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Journal articles on the topic 'Free and Forced vibrations'

Author: Grafiati

Published: 4 June 2021

Last updated: 13 June 2025

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1

HOVER, F. S., A. H. TECHET, and M. S. TRIANTAFYLLOU. "Forces on oscillating uniform and tapered cylinders in cross flow." Journal of Fluid Mechanics 363 (May 25, 1998): 97–114. http://dx.doi.org/10.1017/s0022112098001074.

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Forces are measured at both ends of rigid cylinders with span 60 cm, performing transverse oscillations within an oncoming stream of water, at Reynolds number Re≈3800. Forced harmonic motions and free vibrations of uniform and tapered cylinders are studied. To study free motions, a novel force-feedback control system has been developed, consisting of: (a) a force transducer, which measures forces on a section of a cylinder moving forward at constant speed; (b) a computer using the measured force signal to drive in real time a numerical simulation of an equivalent mass-dashpot-spring system; (c) a servomotor and linear table which impose, also in real time, the numerically calculated motion on the cylinder section. The apparatus allows very low equivalent system damping and strict control of the parametric values and structure of the equivalent system.Calculation of the cross-correlation coefficient between forces at the two ends of the uniform cylinder reveals five distinct regimes as a function of the nominal reduced velocity Vrn: two regimes, for low and high values of Vrn, and far away from the value of VrS corresponding to the Strouhal frequency, show small correlation; two regimes immediately adjacent to, but excluding, VrS show strong correlation, close to 1; surprisingly, there is a regime containing the Strouhal frequency, within which correlation is low. Free vibrations with a 40[ratio ]1 tapered cylinder show that the regime of low correlation, containing the Strouhal frequency, stretches to higher reduced velocities, while lock-in starts at lower reduced velocities.When comparing the amplitude and phase of the lift coefficient measured for free and then for forced vibrations, we obtain close agreement, both for tapered and uniform cylinders. When comparing the cross-correlation coefficient, however, we find that it is much higher in the forced oscillations, especially for the uniform cylinder. Hence, although the force magnitude and phase may be replicated well in forced vibrations, the correlation data suggest that differences exist between free and forced vibration cases.

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2

Yesilce, Yusuf. "Free and Forced Vibrations of an Axially-Loaded Timoshenko Multi-Span Beam Carrying a Number of Various Concentrated Elements." Shock and Vibration 19, no. 4 (2012): 735–52. http://dx.doi.org/10.1155/2012/579287.

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In the existing reports regarding free and forced vibrations of the beams, most of them studied a uniform beam carrying various concentrated elements using Bernoulli-Euler Beam Theory (BET) but without axial force. The purpose of this paper is to utilize the numerical assembly technique to determine the exact frequency-response amplitudes of the axially-loaded Timoshenko multi-span beam carrying a number of various concentrated elements (including point masses, rotary inertias, linear springs and rotational springs) and subjected to a harmonic concentrated force and the exact natural frequencies and mode shapes of the beam for the free vibration analysis. The model allows analyzing the influence of the shear and axial force and harmonic concentrated force effects and intermediate concentrated elements on the dynamic behavior of the beams by using Timoshenko Beam Theory (TBT). At first, the coefficient matrices for the intermediate concentrated elements, an intermediate pinned support, applied harmonic force, left-end support and right-end support of Timoshenko beam are derived. After the derivation of the coefficient matrices, the numerical assembly technique is used to establish the overall coefficient matrix for the whole vibrating system. Finally, solving the equations associated with the last overall coefficient matrix one determines the exact dynamic response amplitudes of the forced vibrating system corresponding to each specified exciting frequency of the harmonic force. Equating the determinant of the overall coefficient matrix to zero one determines the natural frequencies of the free vibrating system (the case of zero harmonic force) and substituting the corresponding values of integration constants into the related eigenfunctions one determines the associated mode shapes. The calculated vibration amplitudes of the forced vibrating systems and the natural frequencies of the free vibrating systems are given in tables for different values of the axial force. The dynamic response amplitudes and the mode shapes are presented in graphs. The effects of axial force and harmonic concentrated force on the vibration analysis of Timoshenko multi-span beam are also investigated.

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3

Kulterbaev, Khusen P., Lyalusya A. Baragunova, and Maryana M. Shogenova. "Free and Forced Longitudinal Vibrations of Rods." Materials Science Forum 931 (September 2018): 47–53. http://dx.doi.org/10.4028/www.scientific.net/msf.931.47.

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Free and forced longitudinal oscillations of homogeneous rods of constant cross section are considered. Analytical and numerical methods for solving problems are used. With free vibration, numerical examples are shown for a rod with a jammed and free end and for a rod with a concentrated non-deformable mass at the end, due to which the mathematical model accordingly changes. Forced oscillations are considered for distributed and concentrated loads. The eigenmodes of oscillations characteristic for continually discrete sisites are obtained.

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4

Bourguet, Rémi, and David Lo Jacono. "Flow-induced vibrations of a rotating cylinder." Journal of Fluid Mechanics 740 (February 6, 2014): 342–80. http://dx.doi.org/10.1017/jfm.2013.665.

