Longitudinal Vibration Research Articles

Mode selection and combination rules of energy-based multimodal pushover method for simply supported beam bridges

The energy-based method (EBM) has been improved as Energy-based Multimodal Pushover Method (EMPM), and is introduced and verified to be effective and convenient for evaluate the seismic performance of the simply supported beam bridges. This paper mainly focuses on the research of vibration mode selection and combination rules of EMPM. Firstly, the longitudinal vibration modes of simply supported beam bridge are categorized into five cases based on mode shapes, and the case definition is emphasized. Then, corresponding to each case, the Pushover loading force are established, and the modal energy, modal displacement, and modal energy capability curve are proposed. After that, the energy-based demand curve and the corresponding energy coefficient for each case is recommended. Finally, only the mode with maximum mode participation factor (MPF) of each case is suggested to take part in the calculation of the seismic response with the proposed mode participation factor combination rule. Case studies of a practice bridge under Chi-Chi and El Centro earthquake waves are used to illustrate the effectiveness and accuracy of the proposed mode selection and combination rules. The study found that the EMPM with the proposed rules could effectively and rapidly assessing the seismic performance of the simply supported beam bridge, resulting in a 70 % decrease in time consumption compared with the Nonlinear Time History Analysis Method (NTHAM). Compared with the CQC and SRSS combination results, the proposed Mode Participation Factor (MPF) combination rule reduced the maximum relative deviation from 39.4 % to 21.09 % between EMPM and NTHAM for peak displacement. Further research showed that the proposed mode selection approach only uses modes with the highest MPF in each case, decreased the number of modes involved more than 50 % and the result accuracy remained almost identical.

Nonlinear resonant bar of approximate Ramberg–Osgood type modulus defect

This study investigates the nonlinear vibration of a material bar with a modulus defect that causes observable hysteresis in the elastic regime. The Ramberg–Osgood equation is used to obtain an approximate model of the quasi-static stress–strain relationship for such a material, from which a phenomenological dynamic hysteresis function of arbitrary order is constructed. The nonlinear hysteresis is described with two parameters. Applying the hysteresis function leads to a nonlinear wave equation which is then solved for the longitudinal vibration of the bar using a perturbation method. The leading-order solution provides the strain-dependent resonance frequency and damping factor which are the two quantities measured in the nonlinear resonance ultrasound spectroscopy (NRUS). It is shown that the resonance frequency shift and damping increment hold, in general, a power-law dependence on the strain amplitude and the conventional linear dependence is a special case for the quadratic hysteresis. The derived formula is applied to existing data from bending and torsional NRUS-type experiments where the conventional linear fit appears to be clearly inadequate. Experimental resonance frequency shift data are fitted to determine the two hysteresis parameters, both of which vary with the changes in the material state. It is shown that the nonlinear damping ratio is a more general measure of the energy dissipation due to the increasing hysteresis and thus can be taken as a damage index. Consequently, this paper proposes a general procedure to analyze NRUS data for a wider range of materials. The present analysis is valid up to the yield strain which is sufficient to cover the strain amplitudes used in NRUS measurements.

An Inverse Matrix Eigenvalue Problem for Constructing a Vibrating Rod

Abstract The free longitudinal vibrations of a rod are described by a differential equation of the form ( P ( x ) y ′ ) ′ + λ P ( x ) y ( x ) = 0 {(P(x)y\prime)^{\prime}+\lambda P(x)y(x)=0} , where P ⁢ ( x ) {P(x)} is the cross section area at point x and λ is an eigenvalue parameter. In this paper, first we discretize this differential equation by using the finite difference method to obtain a matrix eigenvalue problem of the form 𝐀 ⁢ Y = Λ ⁢ 𝐁 ⁢ Y {\mathbf{A}Y=\Lambda\mathbf{B}Y} , where 𝐀 {\mathbf{A}} and 𝐁 {\mathbf{B}} are Jacobi and diagonal matrices dependent to cross section P ⁢ ( x ) {P(x)} , respectively. Then we estimate the eigenvalues of the rod equation by correcting the eigenvalues of the resulting matrix eigenvalue problem. We give a method based on a correction idea to construct the cross section P ⁢ ( x ) {P(x)} by solving an inverse matrix eigenvalue problem. We give some numerical examples to illustrate the efficiency of the proposed method. The results show that the convergence order of the method is O ⁢ ( h 2 ) {O(h^{2})} .

