite piles in fractional viscoelastic unsaturated ground

The analytical representation of the dynamic interaction between a strength composite (SC) pile and unsaturated soil under lateral excitations at the pile head is studied using three-dimensional continuum modelling. The fractional standard line solid (FSLS) model is utilized in the governing equation of unsaturated soil to characterize the flow-independent viscosity of the soil skeleton. Timoshenko beam theory is employed to describe the horizontal dynamic behaviour of SC piles composed of cement-soil mixing (CM) piles and precast high-strength concrete (PHC) pipe piles. A closed series form solution of the horizontal dynamic behaviour for an SC pile embedded in unsaturated soil under lateral excitation at the pile head is deduced theoretically. The solutions of the proposed model are compared with those captured from existing solutions. Finally, the effects of physical parameters in the SC pile-unsaturated soil system on the horizontal dynamic behaviour of the SC pile are evaluated with analytical examples and parametric study. The results indicate that the radius and elastic modulus of the SC pile have a critical influence on the horizontal dynamic behaviour of the SC pile, the FSLS model parameters are the key factors influencing the horizontal dynamic behaviour of the SC pile, and the horizontal dynamic behaviour of the SC pile varies with the change in liquid saturation of unsaturated soil. The research results provide theoretical references for the anti-vibration design and safe operation of SC piles.

D-type K+ current rules the function of electrically coupled neurons in a species-specific fashion.

Electrical synapses supported by gap junctions are known to form networks of electrically coupled neurons in many regions of the mammalian brain, where they play relevant functional roles. Yet, how electrical coupling supports sophisticated network operations and the contribution of the intrinsic electrophysiological properties of neurons to these operations remain incompletely understood. Here, a comparative analysis of electrically coupled mesencephalic trigeminal (MesV) neurons uncovered remarkable difference in the operation of these networks in highly related species. While spiking of MesV neurons might support the recruitment of coupled cells in rats, this rarely occurs in mice. Using whole-cell recordings, we determined that the higher efficacy in postsynaptic recruitment in rat's MesV neurons does not result from coupling strength of larger magnitude, but instead from the higher excitability of coupled neurons. Consistently, MesV neurons from rats present a lower rheobase, more hyperpolarized threshold, as well as a higher ability to generate repetitive discharges, in comparison to their counterparts from mice. This difference in neuronal excitability results from a significantly higher magnitude of the D-type K+ current (ID) in MesV neurons from mice, indicating that the magnitude of this current gates the recruitment of postsynaptic-coupled neurons. Since MesV neurons are primary afferents critically involved in the organization of orofacial behaviors, activation of a coupled partner could support lateral excitation, which by amplifying sensory inputs may significantly contribute to information processing and the organization of motor outputs.

A two-dimensional semi-analytic solution on two-layered liquid sloshing in a rectangular tank with a horizontal elastic baffle

A semi-analytic study on two-layered liquid sloshing in a horizontal excited two-dimensional rectangular tank with a horizontal elastic baffle was performed. The present work is a further development of the semi-analytical technique for solving the single-layer liquid sloshing problem. The horizontal elastic baffle was located in the lower liquid or upper liquid. First, the complex liquid domain in a baffled tank was divided into several simple sub-domains to solve the analytic solution. The wet mode of a horizontal baffle was presented according to the Eulerian Bernoulli beam. The continuity boundary condition on the interfaces between two liquids and the virtual interfaces was given. Then, the formal solution was derived for each sub-domain and a horizontal baffle using the superposition principle and the method of separation of variables. Then, the total velocity potential subject to lateral excitation was summed over the container potential function and the liquid disturbance potential. The dynamic response equation for two-layered liquid sloshing was established. Multiple methods verified the semi-analytic solution's correctness and agreed well with other methods. Finally, the numerical analysis mainly shows that the density ratio becomes more significant for the coupled frequency when the baffle is in the upper liquid. A large baffle's width suppresses the liquid flow in the baffled tank effectively. Furthermore, adjusting the baffle and the layered liquid parameters can significantly suppress layered liquid sloshing. For the seismic response, the elevation energy is mainly located after 2.5 s.

Chronic exposure to odors at naturally occurring concentrations triggers limited plasticity in early stages of Drosophila olfactory processing.