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AbstractThe flow-induced vibrations of a circular cylinder, free to oscillate in the cross-flow direction and subjected to a forced rotation about its axis, are analysed by means of two- and three-dimensional numerical simulations. The impact of the symmetry breaking caused by the forced rotation on the vortex-induced vibration (VIV) mechanisms is investigated for a Reynolds number equal to $100$, based on the cylinder diameter and inflow velocity. The cylinder is found to oscillate freely up to a rotation rate (ratio between the cylinder surface and inflow velocities) close to $4$. Under forced rotation, the vibration amplitude exhibits a bell-shaped evolution as a function of the reduced velocity (inverse of the oscillator natural frequency) and reaches $1.9$ diameters, i.e. three times the maximum amplitude in the non-rotating case. The free vibrations of the rotating cylinder occur under a condition of wake–body synchronization similar to the lock-in condition driving non-rotating cylinder VIV. The largest vibration amplitudes are associated with a novel asymmetric wake pattern composed of a triplet of vortices and a single vortex shed per cycle, the ${\rm T} + {\rm S}$ pattern. In the low-frequency vibration regime, the flow exhibits another new topology, the U pattern, characterized by a transverse undulation of the spanwise vorticity layers without vortex detachment; consequently, free oscillations of the rotating cylinder may also develop in the absence of vortex shedding. The symmetry breaking due to the rotation is shown to directly impact the selection of the higher harmonics appearing in the fluid force spectra. The rotation also influences the mechanism of phasing between the force and the structural response.

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5

Fakhreddine, Hatim, Ahmed Adri, Saïd Rifai, and Rhali Benamar. "Geometrically nonlinear free and forced vibrations of Euler-Bernoulli multi-span beams." MATEC Web of Conferences 211 (2018): 02001. http://dx.doi.org/10.1051/matecconf/201821102001.

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The objective of this paper is to establish the formulation of the problem of nonlinear transverse forced vibrations of uniform multi-span beams, with several intermediate simple supports and general end conditions, including use of translational and rotational springs at the ends. The beam bending vibration equation is first written at each span and then the continuity requirements at each simple support are stated, in addition to the beam end conditions. This leads to a homogeneous linear system whose determinant must vanish in order to allow nontrivial solutions to be obtained. The formulation is based on the application of Hamilton’s principle and spectral analysis to the problem of nonlinear forced vibrations occurring at large displacement amplitudes, leading to the solution of a nonlinear algebraic system using numerical or analytical methods. The nonlinear algebraic system has been solved here in the case of a four span beam in the free regime using an approximate method developed previously (second formulation) leading to the amplitude dependent fundamental nonlinear mode of the multi-span beam and to the corresponding backbone curves. Considering the nonlinear regime, under a uniformly distributed excitation harmonic force, the calculation of the corresponding generalised forces has led to the conclusion that the nonlinear response involves predominately the fourth mode. Consequently, an analysis has been performed in the neighbourhood of this mode, based on the single mode approach, to obtain the multi-span beam nonlinear frequency response functions for various excitation levels.

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6

Quintana, Guillem, Joaquim de Ciurana, Daniel Teixidor, and I. Ferrer. "Experimental Introduction to Forced and Self-Excited Vibrations in Milling Processes and Identification of Stability Lobes Diagrams." Materials Science Forum 692 (July 2011): 24–32. http://dx.doi.org/10.4028/www.scientific.net/msf.692.24.

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In milling operations, cutting edge impacts due to the interaction between the cutter and the workpiece excite vibrations. It is possible to distinguish between free, forced and self-excited vibrations. Chatter is a self-excited vibration that can occur in machining processes, and is considered to be a common limitation of productivity and quality. Stability lobes diagrams (SLDs) show the frontier between chatter-free milling operations, i.e. stable dominated by forced vibrations, and operations with chatter, i.e. unstable. These diagrams are usually obtained from impact hammer testing. However, this method requires trained personnel with advanced knowledge and it is not easily applied in engineering studies or operator training. This paper presents an experimental method that allows engineering students and operators-in-training to observe the chatter phenomenon and to distinguish between forced and chatter vibrations and identify process stability diagrams.

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7

Shooshtari, Alireza, Soheil Razavi, Hadi Ghashochi Bargh, and Mohammad Homayoun Sadr-Lahidjani. "Nonlinear Free and Forced Vibrations of Symmetric Laminated Panels." Key Engineering Materials 471-472 (February 2011): 616–21. http://dx.doi.org/10.4028/www.scientific.net/kem.471-472.616.

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In this paper, free and forced vibrations of symmetric laminated composite plates are studied analytically by using a perturbation method where the analytical results for transverse displacement are compared with the numerical results. The external force is taken to be harmonic in time and having uniform amplitude.

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8

Sturla, F. A., and A. Argento. "Free and Forced Vibrations of a Spinning Viscoelastic Beam." Journal of Vibration and Acoustics 118, no. 3 (1996): 463–68. http://dx.doi.org/10.1115/1.2888206.

