The traveling and standing flexural waves in the micro-beam are studied based on the fraction order nonlocal strain gradient elasticity in the present paper. First, the Hamilton's variational principle is used to derive the governing equations and the boundary conditions with consideration of both the nonlocal effects and the strain gradient effects. The fraction order derivative instead of the integer order derivative is introduced to make the constitutive model more flexible while the integer order constitutive model can be recovered as a special case. Then, the Euler-Bernoulli beam and the Timoshenko beam are both considered and the corresponding formulations for them are derived. Two problems are investigated: 1) the dispersion of traveling flexural waves and the attenuation of the standing waves in the infinite beam. 2) The natural frequency of finite beam. The numerical examples are provided and the effects of the nonlocal and the strain gradient effects are discussed. The influences of the fraction order parameters on the wave motion and vibration behavior are mainly studied. It is found that the strain gradient effects and the nonlocal effect have opposite influences on the wave motion and vibration behavior. The fraction order also has evident influence on the wave motion and vibration behavior and thus can refine the prediction of the model.
{"title":"Traveling and standing flexural waves in the micro-beam based on the fraction order nonlocal strain gradient theory","authors":"Yuqian Xu, P. Wei, Yishuang Huang","doi":"10.1115/1.4054977","DOIUrl":"https://doi.org/10.1115/1.4054977","url":null,"abstract":"\u0000 The traveling and standing flexural waves in the micro-beam are studied based on the fraction order nonlocal strain gradient elasticity in the present paper. First, the Hamilton's variational principle is used to derive the governing equations and the boundary conditions with consideration of both the nonlocal effects and the strain gradient effects. The fraction order derivative instead of the integer order derivative is introduced to make the constitutive model more flexible while the integer order constitutive model can be recovered as a special case. Then, the Euler-Bernoulli beam and the Timoshenko beam are both considered and the corresponding formulations for them are derived. Two problems are investigated: 1) the dispersion of traveling flexural waves and the attenuation of the standing waves in the infinite beam. 2) The natural frequency of finite beam. The numerical examples are provided and the effects of the nonlocal and the strain gradient effects are discussed. The influences of the fraction order parameters on the wave motion and vibration behavior are mainly studied. It is found that the strain gradient effects and the nonlocal effect have opposite influences on the wave motion and vibration behavior. The fraction order also has evident influence on the wave motion and vibration behavior and thus can refine the prediction of the model.","PeriodicalId":49957,"journal":{"name":"Journal of Vibration and Acoustics-Transactions of the Asme","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2022-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77030412","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}
Xiaofei Lyu, H. Sheng, Meng-Xin He, Qian Ding, L.H. Tang, Tianzhi Yang
A lightweight whole-spacecraft vibration isolation system with broadband vibration attenuation capability is of great significance to the protection of satellites during the launch phase. The emergence of metamaterials / phononic crystals provides new ideas for the design of such isolation systems. This letter reports a new type of satellite isolation system to isolate shock and vibrations in an ultrawide frequency range. The labyrinth design of this system integrates acoustic black holes (ABHs) as microstructures, which leads to a significant impedance mismatch and enhances the bandgap effect. The ultrawide vibration and shock attenuation ability of the proposed design is confirmed through band structure and transmission analyses as well as the hammer and falling tests, showing the potential for vast isolation applications.