The Quick Determination of a Fibrous Composite’s Axial Young’s Modulus via the FEM

Knowing the mechanical properties of fiber-reinforced composite materials, which are currently widely used in various industrial branches, represents a major objective for designers. This happens when new materials are used that are not yet in production or for which the manufacturer cannot give values. Given the practical importance of this problem, several methods of determining these properties have been proposed, but most of them are laborious and require a long calculation time. And, some of the proposed calculation methods are very approximate, providing only upper and lower limits for these values. Experimental measurements are obviously the optimal solution for solving this problem, but it must be taken into account that this type of method consumes time and material resources. This paper proposes a sufficiently accurate and fast estimation method for determining Young’s modulus for a homogenized fibrous material. Thus, the FEM is used to determine the natural frequencies of a standard bar, for which there are sufficiently precise classical methods to express the engineering constants according to the mechanical properties of the component phases of the homogenized material. In this paper, Young’s modulus is determined for such a material using the relationships that provide the eigenfrequencies for the longitudinal vibrations. With the adopted model, transverse and torsional vibrations are eliminated by blocking the nodes on the surfaces of the bars. In this way, more longitudinal eigenfrequencies can be obtained, so the precision in calculating Young’s modulus is increased.

Longitudinal forced harmonic vibrations of vertical rods with concentrated mass.

Longitudinal forced harmonic vibrations of vertical rods with concentrated mass.

Comparing the in-plane shear moduli of cardboard measured by flexural vibration, torsional vibration, static torsion, off-axis vibration, and off-axis tension tests

Abstract Flexural vibration (FV), torsional vibration (TV), static torsion (ST), longitudinal vibration (OAV), and tension (OAT) of 45° off-axis tests of flat pieces of cardboards were analyzed to determine the in-plane shear modulus (IPSM) using samples of various widths. The analyses were performed with simulations using the finite element method (FEM) for models with and without lamination and physical experiments using cardboard samples. For the FV, TV, and ST tests, the IPSM was calculated using binary search (BS) and linear regression (LR). The FEM results suggest that the IPSM values obtained from the TV and ST test simulations were affected by lamination. In contrast, the effect of lamination was not clear in the FV, OAV, and OAT test simulations. The coefficient of variation obtained from the FV experiments was often larger than that obtained from other tests. Despite this variation, the FV test is more attractive than the other tests because the experiments could be performed easily, and the effect of lamination could be reduced.

Determination of the absorbed acoustic power of longitudinal vibrations by measuring their amplitude in a chosen area of the waveguide system outside the load

The way of determining the acoustic power of longitudinal ultrasonic vibrations going into the load by measuring the amplitude of longitudinal displacements using an electrodynamic sensor installed near the surface of the waveguide rod is considered. Two possibilities of using the developed method of measurement are analyzed in detail. One of them is based on the registration of the value of longitudinal displacements at the constant position of the electrodynamic sensor in two different states of the ultrasound system: with the load disconnected and after the load is connected, i.e. it uses two measurements at different moments of time, when the states of the system differ from each other. Another way uses two measurements of the amplitude of longitudinal oscillations at two chosen points of the oscillatory system, made at the same time. Formulas have been obtained that make it possible to determine the power entering the load from the measured values and other known values of the system parameters. The role of errors, both in the readings of the sensor and in determining its location on the oscillating system, on the accuracy of calculating the value of the power of the ultrasonic oscillations that went into the load is analyzed.