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The free and forced response of spinning, viscoelastic, Rayleigh shafts is studied. Viscoelasticity is included using the three parameter solid model. The closed form polynomial frequency equation and integral expressions for the response to a general forcing function are derived. A convenient decay parameter is described. Results are given for natural frequencies and decay rates as functions of shaft rotation speed, stiffness, and viscosity. It is found that shaft materials are possible which have desirable damping and natural frequency characteristics. A parameter case is discussed in which natural frequency and damping simultaneous increase, while stiffness is held constant. Also, the special case of forced response to a step load is derived and used to illustrate the combined effects of viscoelasticity and gyroscopic forces.

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9

Tho, Nguyen Chi, Nguyen Tri Ta, and Do Van Thom. "New Numerical Results from Simulations of Beams and Space Frame Systems with a Tuned Mass Damper." Materials 12, no. 8 (2019): 1329. http://dx.doi.org/10.3390/ma12081329.

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In working processes, mechanical systems are often affected by both internal and external forces, which are the cause of the forced vibrations of the structures. They can be destroyed if the amplitude of vibration reaches a high enough value. One of the most popular ways to reduce these forced vibrations is to attach tuned mass damper (TMD) devices, which are commonly added at the maximum displacement point of the structures. This paper presents the computed results of the free vibration and the vibration response of the space frame system under an external random load, which is described as a stationary process with white noise. Static and dynamic equations are formed through the finite element method. In addition, this work also establishes artificial neural networks (ANNs) in order to predict the vibration response of the first frequencies of the structure. Numerical studies show that the data set of the TMD device strongly affects the first frequencies of the mechanical system, and the proposed artificial intelligence (AI) model can predict exactly the vibration response of the first frequencies of the structure. For the forced vibration problem, we can find optimal parameters of the TMD device and thus obtain minimum displacements of the structure. The results of this work can be used as a reference when applying this type of structure to TMD devices.

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10

Kelly, S. Graham. "Free and Forced Vibrations of Elastically Connected Structures." Advances in Acoustics and Vibration 2010 (January 2, 2010): 1–11. http://dx.doi.org/10.1155/2010/984361.

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A general theory for the free and forced responses of elastically connected parallel structures is developed. It is shown that if the stiffness operator for an individual structure is self-adjoint with respect to an inner product defined for , then the stiffness operator for the set of elastically connected structures is self-adjoint with respect to an inner product defined on . This leads to the definition of energy inner products defined on . When a normal mode solution is used to develop the free response, it is shown that the natural frequencies are the square roots of the eigenvalues of an operator that is self-adjoint with respect to the energy inner product. The completeness of the eigenvectors in is used to develop a forced response. Special cases are considered. When the individual stiffness operators are proportional, the problem for the natural frequencies and mode shapes reduces to a matrix eigenvalue problem, and it is shown that for each spatial mode there is a set of intramodal mode shapes. When the structures are identical, uniform, or nonuniform, the differential equations are uncoupled through diagonalization of a coupling stiffness matrix. The most general case requires an iterative solution.

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11

Zhu, Liping, Isaac Elishakoff, and Y. K. Lin. "Free and Forced Vibrations of Periodic Multispan Beams." Shock and Vibration 1, no. 3 (1994): 217–32. http://dx.doi.org/10.1155/1994/961272.

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In this study, the following two topics are considered for uniform multispan beams of both finite and infinite lengths with rigid transversal and elastic rotational constraints at each support: (a) free vibration and the associated frequencies and mode shapes; (b) forced vibration under a convected harmonic loading. The concept of wave propagation in periodic structures of Brillouin is utilized to investigate the wave motion at periodic supports of a multispan beam. A dispersion equation and its asymptotic form is obtained to determine the natural frequencies. For the special case of zero rotational spring stiffness, an explicit asymptotic expression for the natural frequency is also given. New expressions for the mode shapes are obtained in the complex form for multispan beams of both finite and infinite lengths. The orthogonality conditions of the mode shapes for two cases are formulated. The exact responses of both finite and infinite span beams under a convected harmonic loading are obtained. Thus, the position and the value of each peak in the harmonic response function can be determined precisely, as well as the occurrence of the so-called coincidence phenomenon, when the response is greatly enhanced.

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12

Volnikov, M. I. "Application of the finite difference method for modeling cantilever bar vibrations." E3S Web of Conferences 224 (2020): 02002. http://dx.doi.org/10.1051/e3sconf/202022402002.

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The paper is devoted to mathematical modeling of cantilever bars using the finite difference method. This method is widely used in structural mechanics for solving static problems. The novelty lies in the application of the finite difference method to simulate the dynamics of free and forced vibrations of the cantilever. Models have been developed that allow calculating the static and dynamic deflections of the cantilevers during free and forced vibrations, as well as simulating the vibrations of cantilever beams with attached vibration dampers. The resulting models of cantilever structures make it easy to modify system parameters, external influences and damping elements. All calculations were performed using the finite difference approach when moving along geometric and temporal coordinates.

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13

Chen, Lei. "Distributed Hybrid Vibration Absorbers for Shock and Forced Vibrations." Applied Mechanics and Materials 166-169 (May 2012): 1709–12. http://dx.doi.org/10.4028/www.scientific.net/amm.166-169.1709.