{"title":"Satellite vibration isolation using periodic acoustic black hole structures with ultrawide bandgap","authors":"Xiaofei Lyu, H. Sheng, Meng-Xin He, Qian Ding, L.H. Tang, Tianzhi Yang","doi":"10.1115/1.4054978","DOIUrl":"https://doi.org/10.1115/1.4054978","url":null,"abstract":"\u0000 A lightweight whole-spacecraft vibration isolation system with broadband vibration attenuation capability is of great significance to the protection of satellites during the launch phase. The emergence of metamaterials / phononic crystals provides new ideas for the design of such isolation systems. This letter reports a new type of satellite isolation system to isolate shock and vibrations in an ultrawide frequency range. The labyrinth design of this system integrates acoustic black holes (ABHs) as microstructures, which leads to a significant impedance mismatch and enhances the bandgap effect. The ultrawide vibration and shock attenuation ability of the proposed design is confirmed through band structure and transmission analyses as well as the hammer and falling tests, showing the potential for vast isolation applications.","PeriodicalId":49957,"journal":{"name":"Journal of Vibration and Acoustics-Transactions of the Asme","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2022-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76347227","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}
Recent attention has been given to acoustic non-reciprocity in metamaterials with nonlinearity. However, the study of asymmetric wave propagation has been limited to mechanical diodes only. Prior works on electromechanical rectifiers or diodes using passive mechanisms are rare in the literature. This problem is investigated here by analytically and numerically studying a combination of nonlinear and linear metamaterials coupled with electromechanical resonators. The nonlinearity of the system stems from the chain in one case and from the electromechanical resonator in another. The method of multiple scales is used to obtain analytical expressions for the dispersion curves. Numerical examples show potential for wider operation range of electromechanical diode, considerable harvested power, and significant frequency shift. The observed frequency shift is demonstrated using spectro-spatial analyses and it is used to construct an electromechanical diode to guide the wave to propagate in one direction only. This only allows signal sensing for waves propagating in one direction and rejects signals in any other direction. The performance of this electromechanical diode is evaluated using the transmission ratio and the asymmetric ratio for a transient input signal. Design guidelines are provided to obtain the best electromechanical diode performance. The presented analyses show high asymmetry ratio for directional-biased wave propagation in the medium-wavelength limit for the case of nonlinear chain. Indeed, the present asymmetric and transmission ratios are higher than those reported in the literature for a mechanical diode. The operation frequencies can also be broadened to the long-wavelength limit frequencies using the resonator nonlinearity.
{"title":"Broadband electromechanical diode: acoustic non-reciprocity in weakly nonlinear metamaterials with electromechanical resonators","authors":"M. Bukhari, O. Barry","doi":"10.1115/1.4054962","DOIUrl":"https://doi.org/10.1115/1.4054962","url":null,"abstract":"\u0000 Recent attention has been given to acoustic non-reciprocity in metamaterials with nonlinearity. However, the study of asymmetric wave propagation has been limited to mechanical diodes only. Prior works on electromechanical rectifiers or diodes using passive mechanisms are rare in the literature. This problem is investigated here by analytically and numerically studying a combination of nonlinear and linear metamaterials coupled with electromechanical resonators. The nonlinearity of the system stems from the chain in one case and from the electromechanical resonator in another. The method of multiple scales is used to obtain analytical expressions for the dispersion curves. Numerical examples show potential for wider operation range of electromechanical diode, considerable harvested power, and significant frequency shift. The observed frequency shift is demonstrated using spectro-spatial analyses and it is used to construct an electromechanical diode to guide the wave to propagate in one direction only. This only allows signal sensing for waves propagating in one direction and rejects signals in any other direction. The performance of this electromechanical diode is evaluated using the transmission ratio and the asymmetric ratio for a transient input signal. Design guidelines are provided to obtain the best electromechanical diode performance. The presented analyses show high asymmetry ratio for directional-biased wave propagation in the medium-wavelength limit for the case of nonlinear chain. Indeed, the present asymmetric and transmission ratios are higher than those reported in the literature for a mechanical diode. The operation frequencies can also be broadened to the long-wavelength limit frequencies using the resonator nonlinearity.","PeriodicalId":49957,"journal":{"name":"Journal of Vibration and Acoustics-Transactions of the Asme","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2022-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91342911","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}
We derive the generalized Helmholtz equation (GHE) governing non-isentropic acoustic fluctuations in a quasi 1-D duct with non-uniform cross-section, mean temperature gradient and non-uniform mean flow. Non-isentropic effects are included via heat conduction terms in the mean and fluctuating energy equations. To derive the Helmholtz equation exclusively in terms of the fluctuating pressure field, a relationship between density and pressure fluctuations is needed, which is shown to be a second-order differential equation for nonisentropic motions. Novel analytical solutions that are accurate for both low/high frequencies and small/large mean gradients are presented for the GHE based on the Wentzel–Kramers–Brillouin (WKB) method. WKB solutions are developed using the ansatz that the pressure fluctuation field has a travelling wave form, ˆp(x) = exp [∫0x (a + ib) dx], where x is the axial coordinate. Substituting this form into the Helmholtz equation yields coupled, nonlinear ordinary differential equations (ODEs) for a and b. Analytical solutions to the ODEs are obtained using the approximations of high frequency and slowly varying mean properties. This simplification allows us to obtain the lower order solutions b0 and a0. We then enhance solution accuracy by using a0 to solve for b1 without any approximations. Finally, b1 is employed to get a1, giving us the higher order solution. The ˆp calculated from (a1, b1) is in good to excellent agreement with numerical solution of the GHE for both low and high frequencies and for a range of mean Mach numbers, including M ≥ 1.
