TRANSVERSE VIBRATION of the serpentine belt is effective at noise and durability of it. Therefore, understanding of this phenomenon and studying effective parameters can be used in the process of reducing belt noise and increasing life time. In this paper, TRANSVERSE VIBRATION of serpentine belt is measured experimentally and analyzed. In the implementation test steps, the displacement of the belt in two positions has been measured. Then, the time signals were transformed to frequency domain. It is derived and observed that the belt VIBRATION is synchronous with engine speed, accordingly order analysis is selected to analysis the VIBRATION signal. Results show that the natural frequency of serpentine belt in the region between A/C compressor and crankshaft pulley changes due to A/C compressor loading, but this parameter is not affected by engine load variations. In the area between automatic tensioner and idler, natural frequency is constant regardless of A/C compressor on-off condition and engine load changing. In all engine rotating speeds, the dominant frequencies are highly closed to the natural frequencies. In some engine speeds, VIBRATION amplitude is high and the frequency of these points are proportionally equal to 2, 3, 4 and other orders of engine speed.

The dimensionless equations of motion are derived based on the Timoshenko beam theory to study the TRANSVERSE VIBRATION of beams without further usage of any approximate method. The exact closed form characteristic equations are given within the validity of the Timoshenko beam theory for beams having various boundary conditions. Accurate Eigen frequency parameters are presented for a different length to height ratio for each case. The exact closed form mode shapes related to deflection, slope due to bending and stress resultants are also presented and illustrated for some cases. The modal tests are performed for beams with clamped-Free and Free-Free boundary conditions. Finally, the effect of boundary conditions, length to height ratio on the eigenvalues parameters and vibratory behavior of each distinct case are studied. Validity of the derived closed form characteristic equations are checked through comparison of numerical solutions with the available results. It is believed that in the present work, the exact closed form characteristic equations and their associated Eigen functions, except for the beams with simply supported ends, for the rest of considered cases are obtained for the first time.

Modeling and analysis of complicated truss arch bridges are very time consuming process. In this paper, for more convenient modeling and reduction of analysis time, the complicated truss arch bridges are simulated to the continuum curved beam elements. As a matter of fact, the three dimensional body of a truss bridge is modeled based on the equations governing the out of plane performance of a curved beam. To this end, a new mixed finite element formulation (stiffness-softness) is presented using weighted residual method. In order to verify the accuracy of the present method, the TRANSVERSE VIBRATION of three truss arch bridges is investigated under a specific time-history. The results are comparable with those obtained from more exact 3D models simulated with SAP 2000 general purpose software, regarding the acceleration and displacement response. Furthermore, in the proposed method the number of elements is significantly less than complicated 3D models, leading to more suited initial design.

In this paper, in order to analyze the TRANSVERSE VIBRATION of a uniform Bernoulli-Euler beam containing one single edge crack, a new continuous model is proposed for the cracked section. To this end, by using the fracture mechanics, the crack is modeled as a continuous disturbance in the stress and strain fields. By applying the Hamilton’s principle, the equation of motion and the corresponding boundary conditions of the system are derived. The resulting equation is solved by the Galerkin method, and the natural frequencies and mode shapes are obtained. In order to consider the opening and closing effects of the crack, the stiffness at the crack location is modeled by a bilinear function. The results show that the changes in VIBRATION frequencies for a breathing crack are smaller than ones caused by an open crack. The results have been validated by the experimental and theoretical data reported in the previous studies. There is a good agreement between the results obtained through the proposed method and those obtained from the reported experimental data. This agreement shows that present model is more accurate than the previous ones, and it can predict the VIBRATION behavior of beams more precisely.

This work focuses on the dynamical behavior of carbon nanotubes, including VIBRATION, wave propagation and fluid-structure interaction. In the present research, TRANSVERSE VIBRATION of nano fluid conveying carbon nanotubes is investigated. To this end, based on the nonlocal and strain-inertia gradient continuum elasticity theories and by using rod and Euler-Bernoulli beam models, the system’s dynamical behavior is modeled and then, the governing equation of motion is solved and discretized by applying the weighted-residual Galerkin approximate method. Moreover, effect of considering nano-scale fluid flowing through the nanotube, the boundary conditions, the different elastic mediums and the van der Walls interaction between the layers of multi-walled carbon nanotubes on the natural frequencies, critical velocities and stability of the system are considered. The results show that the passing fluid flow and the axially moving of nanotube decrease the system’s natural frequencies especially for nanotubes with large internal radius and in high fluid flow and axially moving speeds of nanotube. In addition, it is observed that the natural frequencies and stability of the system strongly depend on the small-scale parameter (nano-scale), mainly in the longitudinal VIBRATION.

