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In the current paper, the free longitudinal vibration response of axially restrained functionally graded nanorods is presented for the first time based on the doublet mechanics theory. Size dependent nanorod is considered to be made of functionally graded material consist of ceramic and metal constituents. It is assumed that the material properties of the functionally graded nanorod are assumed to vary in the radial direction. The aim of this study is that to investigate the influences of various parameters such as functionally graded index, small size parameter, length of the nanorod, mode number and spring stiffness on vibration behaviors of functionally graded nanorod restrained with axial springs at both ends. For this purpose, Fourier sine series are used to define the axial deflection of the functionally graded nanorod. Then, an eigenvalue approach is established for longitudinal vibrational frequencies thanks to Stokes' transformation to deformable axial springs. Thus, the presented eigenvalue solution method is attributed to both rigid and deformable boundary conditions for the axial vibration of the functionally graded nanorod. With the help of the results obtained with the presented eigenvalue problem, it is observed that the parameters examined cause significant changes in the frequencies of the functionally graded nanorod. [ABSTRACT FROM AUTHOR]

Electronic components assembled in satellites should be able to withstand the vibration, noise, and impact loads generated by space vehicles during launch. To simulate the impact loading in a laboratory environment, a pyroshock test simulates an impact load resulting from explosions during the stage and pairing separation of launch vehicles, which imposes significant stress on the components, potentially leading to failures and damage. To ensure component reliability before the flight model (FM) stage, where components are mounted on the actual launch vehicle and sent into orbit, a pyroshock test is conducted during the qualification model (QM) stage using identical parts and specifications. This process involves measurements of the acceleration induced by pyroshock to calculate the shock response spectrum (SRS) and evaluate the components' reliability against the required SRS to confirm their ability to endure the shock and operate normally in post-tests. The aerospace developer determines the SRS requirements based on the space launch vehicle and the installation location of the electronic components. Configuring a suitable pyroshock test to meet these requirements typically involves extensive trial and error. This study aims to minimize such trial and error by examination of SRS changes through a numerical approach by table structural vibration analysis. The structure is subjected to in-plane impacts using a steel ball via a pendulum method. Various SRS profiles are calculated by test factors such as the weight of the steel ball, the pendulum angle, and the installation position of the test specimen. Furthermore, a genetic algorithm is utilized to derive the optimal test conditions that satisfy the required SRS. An automated pyroshock test system is developed to enhance repeatability and reduce human errors. [ABSTRACT FROM AUTHOR]

Featured Application: Determining Young's modulus is an important step in the analysis of any material that undergoes elastic deformation. A quick estimation of it can be performed using the finite element method (FEM) with the procedure presented in this paper. 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. [ABSTRACT FROM AUTHOR]

Abstract This study aims to potential the potential utilization of nonlinear energy sinks (NESs) for controlling longitudinal vibrations in a double-rod system. The research introduces a longitudinal vibration prediction model for a double-rod system equipped with NESs. The generalized Hamilton principle is employed to derive governing equations of the double-rod system. The longitudinal vibration responses of the double-rod system are numerically solved through the application of Galerkin truncation method. The longitudinal vibration responses of the double-rod system are impacted by NESs, as they yield accurate numerical results. The installation of both NES 1 and NES 2 concurrently is recommended for mitigating the vibration of the double-rod system. Under reasonable single-frequency excitations, modifying the parameters of NESs can significantly alter both the vibration state and magnitudes of vibration in the double-rod system. Furthermore, the synchronous optimization of parameters in NES 1 and NES 2 is crucial for effectively controlling vibrations in the double-rod system. Sensitive parameter areas of NESs provide the possibility of controlling the vibration of the double-rod system by utilizing NESs.

This study aims to potential the potential utilization of nonlinear energy sinks (NESs) for controlling longitudinal vibrations in a double-rod system. The research introduces a longitudinal vibration prediction model for a double-rod system equipped with NESs. The generalized Hamilton principle is employed to derive governing equations of the double-rod system. The longitudinal vibration responses of the double-rod system are numerically solved through the application of Galerkin truncation method. The longitudinal vibration responses of the double-rod system are impacted by NESs, as they yield accurate numerical results. The installation of both NES 1 and NES 2 concurrently is recommended for mitigating the vibration of the double-rod system. Under reasonable single-frequency excitations, modifying the parameters of NESs can significantly alter both the vibration state and magnitudes of vibration in the double-rod system. Furthermore, the synchronous optimization of parameters in NES 1 and NES 2 is crucial for effectively controlling vibrations in the double-rod system. Sensitive parameter areas of NESs provide the possibility of controlling the vibration of the double-rod system by utilizing NESs. [ABSTRACT FROM AUTHOR]

Abstract This study confirmed that the loss tangent (or tangent loss, tan δ) obtained from the longitudinal vibration of a wood log increases with the apparent density difference between sapwood and heartwood, owing to moisture content difference. The reason for this was estimated to be the shear stress occurring when the longitudinal vibration is excited from the calculation of the longitudinal vibration equation for a cylindrical model with different sapwood and heartwood densities. According to the measurement of the vibrational properties of 35 sugi (Cryptomeria japonica) logs with large moisture content variation in the sapwood and heartwood, the tan δ for longitudinal vibration increased compared with that for flexural vibration when the apparent sapwood density exceeded apparent heartwood density, whereas the difference in the specific dynamic Young’s modulus (E/ρ) was small. To discover why tan δ increases, both the axial and shear strain energy were calculated from the numerical solution of the longitudinal vibration of a cylindrical model by only considering the apparent density difference between sapwood and heartwood. It was found that the shear strain energy increases with the apparent density difference. Because it is known from previous studies that tan δ from the shear strain (tan δ S) is larger than that from the axial strain (tan δ A), this study concluded that tan δ increases with the apparent density difference. The ratio of increase of tan δ calculated by the model adequately explaange of the measured tan δ caused by the longitudinal vibration of a sugi log.

