In this paper, vibration analysis of rotating combined thin-walled shells with multiple conical segments has been carried out. Considering the centrifugal force, Coriolis force and initial hoop tension due to rotation, the elastic strain energy and kinetic energy of a single rotating conical shell are expressed based on the Love's first approximation theory. The artificial springs are introduced to simulate the connections of adjacent conical shells and the boundaries of the rotating combined thin-walled shells. Taking characteristic orthogonal polynomial series as the admissible functions, the Rayleigh-Ritz method is employed to derive the frequency equations of the combined shell and corresponding vibration characteristics are then obtained. Given that the cylindrical shell and annular plates can be regarded as conical shells with semi-vertex angles of 0° and 90° respectively, the solution given is also available for the vibration analysis of rotating combined thin-walled shells comprised of any segments of cylindrical, conical shell and annular plate. As examples of rotating combined thin-walled shells with two and five segments, vibrations of rotating conical-conical joined shell and cylindrical-conical-cylindrical-conical-cylindrical joined shell are investigated in the paper. Traveling wave frequencies and corresponding mode shapes are shown and the effects of rotating speed, circumferential wave number, spring stiffness and semi-vertex angles on the vibration behavior are given in detail.
{"title":"Vibration analysis of rotating combined thin-walled shells with multiple conical segments","authors":"Changying Zhao, Shupeng Sun, Yang Yang, D. Cao","doi":"10.1115/1.4055229","DOIUrl":"https://doi.org/10.1115/1.4055229","url":null,"abstract":"\u0000 In this paper, vibration analysis of rotating combined thin-walled shells with multiple conical segments has been carried out. Considering the centrifugal force, Coriolis force and initial hoop tension due to rotation, the elastic strain energy and kinetic energy of a single rotating conical shell are expressed based on the Love's first approximation theory. The artificial springs are introduced to simulate the connections of adjacent conical shells and the boundaries of the rotating combined thin-walled shells. Taking characteristic orthogonal polynomial series as the admissible functions, the Rayleigh-Ritz method is employed to derive the frequency equations of the combined shell and corresponding vibration characteristics are then obtained. Given that the cylindrical shell and annular plates can be regarded as conical shells with semi-vertex angles of 0° and 90° respectively, the solution given is also available for the vibration analysis of rotating combined thin-walled shells comprised of any segments of cylindrical, conical shell and annular plate. As examples of rotating combined thin-walled shells with two and five segments, vibrations of rotating conical-conical joined shell and cylindrical-conical-cylindrical-conical-cylindrical joined shell are investigated in the paper. Traveling wave frequencies and corresponding mode shapes are shown and the effects of rotating speed, circumferential wave number, spring stiffness and semi-vertex angles on the vibration behavior are given in detail.","PeriodicalId":49957,"journal":{"name":"Journal of Vibration and Acoustics-Transactions of the Asme","volume":"51 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2022-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86348789","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}
G. Dorgant, William R. Johnson, W. Delima, M. Leamy
We present experimental verification of pulse shaping in elastic metamaterials together with a procedure to design, fabricate, and verify metamaterial pulse shapers under impact excitation. The Split Hopkinson Pressure Bar (SHPB) test, a fundamental dynamic test introduced more than 70 years ago, often incorporates pulse shaping as a means to alter a stress wave, providing the primary motivation for the presented study. Elastic metamaterials hold promise for enhancing conventional pulse shaping abilities and improving capabilities of the SHPB test. We first design the pulse shaper by numerically optimizing its response using finite element analysis. The pulse shaper consists of repeated unit cells based on a combination of a phononic crystal and a local resonator. We then fabricate and test pulse shaper candidates to validate the procedural efficacy. An iterative element corrects inaccuracies in input force and material properties and allows convergence on an appropriate pulse shaper. We carry-out this procedure by designing pulse shapers fabricated from 3D-printed polylactic acid (PLA) to achieve an extended dwell acceleration pulse shape. In experimental impact tests, the procedure results in rise, dwell, and fall behaviors comparable to that predicted, effectively confirming the efficacy of the presented procedure and verifying the performance of metamaterial-based pulse shapers.