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The control methods used for free/shock vibration suppression are normally different from those used for forced vibration cancellation, because shock vibration is regarded as a type of transient vibration that is different in nature from steady-state forced vibration. However, both steady-state and shock excitations may occur in flexible structures, so there is a need to control both types of vibrations. To show the integration of the two different vibration control strategies, a hybrid control system based on adhesive strain gauges and PZT patches is proposed to construct a distributed resonant absorber and shock absorber together. The hybrid system is governed by a control arbitrator that decides which absorber should be active according to the different excitation conditions. The effectiveness of the integrated system is shown through simulation and experimental studies.

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14

Szcześniak, Wacław, and Magdalena Ataman. "Moving oscillator on the floating bridge." Transportation Overview - Przeglad Komunikacyjny 2017, no. 9 (2017): 55–62. http://dx.doi.org/10.35117/a_eng_17_09_07.

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The paper deals with vibration analysis of three span floating bridge under moving oscillator. Velocity of the oscillator is constant. Forced and free vibrations of pontoon bridge are discussed. Three equations of motion of the system for each span are solved numerically. Solution of damped vibrations and solution for undamped vibrations are presented. Some results are shown in the Figures 3-9.

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15

Wei, S. T., and C. Pierre. "Localization Phenomena in Mistuned Assemblies with Cyclic Symmetry Part II: Forced Vibrations." Journal of Vibration and Acoustics 110, no. 4 (1988): 439–49. http://dx.doi.org/10.1115/1.3269548.

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The effects of disorder on the forced response of nearly periodic structures with cyclic symmetry are investigated. The force model adopted here is relevant to blade assemblies. Perturbation methods for the forced response are developed to gain a physical insight into the effects of mistuning. The study shows that the internal coupling between component systems is the key parameter governing the sensitivity to mistuning and that localized forced vibrations do occur in the disordered assembly for weak internal coupling. However, although both localized free and forced vibrations occur for finite or large values of the mistuning to coupling ratio, the deflection patterns for these two types of localized vibrations are different. Also, for the forced response, the degree of localization does not necessarily increase as this ratio increases—a fundamental difference from localized free modes. An important conclusion is that the common periodicity assumption for cyclic structures may lead to qualitative errors for the forced response of weakly coupled systems when small mistuning is present.

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16

Strelnikova, E., D. Kriutchenko, V. Gnitko, and A. Tonkonozhenko. "Liquid Vibrations in Cylindrical Tanks with and Without Baffles Under Lateral and Longitudinal Excitations." International Journal of Applied Mechanics and Engineering 25, no. 3 (2020): 117–32. http://dx.doi.org/10.2478/ijame-2020-0038.

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AbstractThe paper is devoted to issues of estimating free surface elevations in rigid cylindrical fluid-filled tanks under external loadings. The possibility of baffles installation is provided. The liquid vibrations caused by lateral and longitudinal harmonic loadings are under consideration. Free, forced and parametrical vibrations are examined. Modes of the free liquid vibrations are considered as basic functions for the analysis of forced and parametric vibrations. The modes of the free liquid vibrations in baffled and un-baffled cylindrical tanks are received by using single-domain and multi-domain boundary element methods. Effects of baffle installation are studied. The problems of forced vibrations are reduced to solving the systems of second order ordinary differential equations. For parametric vibrations the system of Mathieu equations is obtained. The numerical simulation of free surface elevations at different loadings and baffle configurations is accomplished. Beat phenomena effects are considered under lateral harmonic excitations. The phenomenon of parametric resonance is examined under longitudinal harmonic excitations.

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17

Baragunova, Lyalusya, Maryana Shogenova, and Lyana Kanukoyeva. "Longitudinal vibrations of rods." E3S Web of Conferences 281 (2021): 01044. http://dx.doi.org/10.1051/e3sconf/202128101044.

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Elastic structures of buildings and machines, the dynamic behavior mathematical model of which is the problem of longitudinal vibrations of rods, are widespread in modern technology. In this regard, the study of issues related to the longitudinal vibrations of the rods is also an urgent problem currently. In terms of solving such problems, we considered the problem formulation of longitudinal (free and forced) vibration of rods, obtained the spectra of natural frequencies ωn and own forms φn(x) vibration, u(x, t) – the function of cross-sections displacement in the longitudinal direction of the rod has been found.

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18

KILIKEVIČIUS, Artūras, Darius BAČINSKAS, Mindaugas JUREVIČIUS, et al. "FIELD TESTING AND DYNAMIC ANALYSIS OF OLD CONTINUOUS TRUSS STEEL BRIDGE." Baltic Journal of Road and Bridge Engineering 13, no. 1 (2018): 54–66. http://dx.doi.org/10.3846/bjrbe.2018.394.

