International Journal of Non-linear Mechanics, Sep 1, 1998
The parametric response of a thick cantilever beam with a tip mass subjected to harmonic axial su... more The parametric response of a thick cantilever beam with a tip mass subjected to harmonic axial support motion is investigated. The Timoshenko beam theory is used to assess the effects of rotary inertia and shear deformation for the beam. In this regard, different modal amplitudes for transverse displacement and angle of rotation of the cross-section are considered. This yields a
An investigation into the dynamics of vehicle-structure interaction of a suspension bridge traver... more An investigation into the dynamics of vehicle-structure interaction of a suspension bridge traversed by a moving vehicle is presented. The vehicle including the occupants is modeled as a half-car model with six degrees-of-freedom, and the bridge is assumed to obey the Euler-Bernoulli beam theory. Due to the continuously moving location of the loads on the bridge, the governing differential equations will have time-varying coefficients and hence, become rather complicated. The relationship between the bridge vibration characteristics and the vehicle speed is rendered, which yields into a search for a particular speed that determines the maximum values of dynamic deflection and the bending moment of the bridge. Results at different vehicle speeds demonstrate that the maximum dynamic deflection occurs at the vicinity of the bridge mid-span (±3%), while the maximum bending moment is found at ±20% of the mid-span. It is shown that one can find a critical speed at which the maximum values of bridge dynamic deflection and bending moment attain their global maxima.
Journal of Intelligent Material Systems and Structures, Nov 12, 2009
This article presents a new modeling approach for the memory-dependent hysteresis phenomenon in a... more This article presents a new modeling approach for the memory-dependent hysteresis phenomenon in a broad class of smart structures and systems. We propose a recursive formulation to relate the minor hysteresis trajectories to their surrounding loops. More specifically, each internal (minor) trajectory targets its previous turning point and converges to its neighboring loop with a tunable exponential rate. By applying the ‘curve alignment’ and the ‘wiping out’ properties at the turning points, we present a new strategy within the context of a memory-based hysteresis modeling framework. A Galfenol-driven micropositioning actuator and a piezoelectrically driven nanopositioning stage are used to experimentally validate the model. Galfenol exhibits large butterfly-type nonlinearity with a small hysteresis effect, while the piezoelectric actuator exhibits wide hysteresis loops. The model is able to precisely predict the major and minor hysteresis loops in both the Galfenol and piezoelectric actuators, and is expected to be effectively and conveniently applicable to general systems exhibiting memory-dependent hysteresis.
Journal of Dynamic Systems Measurement and Control-transactions of The Asme, Aug 4, 2000
A new approach to optimal control of vehicle suspension systems, incorporating actuator time dela... more A new approach to optimal control of vehicle suspension systems, incorporating actuator time delay, is presented. The inclusion of time delay provides a more realistic model for the actuators, and the problem is viewed from a different perspective rather than the conventional optimal control techniques. The objective here is to select a set of feedback gains such that the maximum vertical acceleration of the sprung mass is minimized, over a wide band frequency range and when subjected to certain constraints. The constraints are dictated by the vehicle stability characteristics and the physical bounds placed on the feedback gains. Utilizing a Simple Quarter Car model, the constrained optimization is then carried out in the frequency domain with the road irregularities described as random processes. Due to the presence of the actuator time delay, the characteristic equation is found to be transcendental rather than algebraic, which makes the stability analysis relatively complex. A new scheme for the stability chart strategy with fixed time delay is introduced in order to address the stability issue. The stability characteristics are also verified utilizing other conventional methods such as the Michailov technique. Results demonstrate that the suspension system, when considering the effect of the actuator time delay, exhibits a completely different behavior.
The parametric response of a cantilever thick beam with a tip mass subjected to harmonic axial su... more The parametric response of a cantilever thick beam with a tip mass subjected to harmonic axial support motion is investigated. The governing non-linear equation of motion is derived for an arbitrary axial support motion. To formulate a simple, physically correct dynamic model for the stability and periodicity analyses, the governing equation is truncated to the first characteristic mode of vibration. Using Green’s function and Schauder’s fixed point theorem, the necessary and sufficient conditions for the existence of periodic oscillatory behavior of the beam are established. The influence of the harmonic base excitation parameters, i.e., the excitation amplitude and frequency, on the steady-state amplitude of vibration are determined. Depending on the values of the excitation amplitude and frequency in the stable and unstable regions, the solution exhibits many shapes besides the transition periodic shapes. Numerical results indicate that for a given beam under a known excitation, increasing the tip mass would usually reduce the stable periodic region. To show the effect of rotary inertia and shear deformation, the beam model is reduced to the Euler-Bernoulli and purely flexural beam theories, respectively. The results show that using purely flexural or even Euler-Bernoulli model rather than Timoshenko, would produce an incorrect periodic region.