This research is concentrated on the longitudinal vibration of a tapered pipe pile considering the vertical support of the surrounding soil and construction disturbance. First, the the pile–soil system is partitioned into finite segments in the vertical direction and the Voigt model is applied to simulate the vertical support of the surrounding soil acting on the pile segment. The surrounding soil is divided into finite ring-shaped zones in the radial direction to consider the construction disturbance. Then, the shear complex stiffness at the the pile–soil interface is derived by solving the dynamic equilibrium equation for the soil from the outermost to innermost zone. The displacement impedance at the top of an arbitrary pile segment is obtained by solving the dynamic equilibrium equation for the pile and is combined with the vertical support of the surrounding soil to derive the displacement impedance at the bottom of the upper adjacent segment. Further, the displacement impedance at the pile head is obtained based on the impedance function transfer technique. Finally, the reliability of the proposed solution is verified, followed by a sensitivity analysis concerning the coupling effect of the pile parameters, construction disturbance and the vertical support of the surrounding soil on the displacement impedance of the pile. [ABSTRACT FROM AUTHOR]

This study confirmed that the loss tangent (or tangent loss, tan δ) obtained from the longitudinal vibration of a wood log increases with the apparent density difference between sapwood and heartwood, owing to moisture content difference. The reason for this was estimated to be the shear stress occurring when the longitudinal vibration is excited from the calculation of the longitudinal vibration equation for a cylindrical model with different sapwood and heartwood densities. According to the measurement of the vibrational properties of 35 sugi (Cryptomeria japonica) logs with large moisture content variation in the sapwood and heartwood, the tan δ for longitudinal vibration increased compared with that for flexural vibration when the apparent sapwood density exceeded apparent heartwood density, whereas the difference in the specific dynamic Young's modulus (E/ρ) was small. To discover why tan δ increases, both the axial and shear strain energy were calculated from the numerical solution of the longitudinal vibration of a cylindrical model by only considering the apparent density difference between sapwood and heartwood. It was found that the shear strain energy increases with the apparent density difference. Because it is known from previous studies that tan δ from the shear strain (tan δS) is larger than that from the axial strain (tan δA), this study concluded that tan δ increases with the apparent density difference. The ratio of increase of tan δ calculated by the model adequately explaange of the measured tan δ caused by the longitudinal vibration of a sugi log. [ABSTRACT FROM AUTHOR]

To complete microinjection as quickly as possible, we have developed Vibratory Microinjection Systems (VMSs) that vibrate a micropipette in its longitudinal direction and can significantly reduce the time needed for pronuclear microinjection compared to ordinary (non-vibratory) microinjection. The longest breakdown of the time is the time required to pierce the cell membrane and the pronuclear membrane simultaneously. Because cytoplasmic microinjection, which pierces the cell membrane alone, is far more difficult and time-consuming than pronuclear microinjection, we next aimed to develop a VMS capable of penetrating the cell membrane instantly. In this new and latest version, two types of ultrasonic-wave vibrators were developed: the first for commercially available micropipettes (Femtotip) and the second for self-made micropipettes. The two vibrators differ only in their airtight structure, where the micropipettes connect to their respective vibrators: a female screw plus O-ring for the first vibrator (VMS6_1) and a silicone-rubber tube for the second (VMS6_2). The tube-type joint used in VMS6_2 only slightly damped or amplified vibrations from the vibrator to the micropipette tip, propagating them much more accurately than the screw-type joint in VMS6_1. In addition, VMS6_2 significantly shortened the time taken to pierce the cell membrane of a fertilized egg: an average of 1.52 s (N = 410) vs. 3.62 s (N = 65) in VMS6_1. The VMS6_2 group achieved a piercing time of zero in 86.1% of the allocated eggs, while only 10.8% of the VMS6_1 group did. In each vibrator, we also compared vibratory microinjection (VM; N = 475) and ordinary microinjection (OM; N = 457), which uses injection pressure in place of vibration. None of the eggs in the OM group achieved the zero-second piercing time. Compared to the OM, the VM group showed a significantly shorter piercing time, 1.80 vs. 10.69 s on average, and a significantly better survival rate, 90.3 vs. 81.8% on average. VMS6_2 not only improved on the already demonstrated superiority of VM to OM but also enabled instantaneous piercing of the cell membrane. [ABSTRACT FROM AUTHOR]

In this study, an analytical-based numerical approach was proposed for the analysis of the free axial vibration of homogeneous and functionally graded rods with varying cross-sectional areas. The proposed approach is based on analytical approximation techniques, such as the Adomian decomposition method, variational iteration method, and homotopy perturbation method. However, the governing equations of the problems solved in this study were variable coefficient differential equations. These equations provide analytical solutions for strictly limited cases. Analytical approximation methods easily handle problems with uniform material properties and constant cross-sections, whereas with varying cross-sectional areas, the analytical integration process becomes a difficult task for the software. If the rod’s material is functionally graded with varying cross-sectional areas, the analytical integration process becomes a cumbersome task. The proposed approach eliminates all difficulties and requires computation within several seconds. The application of this method is straightforward, and the results obtained in this study are in excellent agreement with the solutions provided in the literature.