Ultrasonic vibration-assisted single point incremental forming of hemispherical shaped component using AA3003 material

ABSTRACT Ultrasonic vibration-assisted single point incremental forming is a recent hybrid process variant of the single point incremental forming process. In this process, longitudinal ultrasonic vibration is used as an assistance in the conventional forming process. In this paper, the effect of amplitude of vibration in the ultrasonic vibration assisted single point incremental forming process have been researched. For the same, experimental work has been carried out by forming the hemispherical shaped components using multistage forming strategy. Moreover, numerical simulation work has been carried out using the LSDYNA solver and the results have been discussed in the light of depth of forming and strain distribution. The experimental fracture forming line is also developed for the AA3003 material for single point incremental forming process. High amplitude of vibration of 12 micron with 20 kHz frequency leads to poor formability; however, the lower amplitude of vibration of 8 micron with 30 kHz frequency leads to good formability.

Effects of longitudinal ultrasonic vibration on tool wear behaviors in side milling of GH4169D superalloy

The GH4169D superalloy, a novel Nickel-based material widely acknowledged for its exceptional high temperature strength and fatigue resistance properties, plays a pivotal role in the production of critical components of contemporary aero-engines. The material, however, falls under the category of a typical difficult-to-cut metallic material due to the substantial cutting forces and significant tool wear experienced during the machining process. In this paper, a method of longitudinal ultrasonic vibration assisted side milling (LUVM) was developed to extend tool life. The investigation primarily involved an analysis of tool wear behaviors, including milling force, tool life, morphologies of tool wear, and various underlying wear mechanisms in LUVM and conventional milling (CM) of GH4169D superalloy. The results demonstrate that LUVM exhibits the advantage of reducing milling forces and prolonging tool life in comparison to CM. Throughout the entire milling process, the maximum milling force of LUVM is consistently smaller than that of CM, displaying a comparatively slower growth trend. At the conclusion of machining, while CM reaches a maximum milling force of 360.3 N, the maximum milling force of LUVM (195.9 N) is significantly lower. The tool life of LUVM is 28.2 min, representing a 33 % increase compared to CM (21.2 min). Material adhesion, coating delamination, and built-up edge (BUE) phenomena can be observed on both the tool rake face and flank face in CM. LUVM contributes to mitigation of bonding phenomena, prevention of BUE formation, and avoidance of abrasive wear in comparison to CM. However, it is prone to lead to tool tip chipping. For CM, the tool wear mechanisms include adhesive wear, oxidation wear, abrasive wear and diffusion wear; whereas for LUVM, the tool wear mechanisms comprise of adhesive wear, oxidation wear and diffusion wear.

Longitudinal Vibration Transmission Suppression for Propeller-Shaft System by a Lever-Type Isolator with Negative Stiffness

Longitudinal Vibration Transmission Suppression for Propeller-Shaft System by a Lever-Type Isolator with Negative Stiffness

Investigating mechanisms of debris removal in ultrasonic vibration-assisted EDM drilling

In traditional electrical discharge machining (EDM) of micro-holes, the debris removal becomes increasingly challenging as hole depth increases, significantly affecting the machining of difficult-to-machine materials. To address this issue,we first developed a micro-hole gap flow field model for a novel longitudinal–torsional ultrasonic vibration (LTV) electrode EDM drilling method. We analyzed the effects of three types of electrodes — rotation electrodes, longitudinal ultrasonic vibration (LUV) electrodes, and LTV electrodes — on the flow velocity in the micro-hole interstitial flow field. Next, we simulated the motion of fluid and debris in the interstitial flow field of micro-holes, theoretically verifying the advantage of electrode ultrasonic vibration in enhancing debris removal efficiency. Additionally, we observed the electrode tip morphology, the elemental composition on the electrode surface, and the morphology of the micro-hole inlet/outlet and inner wall to further elucidate the debris removal mechanism and confirm the superior drilling performance of the ultrasonic vibration electrodes. At an optimal ultrasonic amplitude (AL=4μm), the LUV electrode demonstrated improved consistency in the micro-hole inlet/outlet and achieved a micro-hole taper of 0.014°. The material removal rate (MRR) using the LTV electrode reached 5.14 × 105μm3/s, nearly 1.5 times higher rotation electrode. This method successfully produced a positively tapered hole suitable for injector nozzles.

