Journal sliding bearings are often used to support rotating machinery to add damping and increase load capacity. These bearings have strong nonlinearities that can cause vibration problems. Various studies have been conducted on vibration phenomena caused by nonlinearities in journal sliding bearings. However, most of these studies have been on horizontally supported rotating machines. Some of these techniques are difficult to apply to vertically supported rotating machines. The most significant difference between horizontal and vertical support is that the weight of the rotor does not act on the journal sliding bearing in the case of vertical support. Therefore, it is not appropriate to use the horizontal journal sliding bearing theory based on the equilibrium point for the vertical shaft, but rather, it should be considered based on the whirling orbit. In this paper, the nonlinear rotor dynamics of vertical rotating machines with journal sliding bearings are investigated and evaluated by theoretical and numerical analyses and experiments of a simple vertical rotating shaft. As a result, some new destabilization and stabilization phenomena are found in the vertical shaft system, and it is clarified that they can not be predicted by the conventional linear analysis around equilibrium point, but can be predicted by the nonlinear dynamical analysis of whirling orbit. Particularly, these destabilization and stabilization phenomena of vertical shaft system are strongly affected by the magnitude of the vibration in the journal sliding bearing due to its nonlinearity, and the unbalance of the rotating body can be a parameter to control them.
{"title":"Characteristics of Self-excited Vibration of Vertical Rotating Shaft System Considering Amplitude dependent Nonlinearity of Sliding Bearing","authors":"Y. Watanabe, T. Inoue","doi":"10.1115/1.4055976","DOIUrl":"https://doi.org/10.1115/1.4055976","url":null,"abstract":"\u0000 Journal sliding bearings are often used to support rotating machinery to add damping and increase load capacity. These bearings have strong nonlinearities that can cause vibration problems. Various studies have been conducted on vibration phenomena caused by nonlinearities in journal sliding bearings. However, most of these studies have been on horizontally supported rotating machines. Some of these techniques are difficult to apply to vertically supported rotating machines. The most significant difference between horizontal and vertical support is that the weight of the rotor does not act on the journal sliding bearing in the case of vertical support. Therefore, it is not appropriate to use the horizontal journal sliding bearing theory based on the equilibrium point for the vertical shaft, but rather, it should be considered based on the whirling orbit. In this paper, the nonlinear rotor dynamics of vertical rotating machines with journal sliding bearings are investigated and evaluated by theoretical and numerical analyses and experiments of a simple vertical rotating shaft. As a result, some new destabilization and stabilization phenomena are found in the vertical shaft system, and it is clarified that they can not be predicted by the conventional linear analysis around equilibrium point, but can be predicted by the nonlinear dynamical analysis of whirling orbit. Particularly, these destabilization and stabilization phenomena of vertical shaft system are strongly affected by the magnitude of the vibration in the journal sliding bearing due to its nonlinearity, and the unbalance of the rotating body can be a parameter to control them.","PeriodicalId":49957,"journal":{"name":"Journal of Vibration and Acoustics-Transactions of the Asme","volume":"1 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2022-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84955803","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
X. Cai, Zhandong Huang, Chunguang Wang, P. Jia, Jun Yang, Liwen Zhang
Metasurfaces are advantageous in wavefront manipulation owing to their compact and flat nature. Particularly, ultrathin and completely smooth metasurfaces with giant phase delay and perfect impedance match are critically required for practical applications. Here we propose an ultrathin and holeless metasurface composed of simply a pair of membranes. This metasurface supports duo unity transmissions with completely conjugate phase shifts occur at two extremely close frequencies. This allows the metasurface to present giant phase delay and endow with high refractive index (n = 18) when the wave penetrates through. Such a property is employed to control the wavefront of acoustic waves to realize planar lens focusing, negative refraction, negative reflection and directional emission. The proposed design principle of acoustic metasurface provides promising avenues for acoustic wave manipulation and may enable extensive applications in beam steering, acoustic imaging, energy harvesting and surface waves.