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Paper presents dynamic field test and analysis results of a three span railway steel continuous truss bridge over river Neris in Jonava. Bridge was originally constructed in 1914. In the period of the World War II and afterwards the bridge was many time destroyed by German and Soviet armies. In 1948 the new railway bridge was constructed. Object of the present paper is to evaluate dynamic behaviour of the railway bridge after 67 years in service. Experimental dynamic analysis was divided into resonance-vibration, forced-vibration and free vibration studies. Resonance-vibrations of the bridge were excited by separate actions of shock loading and standard locomotive 2M62. Forced-vibrations were measured under the action of locomotive 2M62. Additionally, free vibration tests under passage of freight and passenger trains have been carried out. Structural dynamic response of the bridge was analysed using Brüel & Kjær LAN XI dynamic test system and software. As a result, main dynamic parameters of the bridge were obtained. The main results include: mode shapes, frequencies of natural and forced vibrations, damping ratios, maximum amplitudes of accelerations, dynamic displacements. The obtained values were compared to the requirements of different design codes. Based on the achieved results concluding remarks and recommendations regarding the condition of the bridge after long-term period in service were presented.

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19

Su, Guang-Yuan, Ying-Xu Li, Xiang-Yu Li, and Ralf Müller. "Free and forced vibrations of nanowires on elastic substrates." International Journal of Mechanical Sciences 138-139 (April 2018): 62–73. http://dx.doi.org/10.1016/j.ijmecsci.2018.01.039.

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20

Çalım, Faruk Fırat. "Free and forced vibrations of non-uniform composite beams." Composite Structures 88, no. 3 (2009): 413–23. http://dx.doi.org/10.1016/j.compstruct.2008.05.001.

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21

Providakis, C. P., and D. E. Beskos. "Free and forced vibrations of plates by boundary elements." Computer Methods in Applied Mechanics and Engineering 74, no. 3 (1989): 231–50. http://dx.doi.org/10.1016/0045-7825(89)90050-9.

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22

MURALI, R., and A. PONMANA SELVAN. "Hyers-Ulam Stability of a Free and Forced Vibrations." Kragujevac Journal of Mathematics 44, no. 2 (2020): 299–312. http://dx.doi.org/10.46793/kgjmat2002.299m.

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23

Kang, Jae-Hoon. "Closed-Form Exact Solutions for Viscously Damped Free and Forced Vibrations of Longitudinal and Torsional Bars." International Journal of Structural Stability and Dynamics 17, no. 08 (2017): 1750093. http://dx.doi.org/10.1142/s0219455417500936.

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This paper studies the viscously damped free and forced vibrations of longitudinal and torsional bars. The method is exact and yields closed form solution for the vibration displacement in contrast with the well-known eigenfunction superposition (ES) method, which requires expression of the distributed forcing functions and displacement response functions as infinite series sums of free vibration eigenfunctions. The viscously damped natural frequency equation and the critical viscous damping equation are exactly derived for the bars. Then the viscously damped free vibration frequencies and corresponding damped mode shapes are calculated and plotted, aside from the undamped free vibration and corresponding mode shapes typically computed and used in vibration problems. The longitudinal or torsional amplitude versus forcing frequency curves showing the forced response to distributed loadings are plotted for various viscous damping parameters. It is found that the viscous damping affects the natural frequencies and the corresponding mode shapes of longitudinal and torsional bars, especially for the fundamental frequency.

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24

Xu, L., and X. Jia. "Electromechanical-fluidic coupled dynamics for microbeams." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 222, no. 3 (2008): 535–48. http://dx.doi.org/10.1243/09544062jmes694.

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In the current article an electromechanical-fluidic coupled dynamic model of the microbeam is presented and the electromechanical-fluidic coupled dynamic equations are obtained. Using the KBM method, the non-linear coupled dynamic equations are resolved. The explicit equations of the free vibrating displacements of the microbeam are given. Under free vibration, the equations of the electric field fluctuation and the air pressure fluctuation are also given. Besides this, the forced responses of the electromechanical-fluidic coupled system to voltage excitation are also analysed. Changes in the electromechanical-fluidic coupled vibrations along with mechanical, electric, and fluidic parameters are investigated.

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25

Moe, G., and Z. J. Wu. "The Lift Force on a Cylinder Vibrating in a Current." Journal of Offshore Mechanics and Arctic Engineering 112, no. 4 (1990): 297–303. http://dx.doi.org/10.1115/1.2919870.

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This paper reports an extensive program of forced and free vibration tests on a single circular cylinder moving mainly perpendicularly to a uniform current. For both free and forced vibration tests, two cases were investigated: one in which the cylinder was restrained in the in-line direction and the other in which it was supported on suitable springs. The cross-flow vibrational response and hydrodynamic forces on the cylinder were measured. Large variations of motion frequency in the “lock-in” range were found from the free vibration tests. This leads to two different definitions of reduced velocity, namely, a so-called nominal reduced velocity based on one reference frequency and the true reduced velocity based on the actual vibration frequency. When different results are compared, the true reduced velocity should be used. The forced vibration tests showed, as may be expected, that the transverse force in the “lock-in” range on the average will add energy to the cylinder at moderate motion amplitudes and subtract energy at large amplitudes. Some conditions resulting in a steady-state vibration of a flexibly mounted cylinder were analyzed. The actual force traces also show very large and apparently random deviations from the average force amplitude. The results from the forced and the free vibration tests are consistent with each other if the true reduced velocity and reduced amplitude are the same.