Girder quasi-static cumulative displacement-based suspension bridge nonlinear damper leakage diagnosis by eliminating stochastic traffic effects

Fluid viscous dampers (FVDs) are the key energy dissipation devices for long-span suspension bridges, and their leakage poses a threat to the stable and reliable operation of bridge restraint systems. Therefore, this paper proposed an FVD fluid leakage diagnosis method based on girder longitudinal displacement monitoring data. First, the longitudinal vibration equation of the main girder under traffic loads was derived to reveal the displacement characteristic of girder-end motion. On this basis, considering that different displacement components under traffic loads are coupled and transient analysis directly utilizing traffic loads as the excitation is complicated and inefficient, an analysis framework focusing on the influence mechanism of FVD leakage on quasi-static displacement was established. Second, an equivalent mechanical model for simulating the hysteresis relationship of leaked FVD was proposed and verified. Then, the influence of variations in the location, number, leakage level and parameters of the leaked FVD on the quasi-static displacement was studied. Third, the equivalent traffic load (ETL) indicator was constructed to characterize the traffic volume. Furthermore, a quasi-static cumulative displacement and ETL correlation model, which can effectively eliminate the interference of traffic flow variations, was proposed for the leakage diagnosis of FVD. Finally, the proposed method was verified by real suspension bridge monitoring data. The results demonstrated that the proposed method can effectively detect a mild increase in the girder-end cumulative displacement due to FVD fluid leakage.

Stiffness parameter prediction for elastic supports of non-uniform rods

The present research focuses on establishing the stiffness parameter of elastic springs placed at the ends of non-uniform rods. The governing equation for the longitudinal vibrations of the rod was solved using the Haar wavelet integration method. The calculated natural frequency parameters closely aligned with those available in the literature. The normalised values of the first ten natural frequency parameters were used in the feature vector to predict the stiffness parameter of the springs. A feedforward neural network with two hidden layers made accurate predictions when the range of each natural frequency parameterwithin its domain exceeded one. The insights garnered from this study contribute to the design, optimisation and assessment of diverse engineering applications.

Performance study of novel metal corrosion probes based on the adjust method of series and parallel connections

Rod-type metal corrosion probes based on electromechanical impedance (EMI) technique can quantitatively assess the amount of corrosion, which have a promising application in pipeline corrosion monitoring and have received much more attention. In the field of structural health monitoring, the EMI technique based on series and parallel connections has been widely studied and is very promising, but it is yet to be used in the probe design. In this work, a kind of novel metal corrosion probe with two piezoelectric elements in series and parallel connections was proposed, and its performance was investigated comprehensively by combining theoretical analysis with experiment research. Theoretical models of the proposed probe in the longitudinal vibration mode for both series and parallel connections were established, and verified by the experimental results. Influences of the thicknesses of piezoelectric layer and ceramic layer on the probe performance were analyzed. Artificial quantitative corrosion tests and accelerated corrosion tests were designed to evaluate the quantitative corrosion monitoring capacity. Temperature sensitivity tests were conducted to study the temperature dependence. The wireless impedance measurement was performed to confirm the online monitoring ability. Comparisons for the probe performance between the series and parallel connections were also presented. This work provided a comprehensive understanding for this kind of novel probe, which is beneficial to develop low-cost, high-precision, high-stability pipeline corrosion real-time monitoring technology.

Longitudinal low-frequency vibration control of a propeller-shafting system using a hydraulic leveraged dynamic anti-resonance vibration isolator: A theoretical and experimental study

The longitudinal fluctuating forces of a propeller are a major cause of sound radiation of an underwater vehicle in the low frequency range. A hydraulic leveraged dynamic anti-resonance vibration isolator (HLVI) is proposed to attenuate the longitudinal vibration of a shaft system transmitted to the hull. The semi-analytical model of the shafting system with and without the isolator is set up by employing the frequency response synthesis method, in which the elasticity of the foundation is taken into consideration. Compared to the traditional isolation scheme and DVA, the proposed control scheme will not change the longitudinal effective stiffness and needs a small mass to attenuate the longitudinal vibration of the shafting system. A parametric study was conducted to investigate the key parameters of the isolator and their impact on its isolation performance. An experimental apparatus is set up to validate the isolation scheme. The acceleration frequency response results of the shafting system under axial excitation with both the frequency sweep method and discrete sinusoidal frequencies are presented and discussed. The results indicate that the proposed method is capable of attenuating the corresponding longitudinal vibration of the shafting system.

