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This paper describes the use of non-destructive methods to assess the mechanical properties of structural glued laminated timber (GLT) made from poplar. The longitudinal vibration method (LVM) and the transformed section method (TSM) were considered. Full-scale tests were also performed to determine the most relevant mechanical properties of 18 beams, namely modulus of elasticity and bending strength. In addition, the bonding performance of each beam was checked by delamination and shear strength tests. Detailed analysis of the results was performed and combined with Levene and Tukey tests. The accuracy of the two non-destructive test methods was evaluated by linear regression analysis. The TSM showed stronger correlations with modulus of elasticity and shear strength. Slightly lower values were obtained using the LVM. A strength class of GL24c can be assigned for GLT made from poplar, with lower properties at the inner lamellas.

Traditional power ultrasonic vibration systems can process one object at one time and only have one output. A directional converter of longitudinal vibration with multiple outputs composed of an input rod, a hemispherical vibrator, and three output rods is presented. The frequency equation used in the design is derived with free edges at the input and output ends of the converter, as well as the continuity of displacements, forces, and angles of rotation at each component junction. The resonant frequencies of three fabricated converters designed using the proposed method are in good agreement with those from the finite element method and also with tested values. With the input end of the converter joined with a piezoelectric transducer with a resonant frequency of 19.8 kHz, the longitudinal vibration modes and displacement amplitudes of the output ends of the three converters at their resonant frequencies are tested. The results show that longitudinal vibration can be transferred from the input end to the multi-output ends through the converter. Furthermore, there exists a linear relationship between the excitation voltage and the displacements of each output of the converter.

Traction systems are a good choice for high-rise lift systems, especially in deep wells. With increasing lift depth and weight, rope-guided traction systems have become an essential design methodology in the mine lift field. In this paper, a comprehensive mathematical model is established to simulate the dynamical responses of a rope-guided traction system with different terminal tensions acting on the compensating rope. The results and analysis presented in this paper reveal dynamical responses in terms of longitudinal and transverse vibration. Additionally, a wide range of resonances occurs in the target system. Differences in the dynamical responses between a traditional traction system and tensioned traction system are analysed in detail. Through comparison and analysis, it is determined that terminal tension plays an important role in the suppression of longitudinal vibration in a system. However, changes in the amplitude of longitudinal vibration are independent of terminal tension, which only affects longitudinal elastic elongation and does not affect the basic shape of longitudinal and transverse vibrations. Based on this analysis, it can be concluded that longitudinal vibration suppression can be achieved by applying proper tension on the compensating rope to ensure that it reaches a tensioning state. Continuing to increase terminal tension is not beneficial for the vibration suppression of a system. The results presented in this paper will serve as a valuable guide for the design and optimisation of traction systems.

Mekanik titreşim konusu mühendislik uygulamalarındaki en önemli konulardan biridir. Özellikle, mekanik bileşenin veya sistemin dizayn ve test aşamaları boyunca titreşim dikkate alınmalıdır. Bir titreşim konusu teorik olarak çalışıldığında, özdenklem ya da diferansiyel denklem olarak isimlendirilen hareket denklemi elde edilir. Hareket denklemi, çözümü düşünülen cismin titreşim davranışını verir. Sürekli bir sistemin titreşimi çalışıldığında, sonuç olarak ‘transcendental denklem’ elde edilir. Transcendental denklemin çözümü klasik yöntemlerle mümkün değildir. Bu çalışmada, bir ucu sabitlenmiş ve diğer ucunda kütle taşıyan bir çubuğun boyuna titreşiminden elde edilen transcendental denklemin çözümü sunuldu. Bu amaçla, bir YSA modeli oluşturuldu ve bu modelde kullanılmak üzere veriler hazırlandı. Modeldeki nöronlar, giriş verileri, eğitim fonksiyonlarının etkileri incelendi. Bununla birlikte, YSA verileri kullanılarak çoklu regresyon modelleri geliştirildi ayrıca her mod için ANN analizi ile doğal frekans formülasyonları elde edildi. Sonlu elemanlar modal analizi ANSYS kullanılarak yapıldı. YSA ve ANSYS’ten elde edilen sonuçlar analitik çözümle karşılaştırıldı ve hepsinin sonuçlarının oldukça yakın oldugu ortaya çıktı., Study of mechanical vibration is one of the major issues in engineering applications. Especially, during the design and test stages of a mechanical component or system, vibration must be considered. When a vibration issue is studied theoretically, a differential equation called characteristics equation or equation of motion (EOM) is obtained. A solution of EOM gives vibrational behavior of an object considered. When vibration of a continuous system is studied, a transcendental equation is finally obtained, whose solution by classical methods is not possible. In this study, the solution of the transcendental equation which is derived from the longitudinal vibration of a bar with one end fixed and a mass at the other end was presented. For this purpose, an ANN model was constructed and the datasets were created for the ANN model. The effects of the number of neurons, input data, and training function on the model were examined. In addition, multiple regression models were developed using the ANN data also natural frequency formulation was obtained by ANN analysis for each mode. A finite element modal analysis was performed by ANSYS software. The results obtained by ANN and ANSYS were compared with analytic calculation and it was shown that they were in enough agreement.