{"title":"Experimental Verification of Pulse Shaping in Elastic Metamaterials under Impact Excitation","authors":"G. Dorgant, William R. Johnson, W. Delima, M. Leamy","doi":"10.1115/1.4056043","DOIUrl":"https://doi.org/10.1115/1.4056043","url":null,"abstract":"\u0000 We present experimental verification of pulse shaping in elastic metamaterials together with a procedure to design, fabricate, and verify metamaterial pulse shapers under impact excitation. The Split Hopkinson Pressure Bar (SHPB) test, a fundamental dynamic test introduced more than 70 years ago, often incorporates pulse shaping as a means to alter a stress wave, providing the primary motivation for the presented study. Elastic metamaterials hold promise for enhancing conventional pulse shaping abilities and improving capabilities of the SHPB test. We first design the pulse shaper by numerically optimizing its response using finite element analysis. The pulse shaper consists of repeated unit cells based on a combination of a phononic crystal and a local resonator. We then fabricate and test pulse shaper candidates to validate the procedural efficacy. An iterative element corrects inaccuracies in input force and material properties and allows convergence on an appropriate pulse shaper. We carry-out this procedure by designing pulse shapers fabricated from 3D-printed polylactic acid (PLA) to achieve an extended dwell acceleration pulse shape. In experimental impact tests, the procedure results in rise, dwell, and fall behaviors comparable to that predicted, effectively confirming the efficacy of the presented procedure and verifying the performance of metamaterial-based pulse shapers.","PeriodicalId":49957,"journal":{"name":"Journal of Vibration and Acoustics-Transactions of the Asme","volume":"1 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2022-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72795991","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}
In this paper, flexural wave propagation, attenuation and reflection through finite number of rigid elastic combined meta-beam (RECM) elements sandwiched between two Euler Bernoulli beams has been studied, implementing the spectral element, inverse Fourier transform and transfer matrix method. Spectral element has been formulated for the unit representative cell of RECM employing the rigid-body dynamics. Governing dimensionless parameters are identified. Further, the sensitivity analysis has been carried out to comprehend the influence of non-dimensional parameters such as mass ratio, length ratio, and rotary inertia ratio on the attenuation profile. Rotary inertia of rigid body produces Local resonance(LR) band, which may abridge the gap between the two Bragg Scattering(BS) bands and results in an ultra-wide stop-band for the specific combination of governing non-dimensional parameters. 164% normalized attenuation band is possible to obtain in RECM. Natural frequencies for the finite RECM have also been evaluated from the global spectral element matrix and observed that some natural frequencies lies in the attenuation band. Therefore, the level of attenuation near that natural frequencies is significantly less and cannot be identified from the dispersion diagram of the infinite RECM.
{"title":"Flexural wave propagation in rigid elastic combined metabeam","authors":"Abhigna Bhatt, A. Banerjee","doi":"10.1115/1.4055174","DOIUrl":"https://doi.org/10.1115/1.4055174","url":null,"abstract":"\u0000 In this paper, flexural wave propagation, attenuation and reflection through finite number of rigid elastic combined meta-beam (RECM) elements sandwiched between two Euler Bernoulli beams has been studied, implementing the spectral element, inverse Fourier transform and transfer matrix method. Spectral element has been formulated for the unit representative cell of RECM employing the rigid-body dynamics. Governing dimensionless parameters are identified. Further, the sensitivity analysis has been carried out to comprehend the influence of non-dimensional parameters such as mass ratio, length ratio, and rotary inertia ratio on the attenuation profile. Rotary inertia of rigid body produces Local resonance(LR) band, which may abridge the gap between the two Bragg Scattering(BS) bands and results in an ultra-wide stop-band for the specific combination of governing non-dimensional parameters. 164% normalized attenuation band is possible to obtain in RECM. Natural frequencies for the finite RECM have also been evaluated from the global spectral element matrix and observed that some natural frequencies lies in the attenuation band. Therefore, the level of attenuation near that natural frequencies is significantly less and cannot be identified from the dispersion diagram of the infinite RECM.","PeriodicalId":49957,"journal":{"name":"Journal of Vibration and Acoustics-Transactions of the Asme","volume":"12 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2022-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86939898","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}
Output-only modal analysis (OMA) is an indispensable alternative to experimental modal analysis for engineering structures while in operation. Conventional OMA often fails to identify the underlying modal structure with insufficient modal participation. Such low participation is expected when the sampled response is subjected to sensor nonlinearity or when specific modes are not well excited. A novel subband decomposition (SBD) method proposed here resolves modal parameters even with biased modal energy distribution. It isolates the system response within a narrow frequency subband through a finite-impulse-response analysis filter bank. Whenever the filter subband captures a resonance, the filtered system response is close-to-singular and contains mainly the resonant mode contribution. A modal cluster metric is defined to identify the resonant normal modes automatically. The modal parameters are identified and extracted within the subband possessing the locally maximal clustering measure. The proposed method assumes no a priori knowledge of the structure under operation other than the system should have no repeated natural frequencies. Therefore, the SBD algorithm is entirely data-driven and requires minimal user intervention. To illustrate the concept and the accuracy of the proposed SBD, numerical experiments of a linear cantilevered beam with various stationary and non-stationary loading are conducted and compared to other OMA methods. Furthermore, physical experiments on an aluminum cantilever beam examine the method's applicability in field modal testing. Compared to traditional OMA methods, the numerical and physical experiments show orders of magnitude improvement in modal identification error using the proposed SBD.