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26

Collins, K. R., R. H. Plaut, and J. Wauer. "Free and Forced Longitudinal Vibrations of a Cantilevered Bar With a Crack." Journal of Vibration and Acoustics 114, no. 2 (1992): 171–77. http://dx.doi.org/10.1115/1.2930246.

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Longitudinal vibrations of a cantilevered bar with a transverse crack are investigated. For undamped, unforced vibrations, frequency spectra are computed and the effects of the crack location and compliance on the fundamental natural frequency are determined. For vibrations caused by a distributed, longitudinal, harmonic force, the steady-state amplitude of motion of the free end is plotted as a function of the forcing frequency, crack location, and crack compliance, and frequency spectra are also obtained. Results for a breathing crack are compared to those for a crack which remains open and those for an uncracked bar.

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27

Prasanth, T. K., and S. Mittal. "Free v/s forced vibrations of a cylinder at lowRe." International Journal of Computational Fluid Dynamics 22, no. 8 (2008): 583–92. http://dx.doi.org/10.1080/10618560802055943.

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28

Russillo, Andrea Francesco, Giuseppe Failla, and Fernando Fraternali. "Free and forced vibrations of damped locally-resonant sandwich beams." European Journal of Mechanics - A/Solids 86 (March 2021): 104188. http://dx.doi.org/10.1016/j.euromechsol.2020.104188.

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29

Novichkov, Yu N., and D. A. Grishin. "Free and forced beam vibrations on a unilateral elastic foundation." Soviet Applied Mechanics 24, no. 3 (1988): 288–94. http://dx.doi.org/10.1007/bf00883848.

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30

Todorovic, D. M., B. Cretin, P. Vairac, Y. Song, M. D. Rabasovic, and D. D. Markushev. "Photothermal Study of Free and Forced Elastic Vibrations of Microcantilevers." International Journal of Thermophysics 36, no. 5-6 (2015): 1106–15. http://dx.doi.org/10.1007/s10765-015-1836-0.

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31

Yamaguchi, Masaru. "Free and forced vibrations of nonlinear wave equations in ball." Journal of Differential Equations 203, no. 2 (2004): 255–91. http://dx.doi.org/10.1016/j.jde.2004.04.014.

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32

Marchuk, A. V., S. V. Gnedash, and S. A. Levkovskii. "Free and Forced Vibrations of Thick-Walled Anisotropic Cylindrical Shells." International Applied Mechanics 53, no. 2 (2017): 181–95. http://dx.doi.org/10.1007/s10778-017-0804-8.

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33

HSUEH, W. J. "FREE AND FORCED VIBRATIONS OF STEPPED RODS AND COUPLED SYSTEMS." Journal of Sound and Vibration 226, no. 5 (1999): 891–904. http://dx.doi.org/10.1006/jsvi.1999.2249.

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34

Chiang, C. K., C. Mei, and C. E. Gray. "Finite Element Large-Amplitude Free and Forced Vibrations of Rectangular Thin Composite Plates." Journal of Vibration and Acoustics 113, no. 3 (1991): 309–15. http://dx.doi.org/10.1115/1.2930186.

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A finite element formulation is presented for determining the large-amplitude free and steady-state forced vibration responses of arbitrarily laminated anisotropic composite rectangular thin plates. The nonlinear stiffness and harmonic force matrices of an arbitrarily laminated composite rectangular plate element are developed for nonlinear free and forced vibration analyses. The linearized updated-mode method with nonlinear time function approximation is employed for the solution of the system nonlinear eigenvalue equations. The finite element results are compared with available approximate continuum solutions. The amplitude-frequency relations for convergence with gridwork refinement, different boundary conditions, aspect ratios, lamination angles, number of plies, and uniform versus concentrated loads are presented.

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Yang, Feng Liu, and Yan Qing Wang. "Free and Forced Vibration of Beams Reinforced by 3D Graphene Foam." International Journal of Applied Mechanics 12, no. 05 (2020): 2050056. http://dx.doi.org/10.1142/s1758825120500568.

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In this paper, free and forced vibrations of nanocomposite beams reinforced by 3D graphene foam (3D-GrF) are studied. Different distributions of 3D-GrF in the beam thickness direction are considered. In accordance with the rule of mixture, the effective Young’s modulus, Poisson’s ratio and mass density of the 3D-GrF reinforced beams are predicted. Based on the Timoshenko beam theory, the governing equation of the 3D-GrF reinforced beam is derived by using the Lagrange equation. The natural frequencies and dynamic responses of the 3D-GrF reinforced beam are solved by the Ritz method and the Newmark-[Formula: see text] method, respectively. Results show that the foam coefficient, the 3D-GrF distribution, the slenderness ratio and the 3D-GrF mass fraction play important roles on free and forced vibration characteristics of the 3D-GrF reinforced beams.

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Shmukler, Valeriy, Valeriy Zhylyakov, and Oleksandr Shapovalov. "Estimation of the composition of the forced and free vibrations of the casing of the steel rope roof of Ukraine Cinema & Concert Hall located in Kharkov over the area of main line tunnel of working metropolitan railway." MATEC Web of Conferences 230 (2018): 02030. http://dx.doi.org/10.1051/matecconf/201823002030.