{"title":"Acoustic Wave Manipulation by Phase Conjugate Metasurface","authors":"X. Cai, Zhandong Huang, Chunguang Wang, P. Jia, Jun Yang, Liwen Zhang","doi":"10.1115/1.4055917","DOIUrl":"https://doi.org/10.1115/1.4055917","url":null,"abstract":"\u0000 Metasurfaces are advantageous in wavefront manipulation owing to their compact and flat nature. Particularly, ultrathin and completely smooth metasurfaces with giant phase delay and perfect impedance match are critically required for practical applications. Here we propose an ultrathin and holeless metasurface composed of simply a pair of membranes. This metasurface supports duo unity transmissions with completely conjugate phase shifts occur at two extremely close frequencies. This allows the metasurface to present giant phase delay and endow with high refractive index (n = 18) when the wave penetrates through. Such a property is employed to control the wavefront of acoustic waves to realize planar lens focusing, negative refraction, negative reflection and directional emission. The proposed design principle of acoustic metasurface provides promising avenues for acoustic wave manipulation and may enable extensive applications in beam steering, acoustic imaging, energy harvesting and surface waves.","PeriodicalId":49957,"journal":{"name":"Journal of Vibration and Acoustics-Transactions of the Asme","volume":"72 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2022-10-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83952855","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A wave-based model that incorporates the effects of shear deformation, rotary inertia and elastic coupling due to structural anisotropy, is developed to analyze the free vibrations of elastically restrained laminated planar frames. In this work, a generalized frame structure is represented as an assemblage of laminated beam segments that act as one-dimensional waveguides. The segments are assumed to undergo only in-plane motion, which upon applying Hamilton's principle, is described by a sixth order coupled differential equation. Dispersion analysis is conducted and the nature of the wavefields associated with the propagation matrix is discussed. Generally restrained boundaries and internal joints are considered, and the associated reflection and transmission matrices are derived. Using the principle of wave-train closure, a closed-form characteristic equation is obtained by systematically assembling the propagation, reflection and transmission matrices. The wave-based model is inherently deterministic, and solving the characteristic equation offers the advantage of determining the exact natural frequencies using conventional root finding algorithms. Application of the proposed model is demonstrated by analyzing an elastically restrained inclined laminated portal frame. Extensive computational analysis is conducted to illustrate the influence of stacking sequence, frame angle, relative frame length, orthotropicity ratios and spring stiffness on the exact natural frequencies (and in certain cases the mode shapes) of the frame. Independent finite element simulations conducted in ANSYS® APDL are consistently used to verify the validity of the analytical results.
{"title":"Free Vibration Analysis of Elastically Restrained Laminated Planar Frames","authors":"Richard Bachoo","doi":"10.1115/1.4055875","DOIUrl":"https://doi.org/10.1115/1.4055875","url":null,"abstract":"\u0000 A wave-based model that incorporates the effects of shear deformation, rotary inertia and elastic coupling due to structural anisotropy, is developed to analyze the free vibrations of elastically restrained laminated planar frames. In this work, a generalized frame structure is represented as an assemblage of laminated beam segments that act as one-dimensional waveguides. The segments are assumed to undergo only in-plane motion, which upon applying Hamilton's principle, is described by a sixth order coupled differential equation. Dispersion analysis is conducted and the nature of the wavefields associated with the propagation matrix is discussed. Generally restrained boundaries and internal joints are considered, and the associated reflection and transmission matrices are derived. Using the principle of wave-train closure, a closed-form characteristic equation is obtained by systematically assembling the propagation, reflection and transmission matrices. The wave-based model is inherently deterministic, and solving the characteristic equation offers the advantage of determining the exact natural frequencies using conventional root finding algorithms. Application of the proposed model is demonstrated by analyzing an elastically restrained inclined laminated portal frame. Extensive computational analysis is conducted to illustrate the influence of stacking sequence, frame angle, relative frame length, orthotropicity ratios and spring stiffness on the exact natural frequencies (and in certain cases the mode shapes) of the frame. Independent finite element simulations conducted in ANSYS® APDL are consistently used to verify the validity of the analytical results.","PeriodicalId":49957,"journal":{"name":"Journal of Vibration and Acoustics-Transactions of the Asme","volume":"57 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2022-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90708848","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Yuanyuan Ye, Chaosheng Mei, Li Li, Xuelin Wang, L. Ling, Yujin Hu
A new phononic crystal with graded supercell configuration is proposed to broaden the Bragg scattering band gaps. The proposed phononic crystal is made up of a periodic arrangement of supercells, and the supercells are composed of unit cells with graded structural parameters. The mechanical model of the graded phononic crystals is established based on transfer matrix method to investigate in-plane elastic waves propagating and band structures of the periodic system. Numerical results show that the graded structural design can merge adjacent multiple band gaps into an extremely broad one. Modal analysis shows that the mechanism of band gap broadening is that the graded supercell configuration breaks some symmetries of the phononic crystal, resulting in the opening of Dirac cone and creation of new band gaps. The effects of the main structural parameters related to graded supercell design on band gap broadening are studied by simulation and verified by experiment. The present study is beneficial to the design of new functional materials with broadband vibration isolation performance.