<jats:title>Abstract</jats:title> <jats:p>An improvement step in robust control... more <jats:title>Abstract</jats:title> <jats:p>An improvement step in robust control is studied for uncertain (linear or nonlinear) systems. The proposed two-stage control scheme first modifies the original desired trajectory, and then imposes robustness against uncertainties in tracking this modified trajectory. For the trajectory modification stage, a simple scheme is considered : time optimal-rigid body motion (TO). The robustness stage is performed using Sliding Mode Control with Perturbation Estimation (SMCPE), an advanced form of SMC. This routine brings some strong features as demonstrated by examples. A rotating hub with flexible beam attachment is taken as the first example, and an undercontrolled two-mass system with a linear spring as the second. The comparative studies show superior results for the combination of TO-SMCPE over the basic SMCPE. Moreover, this two-stage control exhibits stable and highly advantages performance even for cases where H∞-type of robust control structure is declared unstable by earlier investigations.</jats:p>
In this research, a novel method is developed to manipulate smart structures' natural frequen... more In this research, a novel method is developed to manipulate smart structures' natural frequencies to eliminate or alleviate the detrimental effects caused by vibrating close to the natural frequencies. To this end, this work considers a sandwich plate structure with Terfenol-D, which is a magnetostrictive material, comprising its middle layer. The stiffness of this smart material changes based on the magnetic field that it is exposed to. Thus, natural frequencies and resonances of the whole structure can be manipulated. Furthermore, in this research, the Terfenol-D in the middle layer is divided into five parallel sections so that each of them can be controlled separately. Therefore, it is possible to selectively activate portions of the magnetostrictive layers that run parallel along one of the plate's directions to create periodic changes in the structure's stiffness. Thus, the structure can be kept safe when excitations or disturbances approach one of its natural freq...
Locomotor impairment is a high-prevalent and significant source of disability and significantly i... more Locomotor impairment is a high-prevalent and significant source of disability and significantly impacts a large population’s quality of life. Despite decades of research in human locomotion, the challenges of simulating human movement to study the features of musculoskeletal drivers and clinical conditions remain. Most recent efforts in utilizing reinforcement learning (RL) techniques are promising to simulate human locomotion and reveal musculoskeletal drives. However, these simulations often failed to mimic natural human locomotion because most reinforcement strategies have yet to consider any reference data regarding human movement. To address these challenges, in this study, we designed a reward function based on the trajectory optimization rewards (TOR), and bio-inspired rewards, which includes the rewards obtained from reference motion data captured by a single Intertial Moment Unit (IMU) sensor. The sensor was equipped on the participants’ pelvis to capture reference motion d...
A set of memory-based properties is employed in this paper for modeling multiple-path hysteresis ... more A set of memory-based properties is employed in this paper for modeling multiple-path hysteresis response of piezoelectric actuators. These properties, namely, targeting turning points, curve alignment, and wiping-out effect, are
In this Part 2 of a two-part series, the experimental verification and comparison of this work ar... more In this Part 2 of a two-part series, the experimental verification and comparison of this work are presented. In this paper, the effect of beam-type resonator position on flexible dynamics is determined experimentally. The system is excited using band-limited white noise via electrodynamic shaker, and the data are collected with several transducers and a high-speed camera for each actuator beam mounting location; the first four mode shapes and natural frequencies are determined, and a finite element model (FEM) is developed and updated using these data. An additional set of data is collected using a linear sine chirp forcing function and the updated/experimental frequency response functions (FRFs) and time responses for the base and actuator beam tips are found to correlate. Plots of experimentally determined percent modal strain energy versus attachment position for the first four modes is presented, and a final study is also performed showing the fractional root-mean-square (RMS) ...
Space robots require compact joint drive systems (JDSs), typically comprising of actuator, transm... more Space robots require compact joint drive systems (JDSs), typically comprising of actuator, transmission, joint elements that can deliver high torques through stiff mechanical ports. Today's conventional space drive systems are made from off-the-shelf actuators and multistage transmissions that generally involve three to six stages. This current practice has certain benefits such as short development time due to the availability of mechanical components. However, it lacks a system-level integration that accounts for the actuator structure, size and output force, transmission structure, gear-ratio, and strength, and often leads to long and bulky assemblies with large number of parts. This paper presents a new robotic hardware that integrates the robot's JDS into one compact device that is optimized for its size and maximum torque density. This is done by designing the robotic joint using a special transmission which, when numerically optimized, can produce unlimited gear-ratio...