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The paper discusses issues related to the dynamic parameters of the metro train influence on the building construction of Ukraine Cinema & Concert Hall complicated in terms of construction located in Kharkiv City. The hall roof is of peculiar complexity made in the shape of hyperbolic paraboloid hung to the cable roof system and supported by the inclining reinforced concrete arches. Using the equipment by DIAMEX 2000 LLC we have measured vertical and horizontal forced vibrations in the most relevant points of the casing. Natural vibrations were defined by creating dynamic impact of the falling load weighing 10 kg from a height og 2 m. The vibration parameter measurement was carried out by means of Ahat-M vibration analyzer. As a result we have obtained amplitude-frequency characteristics of the forced vibrations caused by metro train movements. The frequency of base and obertones is within 30-50 Hz. At the same time, vibration amplitudes is up 200-350 pm. Specific range of vibrations leads to the occurrence of the for framing roof framing (concrete and steel strand guy ropes), noise penetrating into the hall significantly worsens operating characteristics for the spectators. A special calculation of guy rope element taking into account fatigue factors has been made.

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Temel, B., and F. F. C¸alim. "Forced Vibration of Cylindrical Helical Rods Subjected to Impulsive Loads." Journal of Applied Mechanics 70, no. 2 (2003): 281–91. http://dx.doi.org/10.1115/1.1554413.

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In this study, the forced vibration of cylindrical helical rods subjected to impulsive loads is theoretically investigated in the Laplace domain. The free vibration is then taken into account as a special case of forced vibration. The governing equations for naturally twisted and curved space rods obtained using Timoshenko beam theory are rewritten for cylindrical helical rods. The material of the rod is assumed to be homogeneous, linear elastic, and isotropic. The axial and shear deformations are also taken into account in the formulation. Ordinary differential equations in scalar form obtained in the Laplace domain are solved numerically using the complementary functions method to calculate exactly the dynamic stiffness matrix of the problem. The desired accuracy is obtained by taking only a few elements. The solutions obtained are transformed to the real space using the Durbin’s numerical inverse Laplace transform method. The free and forced vibrations of cylindrical helical rods are analyzed through various example. The results obtained in this study are found to be in a good agreement with those available in the literature.

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Craifaleanu, Andrei, Cristian Dragomirescu, Nicolaie Orăşanu, and Adrian Costache. "Study on Vibration Transmission, with Application to the Calibration of a Measuring Stand." Applied Mechanics and Materials 430 (September 2013): 153–57. http://dx.doi.org/10.4028/www.scientific.net/amm.430.153.

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The paper studies the vibration transmitted by a mechanical oscillating system to its fixing device. The influence of the mechanical characteristics (inertial and elastic) of the device on the quantities specific to the free and forced vibration, respectively, of the principal system, is analyzed. In this context, the paper investigates the possibility to correlate the vibrations of the mechanical system with the vibrations measured on the fixing device. The conclusions of this study can be used for the calibration of vibration measuring stands. In the final part, a practical application is presented, aimed to compare the theoretical results with the data obtained by measurements performed on an experimental model built by the authors.

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Yang, Yi, Xurong Wang, Mingkun Wang, Hang Li, and Yiping Dai. "Dynamic behaviors of helical geared multishaft rotor systems by modal synthesis." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 231, no. 8 (2016): 1410–26. http://dx.doi.org/10.1177/0954406216681596.

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A theoretical investigation of dynamic behaviors of helical geared multishaft rotor systems is performed in this paper. A modal synthesis is developed to calculate free and forced vibrations for geared rotor systems including more than two shafts and gears. Degrees of freedom can be reduced to save the computing time in this method. Results of reduced model are compared with those of full degrees of freedom model, to obtain the acceptable reduction of degrees of freedom without significant loss of accuracy in predicting free and forced vibrations. Then, with the help of this method, dynamic behaviors of helical geared multishaft rotor systems are investigated. Parametric studies are conducted to reveal the effects of several system parameters on the vibration characteristics. Results show the reliability and accuracy of the modal synthesis as well as its limitations of calculating responses due to high-frequency excitations, and provide some references to designers attempting to obtain desirable dynamic behaviors.

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Mohamed Salleh, Muhammad, and Izzuddin Zaman. "Finite Element Modelling of Fixed-Fixed End Plate Attached with Passive Vibration Absorber." Applied Mechanics and Materials 773-774 (July 2015): 194–98. http://dx.doi.org/10.4028/www.scientific.net/amm.773-774.194.

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Every vibration structure has a certain resonance which tends to oscillate with larger amplitude at certain frequencies. These frequencies are known as resonance frequencies or natural frequencies of the structure. At these resonance frequencies, even a small periodic force can result the structure to vibrate excessively. Thus, in this study, the free and forced vibrations of fixed-fixed ends plate were simulated using a commercial Finite Element Analysis software, such as ANSYS to investigate the natural frequencies, mode shape and the response of the plate. Later, the vibration absorber is attached to the plate in order to decrease the vibration amplitude produced by a shaker. The preliminary result shows that the plate vibration reduced significantly with attached a single vibration absorber.

