External Acceleration Research Articles

Novel High-Resolution Lateral Dual-Axis Quad-Beam Optical MEMS Accelerometer Using Waveguide Bragg Gratings

A novel lateral dual-axis a-Si/SiO2 waveguide Bragg grating based quad-beam accelerometer with high-resolution and large linear range has been presented in this paper. The sensor consists of silicon bulk micromachined proof mass suspended by silica beams. Three ridge gratings are positioned on the suspending beam and proof mass to maximize sensitivity and reduce noise. Impact of external acceleration in the sensing direction on the Bragg wavelength of gratings and MEMS structure has been modelled including the effects of strain, stress and temperature variation. Acceleration induces stress in the beam thus modifying the grating period and introducing chirp. The differential wavelength shift with respect to reference grating on the proof mass is the measure of acceleration. To compensate for the effect of the weight of the proof mass and increase the sensitivity of the sensor, electrostatic force of repulsion is applied to the proof mass. For the chosen parameters, the designed sensor has a linear response over a large range and a sensitivity of 30 pm/g. The temperature of surroundings, which acts as noise in sensor performance is compensated by taking differential wavelength shift with respect to reference grating. By design and choice of material, low cross-axis sensitivity is achieved. The proposed design enables a high-resolution well below 1 μ g/ Hz and is suitable for inertial navigation and seismometry applications.

Diagrams of concrete behavior over time

The article presents a new vision of building diagrams of the work of materials in time. The main starting point is the law of conservation of energy of a closed system. The material is represented by an initial graph of the energy acceleration distribution. The external influence is represented as a rectangular form of energy acceleration distribution. At every moment of time, the external acceleration of energy exceeds the acceleration of the material’s energy. The obtained dependence of the material diagram is analyzed. Graphs of various forms of energy acceleration are obtained. Their summation shows the true diagram of the work of the material. Defining the characteristic points of the concrete behavior diagram, a true diagram of concrete behavior over time is constructed. By changing these characteristic points, we track the changing behavior of concrete over time.

Development of a new method for online parameter identification in seismically excited smart building structures using virtual synchronization and adaptive control design

In this paper a new method for online parameter identification and damage detection in smart building structures that are subjected to arbitrary seismic excitation is proposed. It uses real-time measurements of a structure's motion to identify its unknown constant or piecewise constant parameters such as stiffness, damping and mass over the time. The method is based on elements of system synchronization and adaptive control theories. First, a computational system, called the virtual system, is defined. Next, by using properly designed controller and estimations for the unknown parameters, the state of the virtual system is forced to follow the measured motion of the real structure. The mentioned estimations are computed from a proposed update law which depends on the measured motion of the real structure and the virtual system’s state. A major theoretical novelty of this paper is a proposed convergence condition which is applicable in case of arbitrary external forces or ground acceleration. It is shown that upon the satisfaction of that condition, as the synchronization completes, the computed estimation function converges to the true value of the vector of unknown parameters. In addition, an important practical contribution presented in this study is the introduction of a technique called scale factors. It helps to use available initial guesses of the unknown parameters to improve the speed of online identification. Numerical examples show that the proposed method is promising and has a good performance in both online identification and online damage detection problems.

Study on cantilever piezoelectric energy harvester with tunable function

Piezoelectric energy harvesters tend to convert energy from ambient vibration to electricity, which can gain a higher output voltage at resonance region. How to obtain a larger working bandwidth is urgent to explore at present. In this paper, a cantilever plate energy harvester is designed, with two boxes added at two free edges along the fixed-free direction and one rolling ball placed in each boxes respectively. The natural frequency of the structure can be adjusted by changing the centroid of the structure, which is caused by the balls rolling in the box. The range of adjustment that contains from the maximum (upper limit) to minimum (lower limit) frequency, is defined as the theoretical frequency band. The mode function of tunable cantilever plate is given according to deflection curve. Considering the rigid body motion of boxes and the composite motion of the balls, the Hamilton principle and the Hertz contact theory are taken into account to derive the vibration equations of the system. The experiment is carried out to verify the correctness of the theoretical mode and the dynamic equations. The responses of the structure under different excitation frequencies are calculated by using MATLAB software and verified by frequency sweep experiment. The results show that the working bandwidth of proposed structure under different balls initial positions is wider than with that of beam structure in resonance, thus proving the better tuning ability of the designed system. In addition, the output of the energy harvester under different external excitation acceleration is given. The effects of different length of box on the working bandwidth and output power density are studied. The relationship between conversion rate and external resistance is proposed under different boxes length. A high performance energy harvester with wider operating frequency range is designed.