Electronic components assembled in satellites should be able to withstand the vibration, noise, and impact loads generated by space vehicles during launch. To simulate the impact loading in a laboratory environment, a pyroshock test simulates an impact load resulting from explosions during the stage and pairing separation of launch vehicles, which imposes significant stress on the components, potentially leading to failures and damage. To ensure component reliability before the flight model (FM) stage, where components are mounted on the actual launch vehicle and sent into orbit, a pyroshock test is conducted during the qualification model (QM) stage using identical parts and specifications. This process involves measurements of the acceleration induced by pyroshock to calculate the shock response spectrum (SRS) and evaluate the components’ reliability against the required SRS to confirm their ability to endure the shock and operate normally in post-tests. The aerospace developer determines the SRS requirements based on the space launch vehicle and the installation location of the electronic components. Configuring a suitable pyroshock test to meet these requirements typically involves extensive trial and error. This study aims to minimize such trial and error by examination of SRS changes through a numerical approach by table structural vibration analysis. The structure is subjected to in-plane impacts using a steel ball via a pendulum method. Various SRS profiles are calculated by test factors such as the weight of the steel ball, the pendulum angle, and the installation position of the test specimen. Furthermore, a genetic algorithm is utilized to derive the optimal test conditions that satisfy the required SRS. An automated pyroshock test system is developed to enhance repeatability and reduce human errors.

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.

High-pier railway bridges are mostly applied in mountainous areas. Due to the large spatial flexibility of the high piers under train dynamic loads, especially under braking conditions, the wheel-rail (WR) dynamic interaction may become more intense in the longitudinal direction, which could induce larger deformation and impact on the train-track-bridge (TTB) coupled system. To investigate the dynamic characteristics of such complex and large system during train braking condition, a 3D train-slab track-high pier bridge (TTHPB) coupled dynamics model is established and verified by considering the system longitudinal vibrations and the spatial flexibility of high piers. In this work, the influence of concerned bridge height from 60 to 160 m on the dynamic performances of the TTHPB system under train braking condition is studied. Results indicate that the operation speed has a significant effect on carbody acceleration and WR force. The longitudinal carbody acceleration due to its high-frequency vibration, as well as its noticeable amplitude induced by the long-time frequent braking, should be carefully considered in the evaluation of riding comfort index. The longitudinal dynamic behaviour of the high pier bridge is considerable and should be paid full attention to in bridge design compared with the other two directions. [ABSTRACT FROM AUTHOR]

The present work analytically studies the free longitudinal vibration of nanorods in the presence of cracks based on the surface elasticity theory. To this end, governing equations of motion and corresponding boundary conditions are obtained using Hamilton's principle. Due to considering the surface stress effect, as well as the surface density and the surface Lamé constants, the obtained governing equations of motion become non-homogeneous. The nonhomogeneous governing equations are solved using appropriate analytical methods, and the natural frequencies are extracted. To have a comprehensive research, the effects of various parameters such as the length and radius of the nanorod, the crack severity, the crack position, the type of boundary condition, and the values of surface and bulk material properties on axial frequencies of the nanorod are investigated. Since this work considers the effects of all surface energy parameters, it can be claimed that it is a comprehensive study in this regard. [ABSTRACT FROM AUTHOR]

This manuscript obtained an exact solution for longitudinal vibrating characteristics of generally restrained nanorod structure with multiple internal elastic supports via an improved Fourier series method. Due to the nonlocal elasticity theory, the general boundary restraints have been formulated by introducing artificial springs. Then, classical boundary conditions can be easily realized by setting the restrained stiffness to zero or infinity accordingly. Energy formulation is derived for describing longitudinal vibration characteristics of generally restrained nanorod with multiple internal elastic supports. To improve the differential continuities at the elastically restrained boundary, nonlocal longitudinal vibrating displacement is expanded as the standard Fourier series combined with auxiliary polynomials, which makes the field function sufficiently smooth in the calculation region. By making use Rayleigh–Ritz procedure, the unknown coefficients can be obtained by solving the standard eigenvalue matrix. Then, numerical results are presented and compared with those in the literature to illustrate the reliability and effectiveness of the current model. The influence of parameters of the multiple internal elastic supports, nonlocal structural parameters, and boundary restraints on vibration characteristics are discussed and analyzed. This study provides an effective method for predicting longitudinal vibration characteristics of a generally restrained nanorod with multiple internal elastic supports, in which the nanorod has complex boundary and coupling conditions. [ABSTRACT FROM AUTHOR]

We consider a composite system consisting of two identical straight elastic beams under longitudinal vibration connected by an elastic interface capable of counteracting the relative vibration of the two beams with its shearing stiffness. We construct examples of isospectral composite beams, i.e., countable one-parameter families of beams having different shearing stiffness but exactly the same eigenvalues under a given set of boundary conditions. The construction is explicit and is based on the reduction to a one-dimensional Sturm–Liouville eigenvalue problem and the application of a Darboux's lemma. [ABSTRACT FROM AUTHOR]