{"title":"Subband Decomposition Based Output-only Modal Analysis","authors":"Dalton L. Stein, Hewenxuan Li, D. Chelidze","doi":"10.1115/1.4055135","DOIUrl":"https://doi.org/10.1115/1.4055135","url":null,"abstract":"\u0000 Output-only modal analysis (OMA) is an indispensable alternative to experimental modal analysis for engineering structures while in operation. Conventional OMA often fails to identify the underlying modal structure with insufficient modal participation. Such low participation is expected when the sampled response is subjected to sensor nonlinearity or when specific modes are not well excited. A novel subband decomposition (SBD) method proposed here resolves modal parameters even with biased modal energy distribution. It isolates the system response within a narrow frequency subband through a finite-impulse-response analysis filter bank. Whenever the filter subband captures a resonance, the filtered system response is close-to-singular and contains mainly the resonant mode contribution. A modal cluster metric is defined to identify the resonant normal modes automatically. The modal parameters are identified and extracted within the subband possessing the locally maximal clustering measure. The proposed method assumes no a priori knowledge of the structure under operation other than the system should have no repeated natural frequencies. Therefore, the SBD algorithm is entirely data-driven and requires minimal user intervention. To illustrate the concept and the accuracy of the proposed SBD, numerical experiments of a linear cantilevered beam with various stationary and non-stationary loading are conducted and compared to other OMA methods. Furthermore, physical experiments on an aluminum cantilever beam examine the method's applicability in field modal testing. Compared to traditional OMA methods, the numerical and physical experiments show orders of magnitude improvement in modal identification error using the proposed SBD.","PeriodicalId":49957,"journal":{"name":"Journal of Vibration and Acoustics-Transactions of the Asme","volume":"188 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2022-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89014362","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 frequency-dependent mass and stiffness matrices of a Timoshenko-Ehrenfest beam are developed through extensive application of symbolic computation. Explicit algebraic expressions for the frequency dependent shape functions and each of the independent elements of the frequency-dependent mass and stiffness matrices are presented concisely. The ensuing frequency-dependent mass and stiffness matrices of the Timoshenko-Ehrenfest beam are applied with particular reference to the Wittrick-Williams algorithm to investigate the free vibration characteristics of an individual Timoshenko-Ehrenfest beam and a framework. The results are discussed with significant conclusions drawn. The proposed method retains the exactness of results like the dynamic stiffness method, but importantly, it opens the possibility of including damping in the analysis.