International Journal of Non-linear Mechanics, Sep 1, 1998
The parametric response of a thick cantilever beam with a tip mass subjected to harmonic axial su... more The parametric response of a thick cantilever beam with a tip mass subjected to harmonic axial support motion is investigated. The Timoshenko beam theory is used to assess the effects of rotary inertia and shear deformation for the beam. In this regard, different modal amplitudes for transverse displacement and angle of rotation of the cross-section are considered. This yields a
An investigation into the dynamics of vehicle-structure interaction of a suspension bridge traver... more An investigation into the dynamics of vehicle-structure interaction of a suspension bridge traversed by a moving vehicle is presented. The vehicle including the occupants is modeled as a half-car model with six degrees-of-freedom, and the bridge is assumed to obey the Euler-Bernoulli beam theory. Due to the continuously moving location of the loads on the bridge, the governing differential equations will have time-varying coefficients and hence, become rather complicated. The relationship between the bridge vibration characteristics and the vehicle speed is rendered, which yields into a search for a particular speed that determines the maximum values of dynamic deflection and the bending moment of the bridge. Results at different vehicle speeds demonstrate that the maximum dynamic deflection occurs at the vicinity of the bridge mid-span (±3%), while the maximum bending moment is found at ±20% of the mid-span. It is shown that one can find a critical speed at which the maximum values of bridge dynamic deflection and bending moment attain their global maxima.
Journal of Intelligent Material Systems and Structures, Nov 12, 2009
This article presents a new modeling approach for the memory-dependent hysteresis phenomenon in a... more This article presents a new modeling approach for the memory-dependent hysteresis phenomenon in a broad class of smart structures and systems. We propose a recursive formulation to relate the minor hysteresis trajectories to their surrounding loops. More specifically, each internal (minor) trajectory targets its previous turning point and converges to its neighboring loop with a tunable exponential rate. By applying the ‘curve alignment’ and the ‘wiping out’ properties at the turning points, we present a new strategy within the context of a memory-based hysteresis modeling framework. A Galfenol-driven micropositioning actuator and a piezoelectrically driven nanopositioning stage are used to experimentally validate the model. Galfenol exhibits large butterfly-type nonlinearity with a small hysteresis effect, while the piezoelectric actuator exhibits wide hysteresis loops. The model is able to precisely predict the major and minor hysteresis loops in both the Galfenol and piezoelectric actuators, and is expected to be effectively and conveniently applicable to general systems exhibiting memory-dependent hysteresis.
Journal of Dynamic Systems Measurement and Control-transactions of The Asme, Aug 4, 2000
A new approach to optimal control of vehicle suspension systems, incorporating actuator time dela... more A new approach to optimal control of vehicle suspension systems, incorporating actuator time delay, is presented. The inclusion of time delay provides a more realistic model for the actuators, and the problem is viewed from a different perspective rather than the conventional optimal control techniques. The objective here is to select a set of feedback gains such that the maximum vertical acceleration of the sprung mass is minimized, over a wide band frequency range and when subjected to certain constraints. The constraints are dictated by the vehicle stability characteristics and the physical bounds placed on the feedback gains. Utilizing a Simple Quarter Car model, the constrained optimization is then carried out in the frequency domain with the road irregularities described as random processes. Due to the presence of the actuator time delay, the characteristic equation is found to be transcendental rather than algebraic, which makes the stability analysis relatively complex. A new scheme for the stability chart strategy with fixed time delay is introduced in order to address the stability issue. The stability characteristics are also verified utilizing other conventional methods such as the Michailov technique. Results demonstrate that the suspension system, when considering the effect of the actuator time delay, exhibits a completely different behavior.
The parametric response of a cantilever thick beam with a tip mass subjected to harmonic axial su... more The parametric response of a cantilever thick beam with a tip mass subjected to harmonic axial support motion is investigated. The governing non-linear equation of motion is derived for an arbitrary axial support motion. To formulate a simple, physically correct dynamic model for the stability and periodicity analyses, the governing equation is truncated to the first characteristic mode of vibration. Using Green’s function and Schauder’s fixed point theorem, the necessary and sufficient conditions for the existence of periodic oscillatory behavior of the beam are established. The influence of the harmonic base excitation parameters, i.e., the excitation amplitude and frequency, on the steady-state amplitude of vibration are determined. Depending on the values of the excitation amplitude and frequency in the stable and unstable regions, the solution exhibits many shapes besides the transition periodic shapes. Numerical results indicate that for a given beam under a known excitation, increasing the tip mass would usually reduce the stable periodic region. To show the effect of rotary inertia and shear deformation, the beam model is reduced to the Euler-Bernoulli and purely flexural beam theories, respectively. The results show that using purely flexural or even Euler-Bernoulli model rather than Timoshenko, would produce an incorrect periodic region.