This study proposes the use of a novel nonlinear tuned mass damper inerter device in vibration suppression of the ship propulsion shafting system and evaluates its performance. The device consists of an axial inerter and a pair of lateral inerters to create geometric nonlinearity. The system response subjected to propeller forces is determined by using the harmonic balance method with alternating-frequency-time technique and a numerical time-marching method. The force transmissibility and energy flow variables are employed to assess the performance of the device. The results show that the proposed device can reduce the peak force and energy transmission to the foundation while increase the energy dissipation within the device. Its use can lead to an improved vibration attenuation effect than the traditional mass-spring-damper device for low-frequency vibration. The configurations of the nonlinear inerter-based device can be adjusted to obtain an anti-peak at a resonance frequency of the original system, providing superior vibration suppression performance. [ABSTRACT FROM AUTHOR]

This paper presents the experimental investigation results of the use of the vibration method by impulse excitation of free flexural and longitudinal vibrations of composite materials. The purpose of the study is to establish the sensitivity of the method used for defect detection and localization. To realize the objective, rectangular notch-type defects were simulated at different distances and depths. The influence of the location and depth of the artificial cracks on the dynamic properties of the beams was investigated by measuring the natural frequencies of flexural and longitudinal vibrations. The conducted experiments show a change in the dynamic characteristics of the beam depending on the dimensions and location of the defects. [ABSTRACT FROM AUTHOR]

A finite element formulation is developed in this paper to analyze impact-induced waves in a rod collide with a striking mass. The formulation is established based on St. Venant's contact theory. Effects of mass ratios and boundary conditions, whether fixed, free, or elastic, are investigated. Both uniform rods and composite rods are considered. A shortcoming in traditional finite element models is to consider the rod and the struck mass as separate identities that gives inaccurate results for the discontinuity at the arrival of the impact wave. Instead, the proposed model considers the rod and the struck mass as one system that gives extremely accurate corresponding results. Wave propagation, transmission, and reflection from the constraint end and at the discontinuous interface are thoroughly analyzed. Succession collision that may occur between the struck mass and the rod is also investigated. Whenever it is possible, the finite element results are compared with analytical solutions. The analytical solutions are obtained with either the direct mode superposition method (DMSM) or wave theory. The proposed model can be used to model many systems that are subjected to longitudinal impact loadings and for crack detection. The model has the potential to be extended to perform simulation and analysis for many practical applications, like nanostructures under impact loads.

The present work aims at generating a systematic way for longitudinal vibration (LV) analysis of bars (or rods) with arbitrary boundary conditions (BCs) by mixed-type finite element (MFE) method using the Gâteaux differential. Both materials and geometrical properties of the bar are uniform along the longitudinal direction. The problem is reduced to solution of the classical eigenvalue problem in dynamic analysis. The axial (normal) load and the displacement along the bar are the basic unknowns of the mixed element. The element formulation for the shape function must satisfy only C0 class continuity since the first derivatives of the variables exist in the functional. The functional governed with proper dynamic and geometric BCs of the problem. Results of the recommended method are benchmarked and verified via numerous problems present in the literature. The unique aspects of this study and the possible contributions of the proposed method to the literature can be summarized as follows: by using this new functional, displacements and internal force values can be obtained directly without any mathematical operation. In addition, geometric and dynamic BCs can be obtained easily and a field variable can be included to the functional systematically. To examine the effects of BCs on the longitudinal vibratory motion of a uniform elastic bar and to give a better insight into LV analysis of bars with arbitrary BCs, a set of numerical examples are presented.

The longitudinal vibrationnal analysis of an irregular single-walled carbon nanotube (ISWCNT) with elastic boundary restraints along its ends is invistigated in this study. The Flügge’s principle is employed to model the ISWCNT and the wave propagation approach is utilized to evaluate the natural frequncy of longitudinal vibration of ISWCNT. The boundary conditions and governing equations are formulated based on Flügge’s model. An exact solution is presented in the axial direction and the MATLAB R2013a Software is hired to present a numerical solution for the longitudinal vibration. A novel equation of motion and frequancy equation are derived for vibrational analysis of ISWCNT under the elastic-support boundary conditions in the longitudinal direction and the impacts of surface irregularity parameter are investigated to find a better profile for irregularity varation to maximize the vibration stability of ISWCNTs. It is concluded that, the irregular single-walled carbon nanotubes or those whose natural frequencies decrease from the large irregularity parameter to the small irregularity parameter of SWCNTs are not optimum designs to build appropriate nanodevices for various applications. In addition, it is observed that to improve the vibration stability of ISWCNTs, it is better to decrease surface irregularity from the large to the small irregularity parameter. Results of this work can be utilized to provide optimum designs for nanodevice in which ISWCNT is common nanocomposite structural element.