In insects and mammals, olfactory experience in early life alters olfactory behavior and function in later life. In the vinegar fly Drosophila, flies chronically exposed to a high concentration of a monomolecular odor exhibit reduced behavioral aversion to the familiar odor when it is reencountered. This change in olfactory behavior has been attributed to selective decreases in the sensitivity of second-order olfactory projection neurons (PNs) in the antennal lobe that respond to the overrepresented odor. However, since odorant compounds do not occur at similarly high concentrations in natural sources, the role of odor experience-dependent plasticity in natural environments is unclear. Here, we investigated olfactory plasticity in the antennal lobe of flies chronically exposed to odors at concentrations that are typically encountered in natural odor sources. These stimuli were chosen to each strongly and selectively excite a single class of primary olfactory receptor neuron (ORN), thus facilitating a rigorous assessment of the selectivity of olfactory plasticity for PNs directly excited by overrepresented stimuli. Unexpectedly, we found that chronic exposure to three such odors did not result in decreased PN sensitivity but rather mildly increased responses to weak stimuli in most PN types. Odor-evoked PN activity in response to stronger stimuli was mostly unaffected by odor experience. When present, plasticity was observed broadly in multiple PN types and thus was not selective for PNs receiving direct input from the chronically active ORNs. We further investigated the DL5 olfactory coding channel and found that chronic odor-mediated excitation of its input ORNs did not affect PN intrinsic properties, local inhibitory innervation, ORN responses or ORN-PN synaptic strength; however, broad-acting lateral excitation evoked by some odors was increased. These results show that PN odor coding is only mildly affected by strong persistent activation of a single olfactory input, highlighting the stability of early stages of insect olfactory processing to significant perturbations in the sensory environment.

A fast semi-analytic solution of liquid sloshing in a 2-D tank with dual elastic vertical baffles and walls

Liquid sloshing characteristics in a lateral excited two-dimensional (2-D) rectangular tank with dual elastic vertical baffles and walls have been investigated analytically. The elastic baffle or wall is regarded as an Eulerian Bernoulli beam. The complex liquid domain divides into six simple sub-domains according to the superposition principle. The formal solution of the potential function in each sub-domain is obtained using the separation of variables method. Then the formal baffle or wall deflection solution can be derived from the transverse vibration equation. The Eigen equation can be established according to the free surface, interface, and coupled vibration conditions. The coupled frequency can be obtained by solving the Eigen equation. The velocity potential under lateral excitation consists of the rigid container velocity potential and the disturbance potential. Then the coupled dynamic response equation is established using the free liquid surface equation and the coupled vibration equation. The correctness of the semi-analytic solution is verified against available data. Therefore, the numerical model of the present work can be computed quickly with semi-analytic solution and obtain the mechanism of liquid-structure interaction. Finally, the effect of baffle parameters and excitation frequency on liquid sloshing is discussed in detail.

Relationships between changes in lateral vestibulospinal tract excitability and postural control by dynamic balance intervention in healthy individuals: A preliminary study.

We conducted dynamic balance or static intervention on healthy young adults to examine the changes in lateral vestibulospinal tract (LVST) excitability and postural control that ensued following dynamic balance intervention and to investigate the correlation between these changes. Twenty-eight healthy young adults were randomly assigned to either the dynamic balance group or the control group. They performed either a dynamic balance or static intervention for 10 trials of 30 s each and were assessed for head jerks during the intervention to confirm adaptation to the intervention. The dynamic balance intervention consisted of maintaining balance on a horizontally unstable surface, whereas the control intervention involved standing in the same foot position as the dynamic balance intervention on a stable surface while completing a maze task. LVST excitability and postural stability were assessed before and after the interventions. LVST excitability was assessed as the change rate in the soleus H-reflex amplitude with galvanic vestibular stimulation (GVSH). The velocity and area of the center of pressure (COP) were examined in the eyes closed/foam rubber condition. No significant main and interaction effects (task, time) were observed for GVSH and COP variables. In the dynamic balance intervention, head jerk significantly decreased, and GVSH-change and changes in head jerk and COP area were significantly negatively correlated. The LVST excitability change for the dynamic balance intervention varied among the participants, although increased LVST excitability may have been related to increased postural stability.

Autonomous Vehicle Kinematics and Dynamics Synthesis for Sideslip Angle Estimation Based on Consensus Kalman Filter

An autonomous vehicle sideslip angle estimation algorithm is proposed based on consensus and vehicle kinematics/ dynamics synthesis. Based on the velocity error measurements between the reduced Inertial Navigation System (R-INS) and the global navigation satellite system (GNSS), a velocity-based Kalman filter is formalized to estimate the velocity errors, attitude errors, and gyro bias errors of the R-INS. The observability issue of the heading error, which affects sideslip estimation, is analyzed. Then, to enhance the observability and improve the estimation accuracy of the heading error under normal driving conditions, a consensus Kalman information filter is developed to synthesize the vehicle kinematics and dynamics and estimate the heading error. Within the developed consensus framework, one node augments a novel heading error measurement from a linear vehicle-dynamic-based sideslip estimator and another node adopts the heading error from the GNSS course. Next, based on the vehicle lateral excitation level, a weighting scheme is proposed to fuse the error state estimates from the velocity-based and consensus Kalman state observers. The stability of the proposed state observers is also investigated. Comprehensive experimental studies, including critical slalom, slight/normal double lane change, and normal driving maneuvers, were conducted to verify the proposed estimation framework; they confirm the reliability and accuracy of the estimator in various automated driving conditions even in comparison with state-of-the-art methods that utilize more measurements (dual-antenna GNSS). Also, this novel multisensor framework is extendable to leverage speed information from other sensors such as cameras and light detection and ranging (LiDAR) to increase reliability and accuracy.