Simulating diverse instabilities of dust in magnetized gas

ABSTRACT Recently, Squire & Hopkins showed that charged dust grains moving through magnetized gas under the influence of a uniform external force (such as radiation pressure or gravity) are subject to a spectrum of instabilities. Qualitatively distinct instability families are associated with different Alfvén or magnetosonic waves and drift or gyro motion. We present a suite of simulations exploring these instabilities, for grains in a homogeneous medium subject to an external acceleration. We vary parameters such as the ratio of Lorentz-to-drag forces on dust, plasma β, size scale, and acceleration. All regimes studied drive turbulent motions and dust-to-gas fluctuations in the saturated state, rapidly amplify magnetic fields into equipartition with velocity fluctuations, and produce instabilities that persist indefinitely (despite random grain motions). Different parameters produce diverse morphologies and qualitatively different features in dust, but the saturated gas state can be broadly characterized as anisotropic magnetosonic or Alfvénic turbulence. Quasi-linear theory can qualitatively predict the gas turbulent properties. Turbulence grows from small to large scales, and larger scale modes usually drive more vigorous gas turbulence, but dust velocity and density fluctuations are more complicated. In many regimes, dust forms structures (clumps, filaments, sheets) that reach extreme overdensities (up to ≫109 times mean), and exhibit substantial substructure even in nearly incompressible gas. These can be even more prominent at lower dust-to-gas ratios. In other regimes, dust self-excites scattering via magnetic fluctuations that isotropize and amplify dust velocities, producing fast, diffusive dust motions.

Dynamics of a non-linearly damped microresonator under parametric excitation and its application in developing sensitive inertial sensors with ultra-wide dynamic ranges

We model and investigate the response of a nonlinear cantilever beam under principal parametric excitation. The design is initially assessed, optimized, and tuned using three-dimensional finite element analysis (FEA) to ensure the presence of fundamental parametric resonance and the absence of other internal and higher-order parametric resonances. The derived governing differential equation represents a modified generalized parametrically excited dynamic system under principal parametric excitation. The nonlinear dynamic system is developed and presented in the context of resonators with extensive applications in developing sensors, filters, and switches. The quadratic and cubic nonlinearities include second- and third-order deflection, velocity, acceleration terms describing stiffness, damping, and inertial nonlinearities. To explore and investigate the corresponding generalized nonlinear Mathieu equation, the method of multiple-scales along with the reconstitution method are used and modulation equations are obtained and solved to obtain closed-form amplitude and phase equations. The quadratic damping is modeled and approximated using a Fourier series and analytical models are generated in both Cartesian and Polar frames. To further explore the dynamic system and its applications, a resonator is designed to measure external acceleration and investigated for two cases. It is discussed and shown how the external acceleration modifies the dynamic system, the corresponding reduced-order model, and the modulation equations. The external acceleration affects the amplitude, phase, and frequency of oscillation providing means to estimate the input. These results indicate that the proposed resonator design (dynamic system) is able to significantly improve the dynamic range of shock/acceleration sensors.

Anterolateral ligament reconstruction as an augmented procedure for double-bundle anterior cruciate ligament reconstruction restores rotational stability: Quantitative evaluation of the pivot shift test using an inertial sensor