In this research, an exact solution for free VIBRATION analysis of thick TRANSVERSEly isotropic simply supported rectangular plates on the Pasternak foundation was proposed using the displacement potential function method. By means of the proposed displacement potential functions for dynamic problems by Eskandari-Ghadi, the differential governing equations in terms of displacements were converted into two linear partial differential equations of second and forth order. These differential equations were solved based on the separation of variables method and satisfying exact boundary conditions. In order to validate the results, the obtained results were compared with other available analytical works for isotropic and TRANSVERSEly isotropic plates, and it indicated remarkable agreement. Having no simplifying assumptions for the strain or stress distribution in the plate thickness, the obtained results in this paper were applicable to any arbitrary plate thickness with no limitation on its thickness ratio such as thin, moderately thick, and thick plates. Thus, the obtained results of the present work can be used as a benchmark solution for other analytical and numerical studies. To investigate the effect of various parameters on the VIBRATIONal plate response, the precise non-dimensional frequencies were obtained in different range of thickness ratios, aspect ratios, elastic foundation coefficients, and mechanical characteristics of plates. It was observed that with increasing thickness ratio and aspect ratio of the plate, the non-dimensional natural frequencies of plate decreased and increased, respectively. In addition, comparative results of isotropic and TRANSVERSEly isotropic plates showed that shear modulus in TRANSVERSE direction would have significant influence on the VIBRATIONal behavior of rectangular plates. It was shown that when the value of the thickness ratio increased, the sensitivity of non-dimensional frequency response to values of foundation stiffness coefficients decreased. In addition, it can be conducted that the effect of the shearing layer of elastic foundation coefficient value increased by increasing the thickness ratios of plates.

In this paper, the author studied free TRANSVERSE VIBRATION of a thin isotropic simply-supported functionally graded (FG) rectangular plate with porosity effect based on classical plate theory. The plate is considered to be elastically restrained against rotation. It is assumed that the material properties of the graded plate are porosity-dependent. An even porosity distribution is considered for analysis purposes. Due to the asymmetry of material in the thickness direction, the neutral surface is not the same as the geometrical mid-plane of the plate. The concept of the physical neutral surface of the FG plate along with classical plate theory is used to formulate the problem. Hence, the physical neutral surface is taken as the reference plane. The first three dimensionless frequencies of the plate are obtained using the Rayleigh-Ritz method. Boundary characteristic orthogonal polynomials (eigenfunctions), generated using the Gram-Schmidt process, are used in the Rayleigh-Ritz method. A parametric study shows that porosity and material distribution parameters have remarkable effects on the free VIBRATION response of the plate. Results are compared with those of simply-supported FG plates.

TRANSVERSE VIBRATION of a composite Euler-Bernoulli beam with any arbitrary concentrated masses is developed and analytically solved in this paper. First, dynamic governing equations of a cross-ply beam with taking into account of number, location and amount of concentrated masses as well as the effects of torsional behavior of composite layup (due to bending-twisting coupling) are derived. Concentrated masses are modeled by delta Dirac function. Then, the governing equations are solved for two different boundary conditions (simplysupported, clamped-free) to obtain frequency response and mode shapes. The results of the developed model are validated by the available analytical results in the literature. Thus, the effects of number, location and amount of concentrated masses on the torsional-bending VIBRATION of a composite beam can be investigated.

In the present study, a spectral finite element method is developed for free and forced TRANSVERSE VIBRATION of Levy-type moderately thick rectangular orthotropic plates based on first-order shear deformation theory. Levy solution assumption was used to convert the two-dimensional problem into a one-dimensional problem. In the first step, the governing out-of-plane differential equations are transformed from time domain into frequency domain by discrete Fourier transform theory. Then, the spectral stiffness matrix is formulated, using frequency-dependent dynamic shape functions which are obtained from the exact solution of the governing differential equations. An efficient numerical algorithm, using drawing method is used to extract the natural frequencies. The frequency domain dynamic responses are obtained from solution of the spectral element equation. Also, the time domain dynamic responses are derived by using inverse discrete Fourier transform algorithm. The accuracy and excellent performance of the spectral finite element method is then compared with the results obtained from closed form solution methods in previous studies. Finally, comprehensive results for out-of-plane natural frequencies and TRANSVERSE displacement of the moderately thick rectangular plates with six different combinations of boundary conditions are presented. These results can serve as a benchmark to compare the accuracy and precision of the numerical methods used.

In this paper, to address the problem of using displacement sensors in measuring the TRANSVERSE VIBRATION of engine accessory belt, a novel non-contact method based on machine vision and Mask-RCNN model is proposed. Mask-RCNN model was trained using the videos captured by a high speed camera. The results showed that RCNN model had an accuracy of 93% in detection of the accessory belt during the test. Afterward, the belt curve was obtained by a polynomial regression to obtain its performance parameters. The results showed that normal VIBRATION of the center of the belt was in the range of 2 to 3 mm, but the maximum VIBRATION was 8. 7 mm and happened in the engine speed of 4200 rpm. Also, VIBRATION frequency of the belt was obtained 124 Hz. Moreover, the minimum belt oscillation occurred at the beginning point of the belt on the TVD pulley, whereas the maximum oscillation occurred at a point close to the center of the belt at a distance of 16 mm from it. The results show that the proposed method can effectively be used for determination of the transvers VIBRATION of the engine accessory belts, because despite the precise measurement of the belt VIBRATION at any point, can provide the instantaneous position curve of all belt points and the equation of the belt curve at any moment. Useful information such as the belt point having the maximum VIBRATION, belt slope, VIBRATION frequency and scatter band of the belt VIBRATION can be obtained as well.