Non-ideal Constraints Research Articles

Flexural vibration suppression behavior of sleeved phononic crystal pipes in thermal environment

Design idea of phononic crystal has been introduced into vibration suppression of pipes and presents expected effects. During service period, thermal environment is a common factor that may change the dynamic behavior of system. In this work, thermal influences on wave attenuation effect are studied for the single-component PC pipe which is constructed by attaching sleeves to the original bare pipe. Under the preloading effect of thermal stresses, flexural wave bandgap shifts toward the lower frequency range with temperature increment. Bandwidth gets wider for pipes with sleeves of a relative length larger than 0.5, while the bandgap narrows down or even closes up for pipes with shorter sleeves. The opposite variation trends are caused by the reversal of edge modes and the unequal responses of the two edge frequencies to thermal stress stiffness. Deeper reason is the discrepancy in determining factor for frequency between the two edge modes. As a result, the two edge frequency loci drop asynchronously under thermal load, and the transition point of bandgap shifts leftward. A thermo-vibrational joint test system is constructed and flexural wave transmittance is measured, for the first time, for a heated PC pipe. Experimental phenomena and simulation results suggest that the initial deflection and non-ideal constraint of the specimen make the attenuation band present opposite variation trends compared to the ideal model. The former strengthens the stiffness of the PC pipe, and the latter weakens the thermal influence on the PC pipe. Both the two non-ideal factors have a more significant impact on starting frequency of the attenuation band due to the difference in sensitivity of bandgap edge frequencies to stiffness perturbation of the PC pipe.

Novel Lossless Positive-/Negative-Grounded Capacitance Multipliers Using VCII

In the presented research, the second-generation voltage conveyor (VCII) is used in the design of active capacitance multipliers. In this paper, three positive and one negative lossless grounded capacitance multipliers (GCMs) are designed. All of these GCMs are designed using two VCIIs, one capacitor, and two resistors. There is no need for any passive component matching to implement a GCM. The multiplication factor of GCMs can be set/varied by changing the values of two resistances as per requirement. Considering nonideal constraints, GCMs are analysed mathematically to evaluate the effect of nonideal current and voltage transfer gains on the performance of the proposed GCMs. Also, parasitic analysis is conducted to study the effect of VCII node impedance on the performance of the presented GCMs. The simulation analysis is performed using Cadence Virtuoso in 0.18 µm Silterra Malaysia process design kit (PDK). Additionally, the macro-model of commercially available integrated circuit, AD844, is used to design the proposed GCM-2 to further prove the theoretical findings.

Shape sensing and damage identification with iFEM on a composite structure subjected to impact damage and non-trivial boundary conditions

The inverse Finite Element Method (iFEM) has recently demonstrated to be a valuable tool, not only for shape sensing, but also for damage identification in a Structural Health Monitoring framework. The algorithm computes the displacement field, and consequently the strain field, based on discrete input strain measures in the structure without any a-priori knowledge of the material properties or the loading condition. In particular, the reconstruction is obtained by a least-squares minimization of an error functional defined by comparing the experimental strain measures with their numerical formulation, function of the displacements. Even though the formulation of the method is general for any arbitrary geometry and constraints, the definition of the correct boundary conditions is not trivial for structures subjected to non-ideal constraints. Thus, the work proposes a superimposition of the effects approach to weight the contribution of different basic models to simulate the real behavior of the structure. Once the component displacement and strain fields are correctly reconstructed, the structural assessment is performed by means of a load-independent anomaly index based on the comparison of the numerical strain reconstructions and their experimental counterparts. The discrepancies with respect to a load-independent baseline are highlighted by a Mahalanobis distance index. The procedure is experimentally verified on a CFRP reinforced panel subjected to impact damage and a compressive fatigue test.

DYNAMIC MODELING OF NONIDEAL SYSTEM BASED ON GAUSS'S PRINCIPLE

The Gauss's principle gives the rules to identify the real motion from the possible motion by finding the extreme value of the function, which can make the dynamic problem of the multi-body system not need to solve the differential (algebra) equation, but adopt the optimization method of solving the minimum value, therefore, how to define the appropriate Gaussian constraint function is the prerequisite for the realization of dynamic optimization method. For the ideal system, the effect of constraints on the system can be reflected by the constraint equation and so the Gaussian constraint can be expressed as a function of the particle acceleration of the system, then the dynamic problem of the system can be described as the constrained optimization problem with the objective function as the Gaussian constraint function and the optimization variable as the particle acceleration. When the non-ideal factors such as dry friction need to be taken into account in the system, the partial interaction can not be covered by the defined constraint equation and needs to be described by additional physical laws. This sort of interaction destroys the extreme value characteristics of the original Gaussian restraint function of the system. Based on Gauss's principle of the variable classification, the extreme value principle of non-ideal system is derived and proved, whose objective function is expressed by ideal constraint forces. The Gauss's principle for non-ideal system in the existing literature is discussed and it is pointed out that it is an expression of the extreme value principle given when there is no obvious function correlation between the non-ideal constraint force and the ideal constraint force. But when they have obvious function relation (such as the linear relationship between the sliding friction force and the normal constraint force in the Coulomb friction law), this form will fail. And according to the extreme value principle given, the dynamic optimization model of contact problem for multi-body system considering friction is obtained. In the examples, the optimization model and the corresponding linear complementary model are analyzed, which is found that the two are necessary and sufficient conditions for each other under the condition of satisfying the uniqueness of rigid body sliding problem, thus, the reliability of the optimization model given is proved. And the dynamic simulation is carried out by the optimization calculation method. The simulation results show the feasibility and effectiveness of combining Gaussian principle with optimization algorithm.