PurposeThe purpose of this study was to investigate the biomechanical function of the anterolateral structures (ALS) of the knee regarding rotational stability, and to attempt to verify the effectiveness of anterolateral ligament (ALL) reconstruction concomitant with double-bundle anterior cruciate ligament (ACL) reconstruction by quantifying the pivot shift test (PST) using an inertial sensor. MethodsSix knees of the fresh-frozen cadavers were evaluated during the following phases: (1) [Intact]; (2) ACL-deficient [ACL-D]; (3) ACL-reconstructed [ACL-R]; (4) ACL-reconstructed + ALS-deficient [ACL-R + ALS-D]; and (5) combined ACL and ALL reconstructed [ACL-R + ALL-R]. We evaluated knee rotational instability during each phase using the PST. We used an inertial sensor to calculate tibial external rotational angular velocity (ERAV) and tibial acceleration. Data were analyzed using repeated-measures analysis of variance; statistical significance was accepted as P < 0.05. ResultsRelative to [Intact], [ACL-D] caused a significant increase in ERAV and acceleration. However, there was no difference in these parameters between [ACL-R] and [Intact]. [ACL-R + ALS-D] increased ERAV significantly compared with [ACL-R], and there was a significant difference between ERAV during [ACL-R + ALS-D] and [Intact]. However, ERAV was significantly reduced during [ACL-R + ALL-R] compared with [ACL-R + ALS-D], and there was no significant difference in ERAV or acceleration between [ACL-R + ALL-R] and [Intact]. ConclusionsALS controlled rotational instability in cooperation with the ACL in a cadaveric model. In cases of combined injury of ACL and ALS, concomitant ACL and ALL reconstruction may restore knee stability comparable with the intact state.

Signal extraction and monitoring of motion loads based on wearable online device

Monitoring of human exercise load is a hot area of wearable technology. The mainstream human motion calculation method predicts human motion through offline machine learning techniques. Personalized monitoring poses new challenges to the original learning model. Aiming at the detection of R peak value of motion load signal and the location of QRS complex, an improved R-peak detection algorithm based on adaptive threshold is proposed. The feature extraction method of motion load signal is introduced from multiple dimensions. The characteristics of time domain features and frequency domain features are analyzed. The time domain features and the eigenvalues of frequency domain features are defined and extracted. Experiments show that the proposed algorithm has higher detection accuracy. A multi-threshold-peak step algorithm is proposed and a motion state machine model is established. According to the periodic changes of the trunk movement and the arm swing acceleration in motion, the feature values are extracted, the step detection and the gait discrimination are performed, and the influence of external acceleration interference is excluded. The state machine adopts a nested structure, which is divided into two layers, a parent state and a child state, and calibrates the state transition condition. A verification method for the validity of feature parameters is proposed. The selected feature parameters are taken as an example to analyze and simulate the method. Simulation results show that the characteristic parameters in this paper are effective in the monitoring of the reasonableness of exercise load.

A Novel Fuzzy-Adaptive Extended Kalman Filter for Real-Time Attitude Estimation of Mobile Robots.

This paper proposes a novel fuzzy-adaptive extended Kalman filter (FAEKF) for the real-time attitude estimation of agile mobile platforms equipped with magnetic, angular rate, and gravity (MARG) sensor arrays. The filter structure employs both a quaternion-based EKF and an adaptive extension, in which novel measurement methods are used to calculate the magnitudes of system vibrations, external accelerations, and magnetic distortions. These magnitudes, as external disturbances, are incorporated into a sophisticated fuzzy inference machine, which executes fuzzy IF-THEN rules-based adaption laws to consistently modify the noise covariance matrices of the filter, thereby providing accurate and robust attitude results. A six-degrees of freedom (6 DOF) test bench is designed for filter performance evaluation, which executes various dynamic behaviors and enables measurement of the true attitude angles (ground truth) along with the raw MARG sensor data. The tuning of filter parameters is performed with numerical optimization based on the collected measurements from the test environment. A comprehensive analysis highlights that the proposed adaptive strategy significantly improves the attitude estimation quality. Moreover, the filter structure successfully rejects the effects of both slow and fast external perturbations. The FAEKF can be applied to any mobile system in which attitude estimation is necessary for localization and external disturbances greatly influence the filter accuracy.

Particle–fluid two phase modeling of electro-magneto hydrodynamic pulsatile flow of Jeffrey fluid in a constricted tube under periodic body acceleration