{"title":"Broadening band gaps of Bragg scattering phononic crystal with graded supercell configuration","authors":"Yuanyuan Ye, Chaosheng Mei, Li Li, Xuelin Wang, L. Ling, Yujin Hu","doi":"10.1115/1.4055876","DOIUrl":"https://doi.org/10.1115/1.4055876","url":null,"abstract":"\u0000 A new phononic crystal with graded supercell configuration is proposed to broaden the Bragg scattering band gaps. The proposed phononic crystal is made up of a periodic arrangement of supercells, and the supercells are composed of unit cells with graded structural parameters. The mechanical model of the graded phononic crystals is established based on transfer matrix method to investigate in-plane elastic waves propagating and band structures of the periodic system. Numerical results show that the graded structural design can merge adjacent multiple band gaps into an extremely broad one. Modal analysis shows that the mechanism of band gap broadening is that the graded supercell configuration breaks some symmetries of the phononic crystal, resulting in the opening of Dirac cone and creation of new band gaps. The effects of the main structural parameters related to graded supercell design on band gap broadening are studied by simulation and verified by experiment. The present study is beneficial to the design of new functional materials with broadband vibration isolation performance.","PeriodicalId":49957,"journal":{"name":"Journal of Vibration and Acoustics-Transactions of the Asme","volume":"28 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2022-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86177052","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Preface: The Centennial Anniversary of the Timoshenko-Ehrenfest Beam Model","authors":"I. Elishakoff, D. Segalman, Firas A. Khasawneh","doi":"10.1115/1.4055874","DOIUrl":"https://doi.org/10.1115/1.4055874","url":null,"abstract":"","PeriodicalId":49957,"journal":{"name":"Journal of Vibration and Acoustics-Transactions of the Asme","volume":"86 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2022-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83751047","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Harshavardhan Ronge, Shripad A. Upalkar, A. Wagh, Radhika Choudhary, Shankar Krishnan, S. Ramamoorthy
For applications of porous materials where mean pressure drop is a concern, packaging the material into a corrugated structure is better compared to other geometries such as block or wedge shapes. The goal of this study is to integrate noise reduction functionality within that material, which requires an understanding of the sound propagation through corrugated porous structures, including flow effects. The corrugated porous structure involves porous partitions separating inlet and outlet fluid channels. The porous materials considered are periodic octet-truss and body-centered cubic unit cells, and sound propagation across these porous partitions is modeled using the Johnson-Champoux-Allard model. The predicted transmission loss (TL) is benchmarked using designed additively manufactured corrugated structures measured using a flow duct. The laminar flow regime is maintained across the porous structure to reduce flow-noise effects. It is shown that the TL for a given corrugated structure increases with a decrease in porosity, and the impact of flow becomes significant as the porosity decreases. The influence of flow on TL also depends on the unit cell configuration. Furthermore, the model provides insights on pressure and acoustic particle velocity distributions within the corrugated structure and reveals regions of the porous material that effectively participate in noise reduction.
{"title":"A model for sound propagation through corrugated porous structures with mean flow","authors":"Harshavardhan Ronge, Shripad A. Upalkar, A. Wagh, Radhika Choudhary, Shankar Krishnan, S. Ramamoorthy","doi":"10.1115/1.4055847","DOIUrl":"https://doi.org/10.1115/1.4055847","url":null,"abstract":"\u0000 For applications of porous materials where mean pressure drop is a concern, packaging the material into a corrugated structure is better compared to other geometries such as block or wedge shapes. The goal of this study is to integrate noise reduction functionality within that material, which requires an understanding of the sound propagation through corrugated porous structures, including flow effects. The corrugated porous structure involves porous partitions separating inlet and outlet fluid channels. The porous materials considered are periodic octet-truss and body-centered cubic unit cells, and sound propagation across these porous partitions is modeled using the Johnson-Champoux-Allard model. The predicted transmission loss (TL) is benchmarked using designed additively manufactured corrugated structures measured using a flow duct. The laminar flow regime is maintained across the porous structure to reduce flow-noise effects. It is shown that the TL for a given corrugated structure increases with a decrease in porosity, and the impact of flow becomes significant as the porosity decreases. The influence of flow on TL also depends on the unit cell configuration. Furthermore, the model provides insights on pressure and acoustic particle velocity distributions within the corrugated structure and reveals regions of the porous material that effectively participate in noise reduction.","PeriodicalId":49957,"journal":{"name":"Journal of Vibration and Acoustics-Transactions of the Asme","volume":"67 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2022-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89894122","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The vibration and sound radiation characteristics of a double leaf panel wall with corrugated core are analyzed. The core comprises of repeating unit cell along the length of the panel. Each cell is a combination of a straight beam with uniform cross-section and curved beams with varying cross-section. The vibroacoustics property of the corrugated panel is analysed assuming plain strain condition. The analysis presented in the work shows that the proposed sandwich panel design provides broadband sound transmission loss (STL) characteristics. The dispersion analysis, forced response characteristics and sound radiation characteristics of the structure are presented. It is found that bending frequency band gap obtained from the dispersion analysis is a prominent criterion to achieve a higher STL. The structural and acoustic behaviours of the sandwich panel are analysed through the spectral finite element model. The STL for the core element for various taper ratios is presented. It is found that a higher taper ratio shifts the STL characteristics to the low frequency range.