本文推导了具有非均匀截面、平均温度梯度和非均匀平均流量的准一维管道中非等熵声学波动的广义亥姆霍兹方程(GHE)。非等熵效应通过热传导项包含在平均能量方程和波动能量方程中。为了完全从波动压力场导出亥姆霍兹方程，需要密度和压力波动之间的关系，该关系被证明是非等熵运动的二阶微分方程。基于WKB方法，提出了在低/高频和小/大平均梯度下均准确的GHE解析解。利用压力波动场具有行波形式的分析得到了WKB解，即:p(x) = exp[∫0x (a + ib) dx]，其中x为轴向坐标。将这种形式代入亥姆霍兹方程，得到a和b的耦合非线性常微分方程(ode)。利用高频和缓慢变化的平均性质的近似，得到ode的解析解。这种化简使我们可以得到低阶解b0和a0。然后，我们通过使用a0来解b1而不需要任何近似值来提高解的精度。最后，用b1得到a1，得到高阶解。由式(a1, b1)计算出的p值与GHE的数值解在低频和高频以及包括M≥1在内的平均马赫数范围内都非常吻合。
{"title":"Novel WKB Solutions to the Non-Isentropic Helmholtz Equation in a Non-Uniform Duct with Mean Temperature Gradient and Mean Flow","authors":"Sattik Basu, S. Padma Rani","doi":"10.1115/1.4054853","DOIUrl":"https://doi.org/10.1115/1.4054853","url":null,"abstract":"We derive the generalized Helmholtz equation (GHE) governing non-isentropic acoustic fluctuations in a quasi 1-D duct with non-uniform cross-section, mean temperature gradient and non-uniform mean flow. Non-isentropic effects are included via heat conduction terms in the mean and fluctuating energy equations. To derive the Helmholtz equation exclusively in terms of the fluctuating pressure field, a relationship between density and pressure fluctuations is needed, which is shown to be a second-order differential equation for nonisentropic motions. Novel analytical solutions that are accurate for both low/high frequencies and small/large mean gradients are presented for the GHE based on the Wentzel–Kramers–Brillouin (WKB) method. WKB solutions are developed using the ansatz that the pressure fluctuation field has a travelling wave form, ˆp(x) = exp [∫0x (a + ib) dx], where x is the axial coordinate. Substituting this form into the Helmholtz equation yields coupled, nonlinear ordinary differential equations (ODEs) for a and b. Analytical solutions to the ODEs are obtained using the approximations of high frequency and slowly varying mean properties. This simplification allows us to obtain the lower order solutions b0 and a0. We then enhance solution accuracy by using a0 to solve for b1 without any approximations. Finally, b1 is employed to get a1, giving us the higher order solution. The ˆp calculated from (a1, b1) is in good to excellent agreement with numerical solution of the GHE for both low and high frequencies and for a range of mean Mach numbers, including M ≥ 1.","PeriodicalId":49957,"journal":{"name":"Journal of Vibration and Acoustics-Transactions of the Asme","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2022-06-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89558484","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}
Phononic crystals are periodically engineered structures with special acoustic properties that natural materials cannot have. One typical feature of phononic crystals is the emergence of band gaps wherein the wave propagation is prohibited due to the spatial periodicity of constituents. This paper presents a generalized plane wave expansion method (GPWEM) and a voxel-based discretization technique to calculate the band structures of given three-dimensional phononic crystals. Integrated with the adaptive genetic algorithm (AGA), the proposed method is used to perform topological optimization of constituent distribution to achieve maximized band gap width. Numerical results yielded from the optimization of a three-dimensional cubic phononic crystal verify the effectiveness of the proposed method. Eigenmodes of the phononic crystal with the optimized topology are investigated for a better understanding of the mechanism of band gap broadening.