The present article investigates the combined role of electric and magnetic fields on the pulsatile flow of Jeffrey fluid (blood) with the suspension of particles (blood cells) in a stenosed artery under the influence of external periodic body acceleration. The Debye–Hückel linearization principle is invoked by assuming the zeta potential on the vessel wall is very small, and the coupled non-linear governing equations which comprise the continuity and momentum conservation equations for the fluid phase and particle phase are simplified by using dimensional analysis under the mild stenosis approximation. The closed-form solutions for electric potential, velocity profiles of both fluid and particle, volumetric flux, skin friction, and the flow resistance are derived in terms of Bessel functions by employing Laplace and Hankel transforms under the appropriate initial and boundary conditions. The influence of some evolving physical parameters like pulsatile Reynolds number, the amplitude of blood flow, Jeffrey parameter, hematocrit, body acceleration amplitude, phase angle, Hartmann number, and electro-osmotic parameter on velocity profiles, skin friction, and resistance to flow were shown graphically and debated concisely. The analysis reveals that the flow of blood in a stenosed duct is substantially influenced by the appropriate strength of externally applied electric and magnetic fields. The study further demonstrates that wall shear stress attenuates as the Jeffrey parameter increases, whereas the reverse trend is noticed with the concentration of blood cells. Moreover, it is worth mentioning that the increment in electric field intensity (i.e., decreasing Debye length) causes a reduction in the skin friction and impedance to flow, which, in turn, aids in improving the flow of blood under diseased conditions.

Mild Head Injury Patients; Correlation between admission Computed Tomography Brain Scan and outcome

Background: Traumatic injuries of brain is considered the damage of the brain which result from external force, like impact, deceleration, blast waves, rapid acceleration, and penetration by a projectile. Brain function is permanently or temporarily impaired and the damage of the structure could or could not be revealable with recent technology. Objectives: To assess post-traumatic CT scan brain changes to patients with mild head injuries in correlation to clinical sequelae. Patients and Methods: This prospective cohort study was conducted at Neurosurgery Department, Zigzag University Hospitals, on 75 patients of mild traumatic brain injury (mTBI) presented to emergency department at zagazig university hospital with mean age of 26.7 years, during the period from April 2018 to September 2018. Results: The most common CT finding in patients with mild head injury in our study was a skull fracture by 43% then contusion by32% and Epidural hemorrhage by 21.5% and least one was Subarachnoid hemorrhage by10.7% none of the participants in our current study had a subdural hemorrhage. percent of positive findings on CT scan was 9.3% and 2.6% need surgical intervention , the outcome of the patient was assessed by Glasgow outcome score (GOS) and most of the patient score was 5 which a good score. Conclusion: Patients with mild traumatic head injury with a presenting GCS score of 13 or 14 should undergo a CT scan examination and to be admitted for observation and management.

Effects of centrifugation and whole-body vibrations on blood\u2013brain barrier permeability in mice

Modifications of gravity levels induce generalized adaptation of mammalian physiology, including vascular, brain, muscle, bone and immunity functions. As a crucial interface between the vascular system and the brain, the blood–brain barrier (BBB) acts as a filter to protect neurons from pathogens and inflammation. Here we compare the effects of several protocols of hypergravity induced by centrifugation and whole-body vibrations (WBV) on BBB integrity. The immunohistochemistry revealed immunoglobulin G (IgG) extravasation from blood to hippocampal parenchyma of mice centrifuged at 2 × g during 1 or 50 days, whereas short exposures to higher hypergravity mimicking the profiles of spaceflight landing and take-off (short exposures to 5 × g) had no effects. These results suggest prolonged centrifugation (>1 days) at 2 × g induced a BBB leakage. Moreover, WBV were similarly tested. The short exposure to +2 × g vibrations (900 s/day at 90 Hz) repeated for 63 days induced IgG extravasation in hippocampal parenchyma, whereas the progressive increase of vibrations from +0.5 to +2 × g for 63 days was not able to affect the IgG crossing through the BBB. Overall, these results suggest that the BBB permeability is sensitive to prolonged external accelerations. In conclusion, we advise that the protocols of WBV and centrifugation, proposed as countermeasure to spaceflight, should be designed with progressively increasing exposure to reduce potential side effects on the BBB.

Cascaded Kalman Filtering-Based Attitude and Gyro Bias Estimation With Efficient Compensation of External Accelerations

We consider the problem of attitude estimation of rigid bodies in motion using low cost inertial measurement unit (IMU). An efficient scheme is proposed using two different Kalman filters by deriving their measurement models for precise attitude (pitch and roll) estimation in the presence of high and prolonged dynamic conditions and gyro bias. Both filters work in a coupled fashion where one of the filters provides accurate estimates of rigid body attitude and external acceleration using the accelerometer in conjunction with the gyroscope while the second filter is responsible to estimate the gyro bias, allowing the proposed scheme to be used in any application with minimal calibration. A new threshold based external acceleration detection module is also introduced to change the confidence level on external acceleration prediction to assist the estimation process. The proposed scheme is tested and compared with other existing estimators in the literature under different dynamical conditions and real-world experimental data sets in order to validate its effectiveness.