Experimental investigations of the effects of bending vibrations resonance modes on penetration into granular materials

Inspired by the bending vibration observed in the biological locomotions such as those found in snakes, horned lizards, and sandfish, we have developed a novel vibro probe utilizing bending resonance modes to study the bending vibration effects in assisting penetration into granular materials. This approach contrasts with traditional probes that rely on longitudinal vibrations for penetration. This newly developed probe was used to experimentally investigate the impact of bending vibration in reducing the required penetration force and enhancing the penetration process within granular materials such as lunar or Martian regolith. The bending vibrations were excited by thin piezo patches attached to the probe’s machined surface without increasing the probe’s outside diameter. This simple mechanism enables pushing the whole probe inside the granular materials. Experimental modal analysis was employed to determine the resonance frequencies of the probe. Subsequently, the probe was pushed into granular materials, both with and without the bending vibrations, by a linear actuator. Experimental results indicated that employing bending vibration in one direction led to a reduction in penetration force by up to 27% while utilizing two directions resulted in a reduction of up to 42%. Additionally, when the probe stopped penetrating the soil due to insufficient axial force, bi-directional bending vibration proved more effective in swiftly fluidizing the surrounding soil. These findings highlight the efficacy of bending vibrations in compact subsurface drilling tools.

Understanding the mechanisms behind ultrasonic vibration in resistance spot welding of aluminum and steel

An ultrasonic-assisted resistance spot welding process, which can improve the quality of aluminum/steel spot-welded joints, has been developed. However, the mechanism of the thermal-electrical-mechanical behavior caused by the ultrasonic longitudinal vibration to welding process has not been clarified. In this study, the role and impact mechanisms of ultrasonic longitudinal vibration during the welding process to form joints were confirmed by combining the microstructural characterization of the formed joints with the signal analysis of the process, as well as the analysis of the independent finite element numerical calculation results. Additionally, the interface metallurgical reaction behavior, welding defects, fracture behavior, and joint strength characteristics of ultrasonic-assisted aluminum/steel resistance spot welding joints were comprehensively analyzed, and the results indicated that the sizes of the aluminum/steel nuggets decreased. It could be attributed to the competition among multiple ultrasonic effects. Specifically, ultrasonic vibration decreased the contact resistance between the aluminum/steel sheets, whereas the acoustic cavitation and acoustic streaming effects increased the electrical conductivity of molten steel and thermal conductivity of molten aluminum, respectively. Moreover, ultrasonic vibration promoted the radial creep of molten and near-molten aluminum, which expanded in the effective bonding area between the two workpieces. Furthermore, ultrasonic vibration effectively reduced the thickness of the intermetallic compound layer (<3.0 µm), concurrently inhibited the formation of interfacial welding defects. Finally, the peak tensile-shear load of aluminum/steel joints is significantly increased under multiple ultrasonic optimization mechanisms.

Structural Optimization Study on a Three-Degree-of-Freedom Piezoelectric Ultrasonic Transducer