{"title":"Topology Optimization and Wave Propagation of Three-dimensional Phononic Crystals","authors":"Hao Gao, Y. Qu, Guang Meng","doi":"10.1115/1.4054745","DOIUrl":"https://doi.org/10.1115/1.4054745","url":null,"abstract":"\u0000 Phononic crystals are periodically engineered structures with special acoustic properties that natural materials cannot have. One typical feature of phononic crystals is the emergence of band gaps wherein the wave propagation is prohibited due to the spatial periodicity of constituents. This paper presents a generalized plane wave expansion method (GPWEM) and a voxel-based discretization technique to calculate the band structures of given three-dimensional phononic crystals. Integrated with the adaptive genetic algorithm (AGA), the proposed method is used to perform topological optimization of constituent distribution to achieve maximized band gap width. Numerical results yielded from the optimization of a three-dimensional cubic phononic crystal verify the effectiveness of the proposed method. Eigenmodes of the phononic crystal with the optimized topology are investigated for a better understanding of the mechanism of band gap broadening.","PeriodicalId":49957,"journal":{"name":"Journal of Vibration and Acoustics-Transactions of the Asme","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2022-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72506877","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 the context of tribomechadynamics, hyper-reduction means that the deformations, as well as the contact and friction forces, are not computed based on all involved Finite Element nodes but in a reduced space. The goal is a reduction of the simulation time so that virtual tribomechadynamics becomes an efficient complement to test bench investigations and a useful tool for predictive simulation. In this work, an efficient hyper-reduction strategy for contact and friction forces is proposed. The anyway available and a priori known space of possible gaps is used for the hyper-reduction of contact forces without using any snapshots. Friction forces on the other hand are computed based on snapshots stemming from a model order reduced simulation. After the theory has been explained, a generic example with bolted joints is used to demonstrate the result quality of the method as well as the computational time-savings.
{"title":"Efficient Hyper-Reduced Small Sliding Tribomechadynamics","authors":"W. Witteveen, Lukas Koller","doi":"10.1115/1.4054713","DOIUrl":"https://doi.org/10.1115/1.4054713","url":null,"abstract":"\u0000 In the context of tribomechadynamics, hyper-reduction means that the deformations, as well as the contact and friction forces, are not computed based on all involved Finite Element nodes but in a reduced space. The goal is a reduction of the simulation time so that virtual tribomechadynamics becomes an efficient complement to test bench investigations and a useful tool for predictive simulation. In this work, an efficient hyper-reduction strategy for contact and friction forces is proposed. The anyway available and a priori known space of possible gaps is used for the hyper-reduction of contact forces without using any snapshots. Friction forces on the other hand are computed based on snapshots stemming from a model order reduced simulation. After the theory has been explained, a generic example with bolted joints is used to demonstrate the result quality of the method as well as the computational time-savings.","PeriodicalId":49957,"journal":{"name":"Journal of Vibration and Acoustics-Transactions of the Asme","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2022-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77642058","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}
M. Tatari, Soroush Irandoust, R. Ghosh, Yustianto Tjiptowidjojo, H. Nayeb-Hashemi
Deformation and stress fields in a curved beam can be tailored by changing its mechanical properties such as the elastic modulus/mass density, which is typically done using functionally-graded materials (FGM). Such functional gradation can be done for instance by using particles or fiber reinforced materials with different volume fraction along the beam length. This paper presents in-plane vibrations of functionally-graded (FG) cantilevered curved beams. Both semi-analytical and finite element modeling are employed to find natural frequencies and mode shapes of such beams. The natural frequencies obtained from the analytical solution and finite element analysis are in close agreement with an error of 6.2% when the variance of material properties gradation is relatively small. In the analytical approach, direct method is employed to derive the governing linear differential equations of motion. The natural frequencies and mode shapes are obtained using the Galerkin and the finite element methods. First three natural frequencies and corresponding mode shapes are analyzed for different elastic modulus/mass density distribution functions. Furthermore, the natural frequencies of FG curved beams with a crack are also investigated. Our results indicate that larger cracks near the clamped side of the beam significantly decrease the first natural frequency. In the second and third vibration modes, cracks located in the area with a maximum moment result in lowest natural frequency values. However, the second and third natural frequencies of the cracked curved beam are not affected by presence of a crack, if crack is located at the nodal points of the curved beam.