<jats:title>Abstract</jats:title> <jats:p>An improvement step in robust control... more <jats:title>Abstract</jats:title> <jats:p>An improvement step in robust control is studied for uncertain (linear or nonlinear) systems. The proposed two-stage control scheme first modifies the original desired trajectory, and then imposes robustness against uncertainties in tracking this modified trajectory. For the trajectory modification stage, a simple scheme is considered : time optimal-rigid body motion (TO). The robustness stage is performed using Sliding Mode Control with Perturbation Estimation (SMCPE), an advanced form of SMC. This routine brings some strong features as demonstrated by examples. A rotating hub with flexible beam attachment is taken as the first example, and an undercontrolled two-mass system with a linear spring as the second. The comparative studies show superior results for the combination of TO-SMCPE over the basic SMCPE. Moreover, this two-stage control exhibits stable and highly advantages performance even for cases where H∞-type of robust control structure is declared unstable by earlier investigations.</jats:p>
In this research, a novel method is developed to manipulate smart structures' natural frequen... more In this research, a novel method is developed to manipulate smart structures' natural frequencies to eliminate or alleviate the detrimental effects caused by vibrating close to the natural frequencies. To this end, this work considers a sandwich plate structure with Terfenol-D, which is a magnetostrictive material, comprising its middle layer. The stiffness of this smart material changes based on the magnetic field that it is exposed to. Thus, natural frequencies and resonances of the whole structure can be manipulated. Furthermore, in this research, the Terfenol-D in the middle layer is divided into five parallel sections so that each of them can be controlled separately. Therefore, it is possible to selectively activate portions of the magnetostrictive layers that run parallel along one of the plate's directions to create periodic changes in the structure's stiffness. Thus, the structure can be kept safe when excitations or disturbances approach one of its natural freq...
Locomotor impairment is a high-prevalent and significant source of disability and significantly i... more Locomotor impairment is a high-prevalent and significant source of disability and significantly impacts a large population’s quality of life. Despite decades of research in human locomotion, the challenges of simulating human movement to study the features of musculoskeletal drivers and clinical conditions remain. Most recent efforts in utilizing reinforcement learning (RL) techniques are promising to simulate human locomotion and reveal musculoskeletal drives. However, these simulations often failed to mimic natural human locomotion because most reinforcement strategies have yet to consider any reference data regarding human movement. To address these challenges, in this study, we designed a reward function based on the trajectory optimization rewards (TOR), and bio-inspired rewards, which includes the rewards obtained from reference motion data captured by a single Intertial Moment Unit (IMU) sensor. The sensor was equipped on the participants’ pelvis to capture reference motion d...
A set of memory-based properties is employed in this paper for modeling multiple-path hysteresis ... more A set of memory-based properties is employed in this paper for modeling multiple-path hysteresis response of piezoelectric actuators. These properties, namely, targeting turning points, curve alignment, and wiping-out effect, are
In this Part 2 of a two-part series, the experimental verification and comparison of this work ar... more In this Part 2 of a two-part series, the experimental verification and comparison of this work are presented. In this paper, the effect of beam-type resonator position on flexible dynamics is determined experimentally. The system is excited using band-limited white noise via electrodynamic shaker, and the data are collected with several transducers and a high-speed camera for each actuator beam mounting location; the first four mode shapes and natural frequencies are determined, and a finite element model (FEM) is developed and updated using these data. An additional set of data is collected using a linear sine chirp forcing function and the updated/experimental frequency response functions (FRFs) and time responses for the base and actuator beam tips are found to correlate. Plots of experimentally determined percent modal strain energy versus attachment position for the first four modes is presented, and a final study is also performed showing the fractional root-mean-square (RMS) ...
Space robots require compact joint drive systems (JDSs), typically comprising of actuator, transm... more Space robots require compact joint drive systems (JDSs), typically comprising of actuator, transmission, joint elements that can deliver high torques through stiff mechanical ports. Today's conventional space drive systems are made from off-the-shelf actuators and multistage transmissions that generally involve three to six stages. This current practice has certain benefits such as short development time due to the availability of mechanical components. However, it lacks a system-level integration that accounts for the actuator structure, size and output force, transmission structure, gear-ratio, and strength, and often leads to long and bulky assemblies with large number of parts. This paper presents a new robotic hardware that integrates the robot's JDS into one compact device that is optimized for its size and maximum torque density. This is done by designing the robotic joint using a special transmission which, when numerically optimized, can produce unlimited gear-ratio...
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