In this study, an Artificial Neural Network (ANN) model is designed for the analysis of the longitudinal free vibration of an axially Functional Graded (FG) bar. The material of the bar is varied from one end to the other end according to power law function. Aluminum and Alumina and the mixture of these two materials are used in the analysis. The radius of the bar is also varied along to the longitudinal direction according to power law function. In addition, the effect of the variation in the slenderness ratio is also investigated. An ANN code is written in Matlab in order to obtain a generalized approach for vibration analysis of the FG bar. In the ANN training, some results of free vibration analysis obtained from the SolidWorks program based on Finite Element Method are used. The predicted values that are not used in the training are also obtained in SolidWorks for comparison. A Matlab program code, which based ANN method is used to find new values to be predicted. The process is also made for comparison with the ANN based Matlab nntool program. When the results obtained from SolidWorks and prepared Matlab code and Matlab nntool are compared, it is seen that the results are in harmony. [ABSTRACT FROM AUTHOR]

Considering that the scraper will produce longitudinal and torsional pendulum vibration when passing through the bending section, and have a great influence on the motion characteristics of the scraper conveyor, this paper studies the longitudinal and torsional pendulum coupling vibration characteristics of the scraper conveyor under the working condition of over-bending section for the first time. Firstly, the simplified model of torsional pendulum vibration of scraper chain system is established based on Voigt model and point-by-point tension method. Then, the change law of scraper group vibration and chain tension under the condition of scraper bending is studied. Thirdly, through the influence area and attenuation characteristics of torsional pendulum vibration, the thumbnail model of torsional pendulum vibration is constructed. Finally, the longitudinal and torsional pendulum coupling vibration dynamic model of the scraper chain system is constructed based on the torsional pendulum vibration abbreviation model, and the overall longitudinal and torsional pendulum vibration characteristics of the scraper conveyor are studied when the scraper is over the bending section. The conclusion of this paper provides a theoretical basis for better understanding the operation characteristics of scraper conveyor in coal mine. [ABSTRACT FROM AUTHOR]

To mitigate longitudinal vibration of long-span railway suspension bridges, a Combined Viscous-Steel Damping System (CVSDS) is put forward in this paper. In the CVSDS, the viscous damper is expected to work under train braking and frequent earthquakes, while the steel damper can resist rare earthquakes. Moreover, a fuse-lock device is proposed to work as the switch between the aforementioned two dampers. The working mechanism of the CVSDS was introduced. The locking function was verified by static test, and the vibration reduction efficiency of the proposed system was validated through numerical method. The results show that the combined system is efficient. [ABSTRACT FROM AUTHOR]

The nonlinear interaction of longitudinal vibration and ultrasound in beams with cracks is investigated. The central focus is on the localization effect of this interaction, i.e., the locally enhanced nonlinear vibro-acoustic modulation. Both numerical and experimental investigations are undertaken. The finite element (FE) method is used to investigate different crack models, including the bi-linear crack, open crack, and breathing crack. A parametric study is performed considering different crack depths, locations, and boundary conditions in a two-dimensional beam model. The study shows that observed nonlinearities (i.e., nonlinear crack–wave modulations) are particularly strong in the vicinity of the crack, allowing not only for crack localization but also for the separation of the crack-induced nonlinearity from other sources of nonlinearity. [ABSTRACT FROM AUTHOR]

A finite element formulation is developed in this paper to analyze impact-induced waves in a rod collide with a striking mass. The formulation is established based on St. Venant's contact theory. Effects of mass ratios and boundary conditions, whether fixed, free, or elastic, are investigated. Both uniform rods and composite rods are considered. A shortcoming in traditional finite element models is to consider the rod and the struck mass as separate identities that gives inaccurate results for the discontinuity at the arrival of the impact wave. Instead, the proposed model considers the rod and the struck mass as one system that gives extremely accurate corresponding results. Wave propagation, transmission, and reflection from the constraint end and at the discontinuous interface are thoroughly analyzed. Succession collision that may occur between the struck mass and the rod is also investigated. Whenever it is possible, the finite element results are compared with analytical solutions. The analytical solutions are obtained with either the direct mode superposition method (DMSM) or wave theory. The proposed model can be used to model many systems that are subjected to longitudinal impact loadings and for crack detection. The model has the potential to be extended to perform simulation and analysis for many practical applications, like nanostructures under impact loads. [ABSTRACT FROM AUTHOR]

The present work aims at generating a systematic way for longitudinal vibration (LV) analysis of bars (or rods) with arbitrary boundary conditions (BCs) by mixed-type finite element (MFE) method using the Gâteaux differential. Both materials and geometrical properties of the bar are uniform along the longitudinal direction. The problem is reduced to solution of the classical eigenvalue problem in dynamic analysis. The axial (normal) load and the displacement along the bar are the basic unknowns of the mixed element. The element formulation for the shape function must satisfy only C0 class continuity since the first derivatives of the variables exist in the functional. The functional governed with proper dynamic and geometric BCs of the problem. Results of the recommended method are benchmarked and verified via numerous problems present in the literature. The unique aspects of this study and the possible contributions of the proposed method to the literature can be summarized as follows: by using this new functional, displacements and internal force values can be obtained directly without any mathematical operation. In addition, geometric and dynamic BCs can be obtained easily and a field variable can be included to the functional systematically. To examine the effects of BCs on the longitudinal vibratory motion of a uniform elastic bar and to give a better insight into LV analysis of bars with arbitrary BCs, a set of numerical examples are presented. [ABSTRACT FROM AUTHOR]