Shafting vibration can also produce bearing forces. The purpose of this study is to investigate the characteristics of such bearing forces. First, a new propeller bearing force prediction model tha...

In this study, the compensating ropes and tension device on elevator vibration, as well as the car and hoisting ropes between the top of the car and traction wheel in a high-speed traction elevator lift system, were considered a system to analyze the effect of traction force. In addition, the vertical vibration of the system was used as the research object. The influence of hoisting ropes quality was measured, and a time-varying dynamic model with variable mass, damping, and stiffness for the car–hoisting rope system was constructed from the perspective of time-varying structural mechanics. Simultaneously, the ideal running state of the elevator, which is fitted by using the quintic polynomial, was utilized as input motion parameter. Then, a case study was conducted by using the fine integral method for the vertical vibration dynamic model of the car–hoisting rope system. Finally, the nonlinear vertical vibration response of the car–hoisting rope system during the operation of high-speed traction elevator was obtained. Results indicated that the influence of traction force, compensating ropes, and tension device on the vibration of the car–hoisting rope system when the elevator is in the upward process is greater than when the elevator is in the downward process. In addition, the low quality of the elevator car leads to the production of strong longitudinal vibration. The linear density of the hoisting ropes has a slight effect on the longitudinal vibration of elevator.

Longitudinal vibration of non-uniform rod has been of great significance in various engineering occasions. The existing works are usually limited to the certain area variation and/or classical boundary condition. Motivated by this limitation, an efficient accurate solution is developed for the longitudinal vibration of a general variable cross-section rod with arbitrary boundary condition. Displacement function is invariantly expressed as the summation of standard Fourier series and supplementary polynomials, with an aim to make the calculation of all derivatives more straightforwardly in the whole solving region [0, L]. Energy principle is employed for system dynamics formulation, with the elastic boundaries considered as potential energy stored in the restraining spring. Arbitrary cross-section area variation is uniformly expanded into Fourier series. Numerical examples are presented for the natural frequency and mode shapes of non-uniform rod of free and clamped boundary conditions and compared with literature data. Results show good agreement with the previous analytical solutions. Influence of cross section area variation on vibration characteristics of non-uniform rods is then studied and discussed. One of the most advantages of the proposed model is that there is no need to reformulate the problem or rewrite the codes when the cross-section area distribution and/or boundary conditions change arbitrarily.

There was a previous study to derive the sound absorption coefficient of the powder layers comprising powder particles with a diameter of a few tens of μm. According to this previous method, the impact of air viscosity at the boundary layer generated in the pores between the powder particles is neglected. Therefore, precision is not guaranteed when the particle diameter is relatively large or when the density is relatively high. In the present study, to obtain the sound absorption coefficient of the powder layer more accurately, in addition to the above-described longitudinal vibration mode, the energy damping property of the boundary layer viscosity was calculated using the transfer-matrix method. As a result, when the longitudinal vibration mode and boundary layer viscosity were considered, the theoretical value tended to be closer to the experimental value than when only the longitudinal vibration was considered.