A Robust Indirect Kalman Filter Based on the Gradient Descent Algorithm for Attitude Estimation During Dynamic Conditions

The real-time response and accuracy of the attitude (i.e., roll and pitch) estimation from low-cost inertial measurement unit (IMU) have become the key issues restricting related applications. This paper proposes a robust attitude estimation scheme which can perform well under dynamic conditions. When only accelerometers are used to calculate and correct the attitude, the external acceleration becomes the main source of attitude estimation errors. Moreover, the truncation error in the linearization process of the nonlinear system also affects the attitude estimation. As our first contribution, the external acceleration is modeled as a first-order Gauss Markov model, and its value is calculated under the indirect Kalman filter (IKF) framework. The measurement noise covariance matrix of the IKF is adaptively adjusted to enhance its robustness and reduce the negative impact caused by inaccurate modeling. In the second part of our work, the two-step cascade filter method is used for attitude estimation. The attitude obtained from the gravity field based on the gradient descent (GD) algorithm shows fast response capabilities, and hence, it is embedded as a measurement in the IKF by using the chain-derivation rule. The truncation error introduced into the linearization process of the nonlinear system is effectively avoided. Both simulation and experiments are carried out to verify the feasibility and accuracy of the proposed algorithm. The results show that the approach proposed in this paper can meet the accuracy requirements of consumer products.

Modeling and Experimental Characterization of an Electromagnetic Energy Harvester for Wearable and Biomedical Applications

This work presents the modeling and the experimental validation of a linear electromagnetic energy harvester (EMEH) actuated by random low-g external acceleration or by a very slow imposed movement. By combining these two different ways of energy scavenging, the system is particularly suited for powering wearable and biomedical electronic devices where the human-motion and movement can be considered as random and non predictable. The design is composed of a mobile stack of head-to-head ring-shaped permanent magnets in which a fixed wounded ferromagnetic core, composed of two coils, is located. A custom co-simulation is presented: a finite element analysis (FEA) and a one dimension (1D) two degrees of freedom (2DOF) system model. The FEA is used to optimize the geometry of the EMEH and its form factor, allowing an significative down-scaling. The 1D 2DOF model describes the dynamics of the EMEH in its real environment by considering all the leading mechanical and electrical parameters. The geometry can drastically change the behavior of the system as well as its dynamics: the goal of this double structure is to reduce the magnetic force exerted between the fixed part and the moving part while keeping the magnetic flux gradient in each coil as large as possible. This force was characterized experimentally by using a custom designed test bench, to validate the FEA results. It was observed that the maximum produced energy is reached when the system sweeps across different equilibrium positions rather than oscillating around a given stable position. The second degree of freedom helps the system to settle in a large number of equilibrium positions when submitted to random external accelerations and therefore broadens the frequency response of the EH. Results show a theoretical electrical power output (RMS) of 2 mW for a 10 cm3 cylindrical harvester submitted to a short external acceleration pulse of 27.5 m/s2.

3D Anatomy of the Quail Lumbosacral Spinal Canal-Implications for Putative Mechanosensory Function.

SynopsisBirds are diverse and agile vertebrates capable of aerial, terrestrial, aquatic, and arboreal locomotion. Evidence suggests that birds possess a novel balance sensing organ in the lumbosacral spinal canal, a structure referred to as the “lumbosacral organ” (LSO), which may contribute to their locomotor agility and evolutionary success. The mechanosensing mechanism of this organ remains unclear. Here we quantify the 3D anatomy of the lumbosacral region of the common quail, focusing on establishing the geometric and biomechanical properties relevant to potential mechanosensing functions. We combine digital and classic dissection to create a 3D anatomical model of the quail LSO and estimate the capacity for displacement and deformation of the soft tissues. We observe a hammock-like network of denticulate ligaments supporting the lumbosacral spinal cord, with a close association between the accessory lobes and ligamentous intersections. The relatively dense glycogen body has the potential to apply loads sufficient to pre-stress denticulate ligaments, enabling external accelerations to excite tuned oscillations in the LSO soft tissue, leading to strain-based mechanosensing in the accessory lobe neurons. Considering these anatomical features together, the structure of the LSO is reminiscent of a mass-spring-based accelerometer.