The longitudinal vibrationnal analysis of an irregular single-walled carbon nanotube (ISWCNT) with elastic boundary restraints along its ends is invistigated in this study. The Flügge's principle is employed to model the ISWCNT and the wave propagation approach is utilized to evaluate the natural frequncy of longitudinal vibration of ISWCNT. The boundary conditions and governing equations are formulated based on Flügge's model. An exact solution is presented in the axial direction and the MATLAB R2013a Software is hired to present a numerical solution for the longitudinal vibration. A novel equation of motion and frequancy equation are derived for vibrational analysis of ISWCNT under the elastic-support boundary conditions in the longitudinal direction and the impacts of surface irregularity parameter are investigated to find a better profile for irregularity varation to maximize the vibration stability of ISWCNTs. It is concluded that, the irregular single-walled carbon nanotubes or those whose natural frequencies decrease from the large irregularity parameter to the small irregularity parameter of SWCNTs are not optimum designs to build appropriate nanodevices for various applications. In addition, it is observed that to improve the vibration stability of ISWCNTs, it is better to decrease surface irregularity from the large to the small irregularity parameter. Results of this work can be utilized to provide optimum designs for nanodevice in which ISWCNT is common nanocomposite structural element. [ABSTRACT FROM AUTHOR]

Summary: A novel anaerobic ultrafiltration membrane bio‐fuel cell (UFBFC) was conceptualized to improve the efficiency of wastewater treatment with a reduced footprint and bioenergy recovery. The system with a working volume of 40 L reached a maximum power density of 23.3 mW/m2 while treating synthetic wastewater with initial chemical oxygen demand (COD) of 2026 ± 61 mg/L and 19.1 mW/m2 while treating actual fish processing wastewater with initial COD of 1915 ± 63 mg/L. The average COD removal efficiency of UFBFC was found to be almost similar (>97%) for both types of wastewaters showing the efficacy of the system in real‐life applications comparable to the existing treatment systems. The cost‐effective longitudinal vibrational mechanism (0.25 $/kLD of treated wastewater), with a frequency of 0.5 Hz and an amplitude of 8 mm, revealed superior anti‐biofouling ability for ultrafiltration membrane placed inside the anodic chamber of UFBFC than cost‐intensive conventional techniques (117 $/kLD in conventional MBR with aeration). The capacitor‐based power management circuit improved the maximum normalized energy recovery (58 Wh/m3) of UFBFC by over twice compared to UFBFC when operated with external resistance of 100 Ω (24 Wh/m3). The harvested energy by UFBFC with capacitor‐based power management system thus could successfully compensate the operational power requirement of the system, proving its practical field‐scale applications as an energy‐economic advanced wastewater treatment system. Highlights: Ultrafiltration membrane bio‐fuel cell (UFBFC) for efficient wastewater treatmentCost‐effective longitudinal vibration technique for reduced membrane biofoulingChemical oxygen demand removal efficiency of UFBFC was >97%Capacitor‐based circuit improved normalized energy recovery of UFBFCUFBFC successfully used to treat synthetic as well as fish processing wastewater [ABSTRACT FROM AUTHOR]

Propeller-induced longitudinal vibration resonance in marine propulsion shafting systems causes great harm to the hull structure and is the primary source of shipboard noise. Integrating a friction damper with designed parameters into thrust bearings can prevent these issues. To investigate the performance of the damper-integrated thrust bearing in longitudinal vibration transmission control, an experimental and theoretical study is carried out in a laboratory-assembled test rig, which consists of components similar to the existing marine propulsion system. We developed a prototype of a thrust bearing designed with a friction-damping generation that allows switching from two supporting states, i.e., damper-connected and damper-disconnected states. Furthermore, a nonlinear analysis method for friction dampers is proposed. By this method, the way in which the friction damper changes the dynamic characteristics of the shafting system is analyzed. Based on the test rig, the acceleration frequency response function (AFRF) of the thrust bearing with and without a friction damper is measured. By comparison, the effectiveness of the friction damper is proved. The experimental results show that the friction damper suppresses the shafting longitudinal vibration response in a broadband frequency range and also confirms the stability of the damping effect, which does not change with the shafting rotational speed or static thrust from the propeller. [ABSTRACT FROM AUTHOR]

In this study, the longitudinal vibration of rods with variable cross-sections is studied. For the analytical solution of the problem, a new analytical method based on a recently developed method on the Riccati differential equation is utilized. The governing equation is reduced to Hill's type second-order ordinary differential equation. The transformed equations can readily be solved analytically for various cases according to the method. Seven cases have been considered, and the frequency equations for each case have been obtained. According to the method developed, the problem is solved in the simplest way. By using the present method, the reader can readily decide whether the problem is solved analytically or numerically. The present method can solve the problem of longitudinal vibration of rods having cross-sections of arbitrary shape. Finally, the method is also applied to the longitudinal vibration of stepped rods. Mode shapes are plotted for special values. [ABSTRACT FROM AUTHOR]

Road irregularities induce vertical and longitudinal vibrations of the sprung and unsprung masses, which affect vehicle comfort. While the vertical dynamics and related compensation techniques are extensively covered by the suspension control literature, the longitudinal dynamics on uneven road surfaces are less frequently addressed, and are significantly influenced by the tires and suspension systems. The relatively slow response of internal combustion engines does not allow any form of active compensation of the effect of road irregularities. However, in-wheel electric powertrains, in conjunction with pre-emptive control based on the information on the road profile ahead, have some potential for effective compensation, which, however, has not been explored yet. This paper presents a proof-of-concept nonlinear model predictive control (NMPC) implementation based on road preview, which is preliminarily assessed with a simulation model of an all-wheel drive electric vehicle with in-wheel motors, including a realistic tire model for ride comfort simulation. The major improvement brought by the proposed road preview controller is evaluated through objective performance indicators along multiple maneuvers, and is confirmed by the comparison with two benchmarking feedback controllers from the literature. [ABSTRACT FROM AUTHOR]