{"title":"Dynamic Analysis of a Curved Beam with Tuning of Elastic Modulus and Mass Density in Circumferential Direction","authors":"M. Tatari, Soroush Irandoust, R. Ghosh, Yustianto Tjiptowidjojo, H. Nayeb-Hashemi","doi":"10.1115/1.4054672","DOIUrl":"https://doi.org/10.1115/1.4054672","url":null,"abstract":"\u0000 Deformation and stress fields in a curved beam can be tailored by changing its mechanical properties such as the elastic modulus/mass density, which is typically done using functionally-graded materials (FGM). Such functional gradation can be done for instance by using particles or fiber reinforced materials with different volume fraction along the beam length. This paper presents in-plane vibrations of functionally-graded (FG) cantilevered curved beams. Both semi-analytical and finite element modeling are employed to find natural frequencies and mode shapes of such beams. The natural frequencies obtained from the analytical solution and finite element analysis are in close agreement with an error of 6.2% when the variance of material properties gradation is relatively small. In the analytical approach, direct method is employed to derive the governing linear differential equations of motion. The natural frequencies and mode shapes are obtained using the Galerkin and the finite element methods. First three natural frequencies and corresponding mode shapes are analyzed for different elastic modulus/mass density distribution functions. Furthermore, the natural frequencies of FG curved beams with a crack are also investigated. Our results indicate that larger cracks near the clamped side of the beam significantly decrease the first natural frequency. In the second and third vibration modes, cracks located in the area with a maximum moment result in lowest natural frequency values. However, the second and third natural frequencies of the cracked curved beam are not affected by presence of a crack, if crack is located at the nodal points of the curved beam.","PeriodicalId":49957,"journal":{"name":"Journal of Vibration and Acoustics-Transactions of the Asme","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2022-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75208989","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 framework for modeling the transient response of percussive drilling systems is presented. The proposed approach is based on the Distributed Transfer Function Method (DTFM), which is a semi-analytical modeling technique. Experimental results obtained from a percussion testbed for The Regolith and Ice Drill for the Exploration of New Terrains (TRIDENT) were incorporated into this modeling technique. DTFM is shown to be a convenient, modular modeling approach, capable of handling complex boundary conditions and drill rod geometries. Moreover, this technique is computationally simple and allows for straightforward incorporation of experimentally measured boundary forcing via numerical convolution, as well as control of the frequency content in the transient response. An experimental study is used to demonstrate the ability of the proposed approach to characterize unknown boundary conditions.
{"title":"An Approach to Modeling Percussive Drilling Systems Submitted for Publication","authors":"Samuel Goldman, H. Flashner, Bing Yang","doi":"10.1115/1.4054472","DOIUrl":"https://doi.org/10.1115/1.4054472","url":null,"abstract":"\u0000 A framework for modeling the transient response of percussive drilling systems is presented. The proposed approach is based on the Distributed Transfer Function Method (DTFM), which is a semi-analytical modeling technique. Experimental results obtained from a percussion testbed for The Regolith and Ice Drill for the Exploration of New Terrains (TRIDENT) were incorporated into this modeling technique. DTFM is shown to be a convenient, modular modeling approach, capable of handling complex boundary conditions and drill rod geometries. Moreover, this technique is computationally simple and allows for straightforward incorporation of experimentally measured boundary forcing via numerical convolution, as well as control of the frequency content in the transient response. An experimental study is used to demonstrate the ability of the proposed approach to characterize unknown boundary conditions.","PeriodicalId":49957,"journal":{"name":"Journal of Vibration and Acoustics-Transactions of the Asme","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2022-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89730131","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}
Over the past century, a number of scalar metrics have been proposed to measure the damping of a complex system. The present work explores these metrics in the context of finite element models. Perhaps the most common is the system loss factor, which is proportional to the ratio of energy dissipated over a cycle to the total energy of vibration. However, the total energy of vibration is difficult to define for a damped system because the total energy of vibration may vary considerably over the cycle. The present work addresses this ambiguity by uniquely defining the total energy of vibration as the sum of the kinetic and potential energies averaged over a cycle. Using the proposed definition, the system loss factor is analyzed for the cases of viscous and structural damping. For viscous damping, the system loss factor is found to be equal to twice the modal damping ratio when the system is excited at an undamped natural frequency and responds in the corresponding undamped mode shape. The energy dissipated over a cycle is expressed as a sum over finite elements so that the contribution of each finite element to the system loss factor is quantified. The visual representation of terms in the sum mapped to their spatial locations creates a loss factor image. Moreover, analysis provides an easily computed sensitivity of the loss factor with respect to the damping in one or more finite elements.