The impact of longitudinal vibration on cross-bridge attachments between myofilaments was investigated in single fibres and intact muscle. Sinusoidal length vibration (frequency 50 Hz, amplitude 5% of fibre length) reduced active force by 40% when fibres were activated by elevation of [Ca2+], but did not alter the force when fibres were in rigor state. When vibrated for 30 min in rigor at pH 5.5 and 38 °C (PSE conditions), the lateral shrinkage of the fibres was significantly reduced, suggesting a potential positive influence of vibration on water-holding capacity. In whole muscle incubated at 38 °C until 8 h post mortem, the progress of rigor onset was accessed by measuring the increase in muscle stiffness. Vibration applied 3-5 h post mortem postponed rigor development, but did not have significant influence on water-holding capacity compared with non-vibrated conditions. In conclusion, the results suggest that muscle vibration can be a future technique to delay rigor development and prevent muscle fibre shrinkage and PSE development after slaughter.

In order to reduce the oil consumption, the vehicle in the process of in-situ shift should be quick enough, but the vibration and shock of the vehicle will be deteriorate. Then the effect of a novel semi-active hydraulic damping strut (HDS) on vehicle shock and vibration in the process of in-situ shift quickly in this study is analyzed. Firstly, the shift shock is analyzed from the driver system, and the powertrain mounting system (PMS) is regarded as the object to be optimized in this study. Then the 13 degree of freedoms (DOFs) vehicle dynamic model (VDM) with semi-active HDS is presented in this paper. The excitation force in the process of quick in-situ shift is identified, and the evaluation indexes (EIs) are reduced with semi-active HDS introduced. Finally, the experiments are carried out to validate the effect of the semi-active HDS on vehicle longitudinal vibration and shock in the process of quick in-situ shift, and the results show that the acceleration of the seat rail and steering wheel are reduced to a great extent. Different shift time is discussed and the results show that we can reduce the shift time to save the oil with semi-active HDS introduced.

A novel two-DOF ultrasonic motor based on longitudinal and bending-bending vibrations was introduced in this paper. This proposed two-DOF ultrasonic motor is potential in driving the hyper-redundant manipulator, which would significantly decrease the number of the driving motor, thus reduces the cost of the manipulator. The structure and the working principle of the novel ultrasonic motor was illustrated, the driving mechanism of the proposed ultrasonic motor to drive the hyper-redundant manipulator was proposed. The longitudinal vibration was used to drive the proposed motor runs along the manipulator, and bending-bending vibrations were utilized to rotate the joint of the manipulator. Then, the finite element method was used to design and optimize the configuration of the proposed ultrasonic motor. The longitudinal and orthogonal bending-bending vibrations were obtained. This project provides a new idea for optimizing the hyper-redundant manipulator from the perspective of motor, and provides basis for the two DOF ultrasonic motor to drive the hyper-redundant manipulator.

In this paper, for studying the influence of the randomness of structural parameters of high-speed elevator lifting system (HELS) caused by manufacturing error and installation error, a continuous time-varying model of HELS was constructed, considering the compensation rope mass and the tension of the tensioning system. The Galerkin weighted residual method is employed to transform the partial differential equation with infinite degrees of freedom (DOF) into the ordinary differential equation. The five-order polynomial is used to fit the actual operation state curve of elevator, and input as operation parameters. The precise integration method of time-varying model of HELS is proposed. The determination part and the random part response expression of the longitudinal dynamic response of HELS are derived by the random perturbation method. Using the precise integration method, the sensitivity of random parameters is determined by solving the random part response expression of time-varying model of HELS, and the digital characteristics of the acceleration response are analyzed. It is found that the line density of the hoisting wire rope has the maximum sensitivity on longitudinal vibration velocity response, displacement response and acceleration response, and the sensitivity of the elastic modulus of the wire rope is smallest.

The bending, stability (buckling) and vibration response of nano sized beams is presented in this study based on the Eringen's nonlocal elasticity theory in conjunction with the Euler-Bemoulli beam theory. For this purpose, the bending, buckling and vibration problem of Euler-Bernoulli nanobeams are developed and solved on the basis of nonlocal elasticity theory. The effects of various parameters such as nonlocal parameter eoa, length of beam L, mode number n, distributed load q and cross-section on the bending, buckling and vibration behaviors of carbon nanotubes idealized as Euler-Bernoulli nanobeam is investigated. The transverse deflections, maximum transverse deflections, vibrational frequency and buckling load values of carbon nanotubes are given in tables and graphs.