The longitudinal vibration of the propulsion shaft system is a challenging issue for marine noise management. We conducted various static and dynamic tests on our built test rig for the shafting system, presenting the results in this paper. By combining experimental data and the particle swarm optimization algorithm, we identified the structural parameters that are difficult to obtain. With these parameters we establish a completed theoretical model of a shaft system containing branches, analyze how and why static thrust affects vibration, and give quantitative results of the force transmissibility. Our work provides a reference for subsequent researchers. [ABSTRACT FROM AUTHOR]

We consider a composite system consisting of two identical straight elastic beams under longitudinal vibration connected by an elastic interface capable of counteracting the relative vibration of the two beams with its shearing stiffness. We construct examples of isospectral composite beams, i.e., countable one-parameter families of beams having different shearing stiffness but exactly the same eigenvalues under a given set of boundary conditions. The construction is explicit and is based on the reduction to a one-dimensional Sturm–Liouville eigenvalue problem and the application of a Darboux’s lemma.

The study of pile-soil dynamic characteristics has always been an important issue in the field of pile foundation engineering. The dynamic characteristics of large diameter piles in transversely isotropic soil under longitudinal vibration load were investigated. Based on the constitutive equation of transversely isotropic material, ignoring the radial displacement of soil, the dynamic equation of soil under axisymmetric condition was established. Combined with boundary conditions to solve the equation, the expressions of soil displacement and shear force on pile side were obtained. Then, based on Rayleigh-Love bar model, the longitudinal dynamic equilibrium equation of large-diameter pile was established. By constructing the boundary condition of transversely isotropic soil and large-diameter pile model, the analytical solution was obtained. The influences of pile-soil parameters on the dynamic response of soil and pile top were analyzed. The degradation analysis of the theoretical solution was carried out, and the theoretical solution was compared with the numerical simulation solution to verify the correctness of the theoretical solution. [ABSTRACT FROM AUTHOR]

This research focuses on the analysis of the model and performance of lightweight metastructures encompassing a distributed array of internal homogenous oscillators, integrated into the host structure to create a single-piece element. This metastructure performs longitudinal vibrations, whose axis is colinear with the direction of the transverse vibration of the internal oscillators. First, the mechanical models of the separate elements of the metastructure and the metastructure as a whole are created and considered. The first modal frequencies of longitudinal vibrations of the metastructure with blocked and free internal oscillators are tuned to the first modal frequency of transverse vibration of one internal oscillator, yielding the optimal number of internal oscillators for this to be achieved, which is a new result for the proposed design. This theoretical result is then checked experimentally with the metastructures produced by 3D printing technology, comprising a different number of internal oscillators, all of which have the same natural frequency. Besides validating the theoretical results, experimental investigations with blocked and freely vibrating internal oscillators of the constant natural frequency are used to explore other performance characteristics, such as the width of the regions where the reduced amplitude is achieved. Finally, based on the theoretical and additional numerical results, the internal oscillators are modified in two ways, which is an original approach: their natural frequency is increased linearly and nonlinearly along the metastructure in accordance with the previous new theoretical results. The benefits of such new redesigns for the multi-modal performance characteristics of the metastructure are discussed.

The pulse force generated by the propeller excites the hull through the propulsion shafting system, which is the primary source of vibration and noise of ships. In order to control the transmission of longitudinal vibration of ship shafting, a multimodal dynamic vibration absorber (MDVA) with broadband vibration control performance is proposed. A magnetorheological elastomer (MRE) was prepared and used as an elastic element to construct a semi-active dynamic vibration absorber (SDVA), designed spiral flexible springs and embedded SDVA into the proposed MDVA. An equivalent propeller propulsion shaft system model was established, and its first three longitudinal vibrations were controlled based on the MDVA. Furthermore, the stiffness and damping of the MDVA were optimized by fixed point theory. A design scheme for the MDVA considering the changes in oil film stiffness of thrust bearings under different propeller speed conditions was proposed. The results indicate that the MDVA has excellent vibration transmission control performance at the first three natural frequencies. The proposed MDVA also has a broader frequency band for controlling vibration near first-order resonance than the traditional single degree of freedom DVA, which has excellent vibration control performance under variable speed conditions. [ABSTRACT FROM AUTHOR]

• Multiscale slopes of operating defection shapes (MSODSs) are used for damage detection of bars. • Two schemes of local fitting are proposed to reconstruct MSODSs under virtual intact statuses of bars. • By relying on differences between measured and locally fitted MSODSs, two individual damage indices are established. • The applicability of the proposed schemes is experimentally validated by detecting a two-sided notch in a bar. Longitudinal operating deflection shapes (ODSs) of a bar can be measured by three-dimensional laser scanning. The difference between slopes of ODSs (SODSs) under damaged and intact statuses of the bar can be used to indicate and locate the damage. This study inspects ODSs in a multiscale manner, whereby multiscale ODSs (MODSs) and multiscale SODSs (MSODSs) are produced. Noise interference can be eliminated by increasing scale parameters to their satisfying values. In addition, two schemes of local fitting are applied to measured MODSs to generate locally fitted MSODSs under virtual intact statuses of the bars. By relying on differences between measured and locally fitted MSODSs, two individual damage indices (DIs) are established, namely the type-I DI and the type-II DI, in which damage-induced peaks can indicate and locate the damage. The capability of the two schemes of local fitting is theoretically verified and experimentally validated by detecting two-sided notches in bars. [ABSTRACT FROM AUTHOR]