{"title":"Unique Loss Factor Images for Complex Dynamic Systems","authors":"J. McDaniel, A. Liem, Allison Kaminski`","doi":"10.1115/1.4054360","DOIUrl":"https://doi.org/10.1115/1.4054360","url":null,"abstract":"\u0000 Over the past century, a number of scalar metrics have been proposed to measure the damping of a complex system. The present work explores these metrics in the context of finite element models. Perhaps the most common is the system loss factor, which is proportional to the ratio of energy dissipated over a cycle to the total energy of vibration. However, the total energy of vibration is difficult to define for a damped system because the total energy of vibration may vary considerably over the cycle. The present work addresses this ambiguity by uniquely defining the total energy of vibration as the sum of the kinetic and potential energies averaged over a cycle. Using the proposed definition, the system loss factor is analyzed for the cases of viscous and structural damping. For viscous damping, the system loss factor is found to be equal to twice the modal damping ratio when the system is excited at an undamped natural frequency and responds in the corresponding undamped mode shape. The energy dissipated over a cycle is expressed as a sum over finite elements so that the contribution of each finite element to the system loss factor is quantified. The visual representation of terms in the sum mapped to their spatial locations creates a loss factor image. Moreover, analysis provides an easily computed sensitivity of the loss factor with respect to the damping in one or more finite elements.","PeriodicalId":49957,"journal":{"name":"Journal of Vibration and Acoustics-Transactions of the Asme","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2022-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79227329","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 work, the asymptotic stability bounds are identified for a class of linear quasi-periodic dynamical systems with stochastic parametric excitations and nonlinear perturbations. The application of a Lyapunov-Perron (L-P) transformation converts the linear part of such systems to a linear time-invariant form. In the past, using the Infante approach for linear time-invariant systems, stability theorem and corollary were derived and demonstrated for time periodic systems with variation in stochastic parameters. In this work, the same is extended towards linear quasi-periodic with stochastic parameter variations. Furthermore, the Lyapunov's direct approach is employed to formulate the stability conditions for quasi-periodic system with nonlinear perturbations. If the nonlinearities satisfy a bounding condition, sufficient conditions for asymptotic stability are derived for such systems. The application of both derived stability theorems are demonstrated with practical examples of commutative and non-commutative quasi-periodic systems.
{"title":"Stability and Robustness Analysis of Quasi-Periodic System subjected to Uncertain Parametric Excitations and Nonlinear Perturbations","authors":"Susheelkumar Cherangara Subramanian, S. Redkar","doi":"10.1115/1.4054359","DOIUrl":"https://doi.org/10.1115/1.4054359","url":null,"abstract":"\u0000 In this work, the asymptotic stability bounds are identified for a class of linear quasi-periodic dynamical systems with stochastic parametric excitations and nonlinear perturbations. The application of a Lyapunov-Perron (L-P) transformation converts the linear part of such systems to a linear time-invariant form. In the past, using the Infante approach for linear time-invariant systems, stability theorem and corollary were derived and demonstrated for time periodic systems with variation in stochastic parameters. In this work, the same is extended towards linear quasi-periodic with stochastic parameter variations. Furthermore, the Lyapunov's direct approach is employed to formulate the stability conditions for quasi-periodic system with nonlinear perturbations. If the nonlinearities satisfy a bounding condition, sufficient conditions for asymptotic stability are derived for such systems. The application of both derived stability theorems are demonstrated with practical examples of commutative and non-commutative quasi-periodic systems.","PeriodicalId":49957,"journal":{"name":"Journal of Vibration and Acoustics-Transactions of the Asme","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2022-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76304731","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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