{"title":"Free Vibration of Timoshenko-Ehrenfest Beams and Frameworks Using Frequency-Dependent Mass and Stiffness Matrices","authors":"J. Banerjee","doi":"10.1115/1.4055133","DOIUrl":"https://doi.org/10.1115/1.4055133","url":null,"abstract":"\u0000 The frequency-dependent mass and stiffness matrices of a Timoshenko-Ehrenfest beam are developed through extensive application of symbolic computation. Explicit algebraic expressions for the frequency dependent shape functions and each of the independent elements of the frequency-dependent mass and stiffness matrices are presented concisely. The ensuing frequency-dependent mass and stiffness matrices of the Timoshenko-Ehrenfest beam are applied with particular reference to the Wittrick-Williams algorithm to investigate the free vibration characteristics of an individual Timoshenko-Ehrenfest beam and a framework. The results are discussed with significant conclusions drawn. The proposed method retains the exactness of results like the dynamic stiffness method, but importantly, it opens the possibility of including damping in the analysis.","PeriodicalId":49957,"journal":{"name":"Journal of Vibration and Acoustics-Transactions of the Asme","volume":"100 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2022-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80612362","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}
External fluctuation torques acting on gear trains having clearances often cause vibro-impact motions with resultant rattle noise issues. In this study, an impact-velocity based rattle severity parameter that correlates to the resultant rattling noise is proposed for multi mesh gear trains. An experimental setup is employed to measure torsional vibro-impact motions and the corresponding sound pressure levels of a a three-axis gear train under various torque fluctuation conditions. A discrete torsional model of the experimental setup is developed and validated through comparisons to the vibration measurements. An impact velocity-based rattle severity index defined from the predicted response is proposed and shown to correlate well with the measured rattle noise sound pressure levels within a wide range of operating conditions. The demonstrated ability of the proposed rattle severity index in tracking rattle noise allows for the assessment of rattle consequences of a multi-mesh drivetrain solely from its predicted torsional response.
{"title":"A Rattle Noise Severity Index for Multi-mesh Gear Trains Subjected to Torque Fluctuations","authors":"A. Donmez, A. Kahraman","doi":"10.1115/1.4055134","DOIUrl":"https://doi.org/10.1115/1.4055134","url":null,"abstract":"\u0000 External fluctuation torques acting on gear trains having clearances often cause vibro-impact motions with resultant rattle noise issues. In this study, an impact-velocity based rattle severity parameter that correlates to the resultant rattling noise is proposed for multi mesh gear trains. An experimental setup is employed to measure torsional vibro-impact motions and the corresponding sound pressure levels of a a three-axis gear train under various torque fluctuation conditions. A discrete torsional model of the experimental setup is developed and validated through comparisons to the vibration measurements. An impact velocity-based rattle severity index defined from the predicted response is proposed and shown to correlate well with the measured rattle noise sound pressure levels within a wide range of operating conditions. The demonstrated ability of the proposed rattle severity index in tracking rattle noise allows for the assessment of rattle consequences of a multi-mesh drivetrain solely from its predicted torsional response.","PeriodicalId":49957,"journal":{"name":"Journal of Vibration and Acoustics-Transactions of the Asme","volume":"126 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2022-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75823324","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 simple configuration of an active Nonreciprocal Gyroscopic Meta-Material (NGMM) is presented. In the proposed NGMM system, a one-dimensional acoustic cavity is provided with piezoelectric boundaries acting as a collocated pair of sensors and actuators. The active piezo-boundaries are controlled by a simple control algorithm that synthesizes a virtual gyroscopic control action to impart desirable non-reciprocal characteristics which are tunable both in magnitude and phase. The dynamic model of a prototype of the NGMM cell is experimentally identified in an attempt to provide means for predicting the characteristics of the virtual gyroscopic controller for various control gains during forward and backward propagations. The theoretical predictions are validated experimentally without the need for any physical dynamic controller which was provided, in previous studies, by using a dummy NGMM cell. Such a simplified arrangement enables the fast execution of the controller with enhanced frequency bandwidth capabilities. The experimental and theoretical characteristics of the NGMM cell are monitored and predicted for different control gain in order to evaluate its behavior for both forward and backward propagation. The obtained experimental results are compared with the theoretical predictions and are found to be in close agreement. The presented concepts provide the foundation necessary for implementation of NGMM that can be employed to more complex 2D and 3D critical structures in order to achieve non-reciprocal behavior in a simple and programmable manner.