A three-degree-of-freedom (3-DOF) piezoelectric ultrasonic transducer is a critical component in elliptical and longitudinal ultrasonic vibration-assisted cutting processes, with its geometric structure directly influencing its performance. This paper proposes a structural optimization method based on a convolutional neural network (CNN) and non-dominated sorting genetic algorithm II (NSGA2). This method establishes a transducer lumped model to obtain the electromechanical coupling coefficients (X-ke and Z-ke) and thermal power (X-P) indicators, evaluating the bending and longitudinal vibration performance of the transducer. By creating a finite element model of the transducer with mechanical losses, a dataset of different transducer performance parameters, including the tail mass, piezoelectric stack, and dimensions of the horn, is obtained. Training a CNN model with this dataset yields objective functions for the relationship between different transducer geometric structures and performance parameters. The NSGA2 algorithm solves the X-ke and Z-ke objective functions, obtaining the Pareto set of the transducer geometric dimensions and determining the optimal transducer geometry in conjunction with X-P. This method achieves simultaneous improvements in X-ke and Z-ke of the transducer by 22.33% and 25.89% post-optimization and reduces X-P to 18.97 W. Furthermore, the finite element simulation experiments of the transducer validate the effectiveness of this method.

Dynamic properties of natural fiber-reinforced polymer composite plates and tubes

Thirty-six flax fibre-reinforced epoxy (FFRE) plates with two, three, and four fabric layers and lengths ranging from 160 mm to 270 mm and nine FFRE tubes with a diameter of 60 mm, a length of six times the tube diameter plus an overly of 50 mm with two, three, and four fabric layers were manufactured. One-hundred-eighty impulse excitation tests were conducted on FFRE plates to determine the dynamic properties of the plates in the bending mode, and 91 impulse excitation tests were conducted on the FFRE tubes to determine the dynamic properties of the tubes in the transverse, torsional, and longitudinal directions. FFRE plates showed up to six times larger specific energy capacities compared to counterpart glass fibre-reinforced polymer plates, showing significant potential for FFRE plates to replace the use of GFRP plates where considerable damping of energy is required. The results showed that the damping ratio of the FFRE plates decreased with the increase in layers and natural frequency. For the FFRE tubes, the highest damping ratio belonged to the transverse vibration mode, followed by the torsional or longitudinal vibration modes.

Drilling wells taking into account the dynamic properties of rocks

The application of high-frequency vibrations to a drill bit is a promising means of increasing rate of penetration in deep hard formations. The implementation of such drill bit high-frequency vibrations is possible by installing the cavitation hydraulic vibrator in the drill string in front of the rock-cutting tool. Purpose. Evaluation of resonant modes (frequencies of oscillations) for the dynamic interaction of the mud pressure in the drill string and the drill bit longitudinal vibrations in case of contact with the rock being destroyed while drilling using the cavitation hydraulic vibrator; comparative analysis of the effectiveness of using a high-frequency mechanical vibrator and a cavitation hydraulic vibrator in case of drilling in hard rocks. Methodology. The research is based on a comparative analysis of the amplitudes and power spectral density of mud pressure oscillations of the mud and vibration accelerations in the drill bit cross section of drill string. Findings. The results are presented in the form of amplitude spectra and power spectral densities of mud pressure and vibration acceleration, as well as the dependence of the increase in the rate of penetration on the frequency of forced oscillations of the drill bit. Originality. Taking into account the influence of the cavitation hydraulic vibrator on the drill rig ROP made it possible: - to determine the resonant frequencies of pressure oscillations of the mud of the drilling tool, for the effective removal of drilled rock at the point of its contact with the drilling tool, and the longitudinal vibration accelerations of the drilling tool, to speed up rate of penetration during the construction of a well; - to evaluate the effectiveness of using a cavitation hydraulic vibrator in comparison with a high-frequency mechanical vibrator. For the studied modes of operation of the hydraulic vibrator at values of the cavitation parameter  = 0.19, the well rate of penetration increases by 40 % compared to the traditional rotary method and by 26 % compared to the vibratory hammer. For the cavitation operating mode of the hydraulic vibrator  = 0.41, the increase in the rate of penetration is 62 and 37 %, respectively. At the same time, the operating efficiency of the hydraulic vibrator was ensured at the resonant frequencies of the mud pressure with a frequency of 1,580 Hz at  = 0.19 and 1,980 Hz at  = 0.41. Practical value. For a specific design of the cavitation hydraulic vibrator as part of a drill string, by changing the frequency of the drill bit vibration impact on the rock, resonant frequencies are established that ensure the high ROP of the well.