A Computational Developmental Model of Perceptual Learning for Mobile Robot

During the perceptual learning (PL) of a mobile robot, how to improve the efficiency of its behavior decision is a great challenge. The existing methods suffer from the less flexibility and low efficiency. This article proposes a novel methodology to address these problems. It mimics the principle that the human’s brain can still think, even when he/she neither receives any sensory stimulus nor performs any action, during the off-task process, a gated self-organization mechanism is used to trigger the “brain” of the mobile robot to work, analyze the scenarios that it encountered in the former tasks to decide the best moving direction, then store the sensed scenario information by means of the lateral excitation of the internal neurons in a developmental network (DN), and set up the weight connections from the internal area to high-level decision-making area of the DN. In the following PL, if the robot encounters a similar scenario, it can make a better and faster behavior decision. Therefore, this methodology can greatly enhance the efficiency of behavior decision with the limited training samples, without retraining in facing a new scenario. Most importantly, this methodology makes the robot continuously improve its intelligence through the autonomous learning, even in offline state. Extensive simulation and experiment results of the mobile robot PL demonstrate its potential. Since it is task nonspecific, the same learning principles are potentially suitable for other fields. To the best of our knowledge, it is the first trial to apply the transfer learning through the lateral excitation mechanism of internal neurons to the robot field with the emergent representation.

Lateral dynamics of a monopile partially embedded in layered saturated soil with radial disturbance

A bidirectional transfer matrix method is presented to investigate the impedances of a laterally loaded monopile partially embedded in layered saturated soil with radial disturbance. To characterize the radial variation of soil properties induced by construction excitations or cyclic lateral excitations, the radial transfer matrix of the saturated soil is developed to determine the horizontal resistance of soil to the pile shaft based on Biot's theory. Lateral, rocking and lateral-rocking coupled impedances at the head of the monopile are obtained by solving the differential equations for transverse vibration of the pile shaft based on the Timoshenko beam theory, combined with an axial transfer matrix to treat the layered property of soil along the partially embedded monopile. The proposed model is validated by comparing it with some existing results. The theoretical rigour and broad engineering applicability of the present model are highlighted by a series of parametric analyses for the influences of soil and pile properties on the impedances of the laterally loaded monopile.

Analytic detection of chaos zones in response of a shape memory alloy beam under simultaneous external and parametric excitations

ABTRACT In this article, the dynamic stability and chaotic behavior of a shape memory alloy (SMA) beam with large deformation under simultaneous lateral and axial excitations is investigated through a fully analytic approach. First, the nonlinear governing equation of motion is derived. Second, Melnikov’s method, as an analytic approach, is employed to obtain the chaos zones. After that, by introducing non-dimensional parameters, border curves of chaotic areas were evaluated and plotted for some case studies which give a reader a precise and clear look at how the material and load properties can affect the chaos zones. Finally, the sufficient condition is approved via corresponding poincaré maps.

Application of an integrated nonuniform seismic random excitation method in tunnel engineering in soft soil areas

Nonuniform seismic excitation cannot be neglected in the seismic design of long-span tunnels in soft soil areas, as it might induce tunnel damage. This paper proposes a method that combines an integrated nonuniform seismic random excitation method with the finite element method to solve the problem of nonuniform seismic input for geotechnical tunnel seismic design in soft soil areas. The integrated nonuniform seismic random excitation method of producing multipoint random seismic waves is investigated considering the effects of passage, incoherence, and energy attenuation. Design codes are developed to achieve random seismic ground waves, baseline adjustment and filtering, and inversion of bedrock. The correctness of an integrated nonuniform seismic random excitation is verified by analysis of the differences (5%–10%) between the simulated and theoretical power spectrum functions. Based on this modelling, the dynamic responses of tunnels subjected to longitudinal and lateral seismic excitations are investigated. Nonuniform seismic excitation will cause greater tunnel deformation and internal forces than uniform seismic excitation due to the tunnel consuming more seismic energy under nonuniform seismic excitation. Longitudinal nonuniform seismic excitation induces compressive and tensile states in the tunnel, and the maximum tension is close to the tensile strength of the concrete. Lateral nonuniform seismic excitation can enlarge the bending moment and shear force, and bending moment and shear force distribution ranges are recommended for this case study.