{"title":"A simple configuration of an actively synthesized gyroscopic-nonreciprocal acoustic metamaterial","authors":"Hangrui Zhou, A. Baz","doi":"10.1115/1.4055103","DOIUrl":"https://doi.org/10.1115/1.4055103","url":null,"abstract":"\u0000 A simple configuration of an active Nonreciprocal Gyroscopic Meta-Material (NGMM) is presented. In the proposed NGMM system, a one-dimensional acoustic cavity is provided with piezoelectric boundaries acting as a collocated pair of sensors and actuators. The active piezo-boundaries are controlled by a simple control algorithm that synthesizes a virtual gyroscopic control action to impart desirable non-reciprocal characteristics which are tunable both in magnitude and phase. The dynamic model of a prototype of the NGMM cell is experimentally identified in an attempt to provide means for predicting the characteristics of the virtual gyroscopic controller for various control gains during forward and backward propagations. The theoretical predictions are validated experimentally without the need for any physical dynamic controller which was provided, in previous studies, by using a dummy NGMM cell. Such a simplified arrangement enables the fast execution of the controller with enhanced frequency bandwidth capabilities. The experimental and theoretical characteristics of the NGMM cell are monitored and predicted for different control gain in order to evaluate its behavior for both forward and backward propagation. The obtained experimental results are compared with the theoretical predictions and are found to be in close agreement. The presented concepts provide the foundation necessary for implementation of NGMM that can be employed to more complex 2D and 3D critical structures in order to achieve non-reciprocal behavior in a simple and programmable manner.","PeriodicalId":49957,"journal":{"name":"Journal of Vibration and Acoustics-Transactions of the Asme","volume":"3 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2022-07-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90966511","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}
Vibrations of thin and thick beams containing internal complexities are analyzed through generalized bases made of global piecewise-smooth functions (i.e. GPSFs). Such functional bases allow to globally analyze multiple domains as if these latter were only one, such that a unified formulation can be used for different mechanical systems. Such bases were initially introduced to model a specific part of stress and displacement components through the thickness of multi-layered plates; subsequent extensions were introduced in literature to allow the modeling of thin-walled beams and plates. However, in these latter cases certain analytical difficulties were experienced when inner boundary conditions needed to be englobed into the GPSFs; in this work such mentioned difficulties are successfully overcome through certain affine transformations which allow the analyses of vibrating complex beam systems through a straightforward analytical procedure. The complex mechanical components under investigations are Euler and/or Timoshenko models containing inner complexities (stepped beams, concentrated mass or stiffness, internal constraints etc.). The ability of the models herein analyzed is shown through the comparison of the resulting solutions to exact counterparts, if existing, or to finite elements solutions.
{"title":"Vibration of complex Euler-Bernoulli and Timoshenko-Ehrenfest beams through affine GPSFs","authors":"A. Messina","doi":"10.1115/1.4055077","DOIUrl":"https://doi.org/10.1115/1.4055077","url":null,"abstract":"\u0000 Vibrations of thin and thick beams containing internal complexities are analyzed through generalized bases made of global piecewise-smooth functions (i.e. GPSFs). Such functional bases allow to globally analyze multiple domains as if these latter were only one, such that a unified formulation can be used for different mechanical systems. Such bases were initially introduced to model a specific part of stress and displacement components through the thickness of multi-layered plates; subsequent extensions were introduced in literature to allow the modeling of thin-walled beams and plates. However, in these latter cases certain analytical difficulties were experienced when inner boundary conditions needed to be englobed into the GPSFs; in this work such mentioned difficulties are successfully overcome through certain affine transformations which allow the analyses of vibrating complex beam systems through a straightforward analytical procedure. The complex mechanical components under investigations are Euler and/or Timoshenko models containing inner complexities (stepped beams, concentrated mass or stiffness, internal constraints etc.). The ability of the models herein analyzed is shown through the comparison of the resulting solutions to exact counterparts, if existing, or to finite elements solutions.","PeriodicalId":49957,"journal":{"name":"Journal of Vibration and Acoustics-Transactions of the Asme","volume":"29 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2022-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84284748","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 emergence of the use of mechanical metamaterials for vibration suppression and the creation of frequency gaps in structures requires an understanding of the fundament underlying dynamics partial differential equations coupled to ordinary differential equations. Essentially periodic structures consist of a distributed parameter structure connected (embedded) to a series of spring-mass-dampers. Such systems in the past have been studied as combined dynamical systems. This work deals with modal analysis of non-conservative combined dynamic systems formed by assembling distributed parameter structures and linear, viscously damped, lumped parameter oscillators. The mathematical model of the forced response of such dynamic systems is presented via differential operators. The related non-linear eigenproblem is formulated next and a proper solution is provided. Furthermore, the orthogonality of the eigenfunctions is studied and the completeness of the generated solution space is verified. Coupled modal coordinate differential equations result through modal analysis, thus revealing the non-proportional damping configuration, while the proportional damping conditions are also derived and discuss. The theory is applied to non-conservative Euler-Bernoulli beams subject to different types of boundary conditions and coupled to linear, viscously damped oscillators. Additional numerical examples yield interesting conclusions about the non-proportionality and the applicability of the associated methods to solving the coupled differential equations.