Deep brain stimulation (DBS) is an effective treatment for Parkinson's disease. The insertion of brain tissue is an important procedure that affects the whole operation and the sequela. During the insertion process, the friction between the tissue and the needle shaft is the main factor affecting the degree of tissue damage and the accuracy of target location. Vibration-assisted needle insertion has been shown to reduce friction during needle insertion into biological tissue. LuGre model is a friction model that includes coulomb friction and viscous friction between two contact surfaces and accurately describes the Stribeck effect. This paper studies the influence of longitudinal vibration on the friction force during needle insertion. Based on LuGre model, the influence of longitudinal vibration parameters on friction force is discussed. Through experiments on porcine brain tissue and gel phantom, the friction force during insertion and the positive pressure of tissue against the needle under different vibration parameters were investigated. The experiment showed that the vibration can change the friction force by affecting the equivalent friction coefficient and the positive pressure of tissue against the needle. The equivalent friction coefficient showed a specific trend with the change of vibration parameters, while the positive pressure does not change with the vibration parameters.

In this paper, the longitudinal vibration model of the wire rope lifting equipment is established, and its vibration characteristics are analyzed. An intelligent active damping device based on the displacement of the active guide wheel is designed. By changing the phase of the reflection wave of the original vibration, to achieve the purpose of vibration reduction. The effects of the designed devices and methods were analyzed through simulation experiments.

The relations from which Young's modulus may be computed from mechanical flexural and longitudinal resonance frequencies have been established by an empirical method using two sets of steel bars. Both sets contained rectangular and cylindrical specimens. For longitudinal vibration of cylindrical specimens, the agreement between the empirical curves and Bancroft's corresponding theoretical relation was within experimental error if Poisson's ratio for both sets is taken to be 0.292. For flexural vibrations, the agreement between the empirical curve and the corresponding theoretical relation developed by Pickett is also within experimental error for about the same value of Poisson's ratio for the rectangular specimens of both sets; but for cylindrical specimens, the empirical values are somewhat lower than those predicted by the theory.

As an illustration of a set of two linear hyperbolic partial differential equations, we consider first longitudinal vibration in a bar, and second transverse vibration in a string. We begin by deriving the equations that govern these two cases of vibration, which are similar in form. We examined the coefficients in these equations in Chapter 7 and established that the system is hyperbolic. We write the differential equations in the characteristic directions, and both determine and examine the solution.

A study on longitudinal vibration of a pile with variable sectional acoustic impedance subjected to arbitrary form of external excitation is conducted. The analytical solution of transfer function is primarily solved by Laplace transform, and then its corresponding impulse response function is solved by residue method of inverse Laplace transformation. With impulse response function, the analytical solution of response at pile top can be obtained by convolution calculation, which overcomes the limit of previous analytical solutions subjected to prescribed time-harmonic load. The accuracy of presented solution is verified by compared with existing solutions subjected to semi-sine excitation and low-strain test of model piles. To take advantage of presented solution, this paper also proposes a case study of imposed excitation considering superimposed high-frequency interference component, and some conclusions derived from this case can provide practical guidance for engineering implementation.

With the blowout of electric vehicles recently, the key parts of the electric vehicles driven by in-wheel motors named the electric wheel system become the core of development research. The torque ripple of the in-wheel motor mainly results in the longitudinal dynamics of the electric wheel system. The excitation sources are first analyzed through the finite element method, including the torque ripple induced by the in-wheel motor and the unbalanced magnetic pull produced by the relative motion between the stator and rotor. The accuracy of the finite element model is verified by the back electromotive force test of the in-wheel motor. Second, the longitudinal-torsional coupled dynamic model is established. The proposed model can take into account the unbalanced magnetic pull. Based on the model, the modal characteristics and the longitudinal dynamics of the electric wheel system are analyzed. The coupled dynamic model is verified by the vibration test of the electric wheel system. Two indexes, namely, the root mean square of longitudinal vibration of the stator and the signal-to-noise ratio of the tire slip rate, are proposed to evaluate the electric wheel longitudinal performance. The influence of unbalanced magnetic pull on the evaluation indexes of the longitudinal dynamics is analyzed. Finally, the influence of motor’s structural parameters on the average torque, torque ripple, and equivalent electromagnetic stiffness are analyzed through the orthogonal test. A surrogate model between the structural parameters of the in-wheel motor and the average torque, torque ripple, and equivalent electromagnetic stiffness is established based on the Bp neural network. The torque ripple and the equivalent electromagnetic stiffness are then reduced through optimizing the structural parameters of the in-wheel motor. It turns out that the proposed Bp neural network–based method is effective to suppress the longitudinal vibration of the electric wheel system.