{"title":"Broadband sound transmission loss in a corrugated sound panel using periodic structure theory","authors":"Rajan Prasad, A. Baxy, A. Banerjee","doi":"10.1115/1.4055806","DOIUrl":"https://doi.org/10.1115/1.4055806","url":null,"abstract":"\u0000 The vibration and sound radiation characteristics of a double leaf panel wall with corrugated core are analyzed. The core comprises of repeating unit cell along the length of the panel. Each cell is a combination of a straight beam with uniform cross-section and curved beams with varying cross-section. The vibroacoustics property of the corrugated panel is analysed assuming plain strain condition. The analysis presented in the work shows that the proposed sandwich panel design provides broadband sound transmission loss (STL) characteristics. The dispersion analysis, forced response characteristics and sound radiation characteristics of the structure are presented. It is found that bending frequency band gap obtained from the dispersion analysis is a prominent criterion to achieve a higher STL. The structural and acoustic behaviours of the sandwich panel are analysed through the spectral finite element model. The STL for the core element for various taper ratios is presented. It is found that a higher taper ratio shifts the STL characteristics to the low frequency range.","PeriodicalId":49957,"journal":{"name":"Journal of Vibration and Acoustics-Transactions of the Asme","volume":"18 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2022-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81301819","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Structures with inertia periodicity present the phenomenon of band gap formation, i.e. the appearance of regions in the frequency spectrum with a higher modal spacing and lower vibration response. Rotating machines can also present such phenomenon when their working elements are mounted periodically along the shaft (longitudinal periodicity). In the present work, this phenomenon in rotating machines is reviewed and it is shown that band gaps can be moved towards desired locations in the frequency spectrum by mounting the working elements at optimized positions along the shaft. For that, a mathematical model of the rotating machine is correlated to experimental results, and the model is used to optimize the position of the working elements (disks) in the rotor. The optimized rotor is then experimentally tested, and the resultant band gap is measured. The obtained experimental results show that one can indeed tailor the ban gaps, and move them towards higher or lower frequencies as desired without changing the inertia of the working elements.
{"title":"Optimization of Band Gaps in Rotors With Longitudinal Periodicity and Quasi-Periodicity","authors":"Patrick Bueno Lamas, R. Nicoletti","doi":"10.1115/1.4055808","DOIUrl":"https://doi.org/10.1115/1.4055808","url":null,"abstract":"\u0000 Structures with inertia periodicity present the phenomenon of band gap formation, i.e. the appearance of regions in the frequency spectrum with a higher modal spacing and lower vibration response. Rotating machines can also present such phenomenon when their working elements are mounted periodically along the shaft (longitudinal periodicity). In the present work, this phenomenon in rotating machines is reviewed and it is shown that band gaps can be moved towards desired locations in the frequency spectrum by mounting the working elements at optimized positions along the shaft. For that, a mathematical model of the rotating machine is correlated to experimental results, and the model is used to optimize the position of the working elements (disks) in the rotor. The optimized rotor is then experimentally tested, and the resultant band gap is measured. The obtained experimental results show that one can indeed tailor the ban gaps, and move them towards higher or lower frequencies as desired without changing the inertia of the working elements.","PeriodicalId":49957,"journal":{"name":"Journal of Vibration and Acoustics-Transactions of the Asme","volume":"1 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2022-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79106053","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A size-dependent elasticity theory, founded on variationally consistent formulations, is developed to analyze the wave propagation in nano-sized beams. The mixture unified gradient theory of elasticity, integrating the stress gradient theory, the strain gradient model, and the traditional elasticity theory, is invoked to realize the size-effects at the ultra-small scale. Compatible with the kinematics of the Timoshenko–Ehrenfest beam, a stationary variational framework is established. The boundary-value problem of dynamic equilibrium along with the constitutive model is appropriately integrated into a single functional. Various generalized elasticity theories of gradient type are restored as particular cases of the developed mixture unified gradient theory. The flexural wave propagation is formulated within the context of the introduced size-dependent elasticity theory and the propagation characteristics of flexural waves are analytically addressed. The phase velocity of propagating waves in CNTs is inversely reconstructed and compared with the numerical simulation results. A viable approach to inversely determine the characteristic length-scale parameters associated with the generalized continuum theory is proposed. A comprehensive numerical study is performed to demonstrate the wave dispersion features in a Timoshenko–Ehrenfest nanobeam. Based on the presented wave propagation response and ensuing numerical illustrations, original benchmark for numerical analysis is detected.