{"title":"Modal Analysis of Non-conservative Combined Dynamic Systems","authors":"J. Bellos, D. Inman","doi":"10.1115/1.4055078","DOIUrl":"https://doi.org/10.1115/1.4055078","url":null,"abstract":"\u0000 The emergence of the use of mechanical metamaterials for vibration suppression and the creation of frequency gaps in structures requires an understanding of the fundament underlying dynamics partial differential equations coupled to ordinary differential equations. Essentially periodic structures consist of a distributed parameter structure connected (embedded) to a series of spring-mass-dampers. Such systems in the past have been studied as combined dynamical systems. This work deals with modal analysis of non-conservative combined dynamic systems formed by assembling distributed parameter structures and linear, viscously damped, lumped parameter oscillators. The mathematical model of the forced response of such dynamic systems is presented via differential operators. The related non-linear eigenproblem is formulated next and a proper solution is provided. Furthermore, the orthogonality of the eigenfunctions is studied and the completeness of the generated solution space is verified. Coupled modal coordinate differential equations result through modal analysis, thus revealing the non-proportional damping configuration, while the proportional damping conditions are also derived and discuss. The theory is applied to non-conservative Euler-Bernoulli beams subject to different types of boundary conditions and coupled to linear, viscously damped oscillators. Additional numerical examples yield interesting conclusions about the non-proportionality and the applicability of the associated methods to solving the coupled differential equations.","PeriodicalId":49957,"journal":{"name":"Journal of Vibration and Acoustics-Transactions of the Asme","volume":"13 2 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2022-07-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90233013","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}
Acoustic black holes (ABH) have shown great potential in vibration and noise control. Merging the ABH effect and the metamaterial can be a more efficient approach for vibration control. The aim of this paper is to study the dynamics of a metamaterial plate with crossed acoustic black holes. The band gap properties of the infinite structure and the influence of the design variables are investigated by using the finite element method and the Floquet-Bloch theorem. The vibration transmission and frequency response functions of the finite structure are presented to reveal the vibration attenuation mechanism. The effect of elastic boundary conditions on the vibration properties of the metamaterial plate is also studied. Numerical results demonstrate that the vibration is remarkably weakened due to the band gap and local modes induced by the ABH effect. Then, experimental validation is given by using 3D printing techniques. Finally, we study the multi-objective optimal design problem of the ABH plate to reduce the vibration amplitude and the structural mass simultaneously. Optimization results provide more options for the trade-off design of metamaterial plates between the lightweight design and vibration suppression capability.
{"title":"Dynamic analysis and design of metamaterial plates with crossed acoustic black holes for vibration control","authors":"Meng-Xin He, Q. Ding","doi":"10.1115/1.4055029","DOIUrl":"https://doi.org/10.1115/1.4055029","url":null,"abstract":"\u0000 Acoustic black holes (ABH) have shown great potential in vibration and noise control. Merging the ABH effect and the metamaterial can be a more efficient approach for vibration control. The aim of this paper is to study the dynamics of a metamaterial plate with crossed acoustic black holes. The band gap properties of the infinite structure and the influence of the design variables are investigated by using the finite element method and the Floquet-Bloch theorem. The vibration transmission and frequency response functions of the finite structure are presented to reveal the vibration attenuation mechanism. The effect of elastic boundary conditions on the vibration properties of the metamaterial plate is also studied. Numerical results demonstrate that the vibration is remarkably weakened due to the band gap and local modes induced by the ABH effect. Then, experimental validation is given by using 3D printing techniques. Finally, we study the multi-objective optimal design problem of the ABH plate to reduce the vibration amplitude and the structural mass simultaneously. Optimization results provide more options for the trade-off design of metamaterial plates between the lightweight design and vibration suppression capability.","PeriodicalId":49957,"journal":{"name":"Journal of Vibration and Acoustics-Transactions of the Asme","volume":"2 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2022-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85609155","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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