In this paper a new non-iterative computational technique referred to as the symbolic-numeric method of initial parameters (SNMIP) is proposed. The SNMIP represents a modification of the iterative numeric method of initial parameters in differential form known in the literature. The SNMIP is applied to study free vibrations of Euler-Bernoulli axially functionally graded tapered, stepped, and continuously segmented rods and beams with elastically restrained end with attached masses. Both the longitudinal vibration of rods and transverse vibration of beams are considered. The influence of the attached masses and springs on the natural frequencies of vibration of axially functionally graded rods and beams is examined. The validity and accuracy of the method are proven through the comparison with the known results in the available literature.

In order to study the longitudinal vibration law of a resilient wheel under the adhesion limit of different working conditions, two longitudinal vibration models of the resilient wheel of a motor vehicle are established, and the vibration laws and influencing factors of the resilient wheel under different operating conditions are studied by simulation. The model of the resilient wheel under low-speed driving and low adhesive operating conditions is established based on the Fastsim wheel/rail contact theory, and the other high-speed model of the resilient wheel is established by considering adhesion curve negative slope characteristics based on the Polach wheel/rail contact theory. The results show that at low-speed driving conditions, the longitudinal vibration of the resilient wheel is more violent than that of the solid wheel, and the sliding vibration of the resilient wheel at the adhesion limit is far greater than the nonadhesion limit at low-speed driving conditions. When the rail surface is polluted and the adhesion coefficient is low, with the speed increasing to 80 km/h, stick-slip vibration occurs on the resilient wheel due to the increased vibration between the wheel rim and the wheel hub. Under high-speed conditions, owing to the negative slope characteristic of the adhesion curve, the wheel adhesion recovery time decreases with the reduction of driving torque. The amplitude of vibration for the above two conditions increases with the increase in the stiffness of the motor boom and the longitudinal stiffness of the primary suspension. With the increase in the value of the radial stiffness and torsional stiffness of the resilient wheel, the vibration amplitude of the resilient wheel becomes smaller or suppressed. The vibration of the resilient wheel is transmitted to the frame through the primary suspension, which has little effect on the vibration of the vehicle body.

This study developed to solve the problem of prediction of the natural frequencies of free vibration for laminated beams. The study presented the natural frequencies of composite beams with four layered and different boundary conditions. In each boundary condition, two cases are assumed: movable ends and immovable ends. Numerical results are obtained for the same material to demonstrate the effects of the aspect ratio, fiber orientation, and the beam end-movements on the non-dimensional natural frequencies of beams. Two aspect ratios are given in the numerical results, one is for relatively short-thick beams, while the other is for slender beams. It was found that the results of the non-dimensional frequencies obtained from the short-thick beams are generally much less than those obtained from the other slender beams for same fiber orientation and generally, the frequencies of longitudinal vibration increase as the aspect ratio increased. It was also found the values of the non-dimensional frequencies of the transverse modes are not affected by the longitudinal movements of the ends since these modes are generated by lateral movements only. However, the values of the natural frequencies of longitudinal modes are found to be the same for all beams with movable ends since they are generated by longitudinal movements only.

Non-destructive techniques (NDTs) are well suited for rapid estimation of timber properties, but NDT results are affected by several factors, the most important of which is the moisture content (MC) of wood. Much of the research in this context was limited to ultrasound measurement of a few wood species, mainly to Norway spruce. The present paper investigates the MC influence on the NDT results obtained by instruments based on ultrasound (two devices), impact stress waves (one device) and longitudinal vibrations (two devices). A hundred large cross-section specimens of four timber species were tested, namely: radiata pine, Scots pine, Salzmann pine and maritime pine. The influence of MC on velocity was found to be stronger below the fiber saturation point (FSP) than above FSP. MC adjustment factors below FSP are proposed for these wood species.