Diseño y construcción de un pico-satélite educativo CanSat tipo rover denominado EagleSat V2.1

It is described how a CanSat pico-satellite type rover was designed and built to compete in the Fourth CanSat National Educational Satellites Competition. Students of Engineering in Information Technologies and Communications with the support of teachers of that career designed and built the pico-satellite called EagleSat V2.0. Using the methodology of the "V" model, the mission was conceptualized which was the sending of data of: internal and external temperature, pressure, relative humidity, altitude, longitude, latitude, battery level, vibration and acceleration through telemetry to an earth station; take video and return to the starting point using a rover type vehicle; the requirements and architecture of all stages of the EagleSatV2.1 were specified. Starting from the architecture, the printed circuits were designed and built, the components and the different sensors were welded to measure the data. In addition, a mechanical structure and tires were designed and printed on a 3D printer which would make up the Rover type vehicle. Thanks to the excellent work done, the first place was obtained in the Fourth CanSat National Satellites Educational Contest in the comeback category.

A Heterogeneous Integrated MEMS Inertial Switch With Compliant Cantilevers Fixed Electrode and Electrostatic Locking to Realize Stable On-State

A novel heterogeneous integrated inertial micro-switch has been designed with adjustable acceleration threshold and a stable ‘on’-state due to a predefined bias voltage. The bias voltage is applied onto the large-area parallel-plate electrodes, which endows the movable proof-mass with electrostatic forces. With an external excitation acceleration, the movable electrode moves to the fixed electrode and it can be locked by the electrostatic force onto the compliant electrical contacts, which are composed of micro-cantilever array to eliminate the contact rebound during electrostatic pull-in process. Both the dynamic response of the proof-mass and the relationship between the bias voltage and the inertial excitation acceleration were analyzed using theoretical model and finite element simulation. A unique heterogeneous integration process including both the silicon-based and non-silicon surface micromachining processes was adopted to fabricate the switch. The tests using a standard dropping hammer system demonstrated that the switch could keep a stable switch-on at the 57 g excitation acceleration and 38 V bias voltage. As wide as 52% adjustment range of the acceleration threshold was obtained when the applied bias voltage was from 38 V to 44 V. The tested relationship between the bias voltage and the external acceleration was very consistent with the simulated relationship. [2019-0038]

A Model-Based Method for Estimating the Attitude of Underground Articulated Vehicles.

This paper presents a novel model-based method for estimating the attitude of underground articulated vehicles (UAV). We selected the Load–Haul–Dump (LHD) vehicle as our application object, as it is a typical UAV. First, we established the involved models of the LHD vehicle, including a kinematic model, the linear and angular constraints of a center articulation model, and a dynamic four degrees-of-freedom (DOF) yaw model. Second, we designed a Kalman filter (KF) to integrate the kinematic and constraint models with the data from an inertial measurement unit (IMU), overcoming gyroscope drift and disturbances in external acceleration. In addition, we designed another KF to estimate the yaw based on the dynamic yaw model. The accuracy of the estimations was further enhanced by data fusion. Then, the proposed method was validated by a simulation and a field test under different dynamic conditions. The errors in the estimation of roll, pitch, and yaw were 3.8%, 2.4%, and 4.2%, respectively, in the field test. The estimated longitudinal acceleration was used to obtain the velocity of the LHD vehicle; the error was found to be 1.2%. A comparison of these results to those of other methods showed that the proposed method has high precision. The proposed model-based method will greatly benefit the location, navigation, and control of UAVs without any artificial infrastructure in a global positioning system (GPS)-free environment.

Dynamic pressure on lock gate structure coupled with fluid

The effect of fluid on the dynamic pressure distribution of a rectangular lock gate structure subjected to external harmonic ground acceleration is studied. The fluid is assumed to be inviscid and incompressible, having an irrotational flow. Pressure for fluid domain and displacement for lock gate are considered as nodal variables in the finite element formulation. The interaction of coupled problem is maintained by transferring acceleration of the lock gate to fluid and pressure of the fluid to lock gate. Mindlin’s plate theory is used to formulate the lock gate. The Laplace equation is solved using Fourier half range cosine series expansion to truncate the far boundary nearer to the lock gate. The time dependent forced vibration equations are solved by using Newmark-beta time integration method.