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El Hantati, Issam, Ahmed Adri, Hatim Fakhreddine, Said Rifai, and Rhali Benamar. "A Multimode Approach to Geometrically Nonlinear Free and Forced Vibrations of Multistepped Beams." Shock and Vibration 2021 (April 15, 2021): 1–18. http://dx.doi.org/10.1155/2021/6697344.

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The scope of this study is to present a contribution to the geometrically nonlinear free and forced vibration of multiple-stepped beams, based on the theories of Euler–Bernoulli and von Karman, in order to calculate their corresponding amplitude-dependent modes and frequencies. Discrete expressions of the strain energy and kinetic energies are derived, and Hamilton’s principle is applied to reduce the problem to a solution of a nonlinear algebraic system and then solved by an approximate method. The forced vibration is then studied based on a multimode approach. The effect of nonlinearity on the dynamic behaviour of multistepped beams in the free and forced vibration is demonstrated and discussed. The effect of varying some geometrical parameters of the stepped beams in the free and forced cases is investigated and illustrated, among which is the variation in the level of excitation.

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Gromysz, Krzysztof. "Nonlinear Analytical Model of Composite Concrete Slab Free and Forced Vibrations." Procedia Engineering 193 (2017): 281–88. http://dx.doi.org/10.1016/j.proeng.2017.06.215.

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Ebenezer, D. D., K. Ravichandran, and Chandramouli Padmanabhan. "Free and forced vibrations of hollow elastic cylinders of finite length." Journal of the Acoustical Society of America 137, no. 5 (2015): 2927–38. http://dx.doi.org/10.1121/1.4919339.

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Ebenezer, D. D., K. Ravichandran, and Chandramouli Padmanabhan. "Free and forced vibrations of hollow elastic cylinders of finite length." Journal of the Acoustical Society of America 135, no. 4 (2014): 2388. http://dx.doi.org/10.1121/1.4877897.

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Providakis, C. P., and D. E. Beskos. "Free and forced vibrations of plates by boundary and interior elements." International Journal for Numerical Methods in Engineering 28, no. 9 (1989): 1977–94. http://dx.doi.org/10.1002/nme.1620280902.

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Chen, Da, Jie Yang, and Sritawat Kitipornchai. "Free and forced vibrations of shear deformable functionally graded porous beams." International Journal of Mechanical Sciences 108-109 (April 2016): 14–22. http://dx.doi.org/10.1016/j.ijmecsci.2016.01.025.

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Radhakrishnan, V. M. "Response of a Cracked Cantilever Beam to Free and Forced Vibrations." Defence Science Journal 54, no. 1 (2004): 31–38. http://dx.doi.org/10.14429/dsj.54.2019.

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Domagalski, Łukasz. "Free and forced large amplitude vibrations of periodically inhomogeneous slender beams." Archives of Civil and Mechanical Engineering 18, no. 4 (2018): 1506–19. http://dx.doi.org/10.1016/j.acme.2018.06.005.

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Tirelli, Daniel. "Vibration Mitigation without Dissipative Devices: First Large-Scale Testing of a State Switched Inducer." Shock and Vibration 2014 (2014): 1–14. http://dx.doi.org/10.1155/2014/135767.

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A new passive device for mitigating cable vibrations is proposed and its efficiency is assessed on 45-meter long taut cables through a series of free and forced vibration tests. It consists of a unilateral spring attached perpendicularly to the cable near the anchorage. Because of its ability to change the cable dynamic behaviour through intermittent activation, the device has been called state switched inducer (SSI). The cable behaviour is shown to be deeply modified by the SSI: the forced vibration response is anharmonicc and substantially reduced in amplitude whereas the free vibration decay is largely sped up through a beating phenomenon. The vibration mitigation effect is mainly due to the activation and coupling of various vibration modes, as evidenced in the response spectra of the equipped cable. This first large-scale experimental campaign shows that the SSI outperforms classical passive devices, thus paving the way to a new kind of low-cost vibration mitigation systems which do not rely on dissipation.

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Kubur, M., A. Kahraman, D. M. Zini, and K. Kienzle. "Dynamic Analysis of a Multi-Shaft Helical Gear Transmission by Finite Elements: Model and Experiment." Journal of Vibration and Acoustics 126, no. 3 (2004): 398–406. http://dx.doi.org/10.1115/1.1760561.

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A dynamic model of a multi-shaft helical gear reduction unit formed by N flexible shafts is proposed in this study. The model consists of a finite element model of shaft structures combined with a three-dimensional discrete model of helical gear pairs. Bearing and housing flexibilities are included in the model as well. Eigenvalue solution and the Modal Summation Technique are used to predict the free and forced vibrations of the system. Results of experimental study on a helical gear-shaft-bearing system are also presented for validation of the model. It is demonstrated that the predictions match well with the experimental data in terms of excited modes and the forced response given in the form of the dynamic transmission error. Forced vibrations of an example system formed by three shafts are also studied to demonstrate the influence of some of the key system parameters.

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