{"title":"Wave propagation in Timoshenko-Ehrenfest nanobeam: A mixture unified gradient theory","authors":"S. Faghidian, I. Elishakoff","doi":"10.1115/1.4055805","DOIUrl":"https://doi.org/10.1115/1.4055805","url":null,"abstract":"\u0000 A size-dependent elasticity theory, founded on variationally consistent formulations, is developed to analyze the wave propagation in nano-sized beams. The mixture unified gradient theory of elasticity, integrating the stress gradient theory, the strain gradient model, and the traditional elasticity theory, is invoked to realize the size-effects at the ultra-small scale. Compatible with the kinematics of the Timoshenko–Ehrenfest beam, a stationary variational framework is established. The boundary-value problem of dynamic equilibrium along with the constitutive model is appropriately integrated into a single functional. Various generalized elasticity theories of gradient type are restored as particular cases of the developed mixture unified gradient theory. The flexural wave propagation is formulated within the context of the introduced size-dependent elasticity theory and the propagation characteristics of flexural waves are analytically addressed. The phase velocity of propagating waves in CNTs is inversely reconstructed and compared with the numerical simulation results. A viable approach to inversely determine the characteristic length-scale parameters associated with the generalized continuum theory is proposed. A comprehensive numerical study is performed to demonstrate the wave dispersion features in a Timoshenko–Ehrenfest nanobeam. Based on the presented wave propagation response and ensuing numerical illustrations, original benchmark for numerical analysis is detected.","PeriodicalId":49957,"journal":{"name":"Journal of Vibration and Acoustics-Transactions of the Asme","volume":"140 5 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2022-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91063456","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Stepped beams constitute an important class of engineering structures whose vibration response has been widely studied. Many of the existing methods for studying stepped beams manifest serious numerical difficulties as the number of segments or the frequency of excitation increase. In this paper, we focus on the Transfer Matrix Method (TMM), which provides a simple and elegant formulation for multi-step beams. The main idea in the TMM is to model each step in the beam as a uniform element whose vibration configurations are spanned by the segment's local eigenfunctions. Utilizing these local expressions, the boundary conditions at the ends of the multi-step beam as well as the continuity and compatibility conditions across each step are used to obtain the nonlinear eigenvalue problem. Also, and perhaps more importantly, we provide a reformulation for multi-step Euler-Bernoulli beams that avoids much of the numerical singularity problems that have plagued most of the earlier efforts. When this reformulation is extended to multi-segment Timoshenko beams, the numerical difficulties appear to be mitigated, but not solved.
{"title":"Reformulation for the Solution of the Dynamic Response of Co-axial Segmented Beams","authors":"D. Segalman, Firas A. Khasawneh","doi":"10.1115/1.4055807","DOIUrl":"https://doi.org/10.1115/1.4055807","url":null,"abstract":"\u0000 Stepped beams constitute an important class of engineering structures whose vibration response has been widely studied. Many of the existing methods for studying stepped beams manifest serious numerical difficulties as the number of segments or the frequency of excitation increase. In this paper, we focus on the Transfer Matrix Method (TMM), which provides a simple and elegant formulation for multi-step beams. The main idea in the TMM is to model each step in the beam as a uniform element whose vibration configurations are spanned by the segment's local eigenfunctions. Utilizing these local expressions, the boundary conditions at the ends of the multi-step beam as well as the continuity and compatibility conditions across each step are used to obtain the nonlinear eigenvalue problem. Also, and perhaps more importantly, we provide a reformulation for multi-step Euler-Bernoulli beams that avoids much of the numerical singularity problems that have plagued most of the earlier efforts. When this reformulation is extended to multi-segment Timoshenko beams, the numerical difficulties appear to be mitigated, but not solved.","PeriodicalId":49957,"journal":{"name":"Journal of Vibration and Acoustics-Transactions of the Asme","volume":"1 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2022-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87738225","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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