According to the theories of wave propagation in visco-elastic continuum and Rayleigh-Love rod, a simplified model in axisymmetric conditions for the longitudinal vibration of large-diameter pipe pile (LDPP) in radially heterogeneous surrounding soil with viscous damping is presented. The relevant analytical solution for dynamic impedance at pile head is derived by using complex stiffness transfer method, which is also validated via independent comparisons with previous solutions. Besides, parametric analyses are carried out to reveal both the radial heterogeneity of surrounding soil and the lateral inertia effect of pile shaft on the dynamic impedance of LDPP. The obtained analytical solutions are suitable for the longitudinal vibration issues of floating LDPP in visco-elastic surrounding soil with radial heterogeneity, which can be conveniently degenerated to describe the longitudinal vibration of a floating solid pile in soil with radial heterogeneity as well as a floating LDPP or solid pile in radially homogenous soil. [ABSTRACT FROM AUTHOR]

The longitudinal harmonic vibrations found in the suspended monorail train (SMT) seriously affected the ride quality and dynamic behaviour. In this work, the experimental and simulated analyses are carried out to reveal the essential phenomenon, occurring mechanism and possible solutions to this issue. Firstly, the ride quality and vibration transmission of the tested SMT system are investigated. It is found that the longitudinal vibrations with the frequency of 2.7Hz occur to the carbody, bogie frame and suspension of the train system. Due to the secondary suspension is lower than the gravity center of the bogie frame, the bogie pitch motion with low damping ratio can be easily excited. The longitudinal components of the bogie pitch motion will transfer to the carbody and wheelset through traction rod and primary suspension, respectively. After that, the multibody dynamic model of a suspended monorail train is developed. Based on the numerical model, some parametric simulations, e.g. rubber stiffness, traction rod height and secondary damping, etc., are carried out to propose solutions to relieve the longitudinal vibrations. Finally, the field tests for the SMT arranging the longitudinal dampers are conducted to verify its improvement to longitudinal vibrations. [ABSTRACT FROM AUTHOR]

The accurate understanding of the behavior and analysis of the structures is necessary to appropriate design of them. Over the past decades, various methods have been proposed for the analysis of structures that each of them include some deficiencies. The peridynamic is a new method for solving the problems. This method overcomes the deficiencies and limitations of conventional methods such as the finite element method due to its unique capabilities. Nowadays, it uses as a powerful method to solve problems. After the proposition of peridynamic theory in 2000, various problems have been solved. However, very limited work has been done in the solving longitudinal vibration of axial members and modeling of lattice structures. In this paper, the behavior of this type of members was examined by the peridynamics method and its capability to take into account the static and dynamic loading, as well as temperature variations, was shown using MATLAB software. The peridynamic results are in good agreement with analytical results. Also, for certain states of the problem, it is impossible or difficult to find an answer by analytical methods or other methods, while using the peridynamic method can easily be answered. Finally, the peridynamic model has been extended to truss modeling and the ability of this method to analyze any types of trusses were shown.

To reduce the transmission of shafting longitudinal vibration in surface ships, a design of thrust bearing integrated with internal disc springs is proposed and the longitudinal vibration characteristics of the shafting are studied. According to the structural characteristics of thrust bearing and the deformation characteristics of disc springs, the specific size and combination forms of disc springs in the thrust bearing are designed, and the effective disc springs schemes are achieved according to the static and dynamic design requirements. With the integration of the disc springs into the thrust bearing, the peak of longitudinal displacement response at the base of thrust bearing can be reduced by 10 dB by two schemes of disc springs. The proposed design can effectively suppress the transmission of shaft longitudinal vibration to the hull, which has engineering significance for the longitudinal vibration control of the shafting of the surface ship. [ABSTRACT FROM AUTHOR]

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• Longitudinal vibrations in two directions of a viscoelastic growing rod are analysed. • Exact and approximate WKB solutions for the single mode are obtained. • Both damped and undamped vibrations are investigated. • Numerical analyses are conducted for a coupled multi-mode system. • The notion of "critical damping" for a growing rod is introduced. Free longitudinal vibrations of a viscoelastic growing rod in both lateral and axial directions are considered in terms of the classical model. Exact and approximate WKB solutions are obtained for the single-mode case for both undamped and damped vibrations of the rod. The coupled multi-mode system is investigated numerically. It is shown that because of the rod's growth in the axial direction, the amplitude of vibration tends to increase, and vice versa, because of the rod's growth in the lateral direction its amplitude tends to decrease. The notion of "critical damping" of a growing rod is introduced. At critical damping, the vibration amplitude remains constant. It is found that because of initial excitation of the lower-order vibration modes, the coupled higher-order mode amplitudes decrease with the growth of the mode number. However, with the growth of the mode number , the initial excitation of higher-order modes in the rod's vibrations induces an effective amplitude increase in the lower-order modes. [ABSTRACT FROM AUTHOR]