The Non-Smooth Problem of Wheel Motion

Planar motion of a non-deformable wheel under the action of non-ideal unilateral constraints is considered. The mathematical description of this phenomenon has a form of a non-smooth initial value problem. The non-smoothness of this problem means that its solution is determined by an absolutely continuous function having a discontinuous first derivative. For this reason, a collision problem describing abrupt changes of velocity has been formulated next to the equations of motion specifying the acceleration. The non-idealness of constraints means that the constraint reaction force includes also a component resulting from the friction between the wheel and the constraints. Differential equations specifying acceleration of the wheel making contact with the constraints and algebraic equations for determining the changes in the wheel’s velocity at the moment of collision have been formulated in the paper. The principal task in these formulations is to determine the reaction forces of the considered constraints. This task is specified by the relationships between acceleration and the constraint reaction force components. In the description of the collision, these relations refer to the post-collision velocities and reaction force impulses. For determining an approximate solution of the formulated wheel motion problem, an original numerical method and a computer program for wheel motion simulation have been developed. Selected results illustrating the changes in displacements and velocity have been presented.

Influence of non-ideal fixed-end constraints on kinetostatic behaviors of compliant bistable mechanisms

Bistable mechanisms can maintain two distinct positions without energy consumption, which made them widely used in many special situations. The performance of bistable mechanisms may suffer from its non-ideal fixed-end constraints (the deformation of its ostensibly rigid frame), which may even incapacitate the bistability of the mechanisms. To capture the influence of non-ideal constraints on the behaviors of the mechanisms, a kinetostatic model for bistable mechanisms is presented in this paper. In the model, behaviors of both the frame and flexible beams are considered and characterized using the Chained Beam Constraint Model (CBCM). Three examples are modeled and analyzed to show the effectiveness of the model for evaluating the influence of non-ideal constraints on the behaviors of the mechanisms. The results are validated by the results of finite element analysis as well as experiments.

Modern explorations of the Brachistochrone-related problem: using the Udwadia–Kalaba approach

Modern explorations regarding the search for a curve subject to a minimization principle and its inverse, namely the search for the minimization object based on a given curve, are made. By using the Udwadia–Kalaba theory, which subsumes the Coulomb friction force as a non-ideal constraint, we obtain the analytic expression of the equation of motion for a particle moving along the Brachistochrone cycloid curve under Coulomb friction. Then we perform the inverse problem for the moving particle. That is, while the Brachistochrone cycloid curve is given, we seek the corresponding minimization object. Both the situations with and without friction are addressed. Finally, we return to the search for a curve subject to a minimization principle to complete the loop. However, this time we presume the minimization object is the total travel time, which was addressed in the classical Brachistochrone problem (hence, frictionless), while recognizing the presence of Coulomb friction. All three analyses come to meet at the special case when there is no friction. Our research reveals profound insights that have not been reported previously. The loop analysis also suggests a new angle for the study of dynamic systems.

An adaptive localization of pupil degraded by eyelash occlusion and poor contrast

The inner boundary of iris represents the pupil’s edge. Hence, to work an Iris Recognition System (IRS) and the gaze tracking system expeditiously it is important to locate it as precisely as possible in a significant amout of time. In the presence of non-ideal constraints e.g. non-uniform illumination, poor contrast, eyelashes, hairs, glasses, off-angle orientation, these systems may not work well. In this paper we present an adaptive pupil localization method based on the roundness criteria. First, it applies a gray level inversion to suppress the reflections, then it performs Gray level co-occurrence matrix (GLCM) based contrast estimation. If this estimated contrast is lower than a certain threshold, the input image is made to undergo gamma correction to adjust the contrast. Subsequently, anisotropic diffusion filtering followed by log transformation is applied, which suppresses the effect of eyelash occlusion, limits the creation of small regions and highlight the dark pixels. Afterwards, a clean binary image with few regions is acquired using adaptive thresholding and some morphological operations. Finally, the roundness metric is computed for each of these regions and the region with largest roundness metric, also being greater than a prescribed threshold, declared as pupil. Experiments were carried out on few well known databases, NICE1, CASIA V3 lamp, MMU, WVU and IITD. The results are grounded upon subjective and objective evaluation; which in turn, indicate that our method outperforms a state-of-the-art approach and a deep learning approach in terms of localization capability in some unconstrained scenarios and shorter processing time. After assessing the performance of the proposed algorithm, it is manifested that it ensures a fast and robust localization of pupil in the presence of corneal reflection, poor contrast, glasses and eyelash occlusion.

A reduced-order approach to the adaptive fuzzy sliding mode control of the constrained manipulator

A reduced-order approach to the adaptive fuzzy sliding mode control of the constrained manipulator is proposed. Based on the Udwadia–Kalaba motion constraint equation, the dynamic equation of the constrained manipulator with both ideal and non-ideal constraints is obtained. Considering the uncertainty of the terminal non-ideal constrained force and the chattering phenomenon of sliding mode control, the adaptive fuzzy and the sliding mode control method are combined to control the constrained manipulator. Because the system is constrained, the model order reduction method is innovatively used in the control algorithm. The stability of the system is proved by Lyapunov theorem. For demonstrating the effectiveness of the control algorithm, the 2-degree-of-freedom manipulator is taken as the research object. Finally, the high-precision control of the manipulator is achieved and the chattering phenomenon caused by the sliding mode control is weakened.

An approach to the dynamic modeling and sliding mode control of the constrained robot

An approach to the dynamic modeling and sliding mode control of the constrained robot is proposed in this article. On the basis of the Udwadia–Kalaba approach, the explicit equation of the constrained robot system is obtained first. This equation is applicable to systems with either holonomic or non-holonomic constraints, as well as with either ideal or non-ideal constraint forces. Second, fully considering the uncertainty of the non-ideal force, that is, the dynamic friction in the constrained robot system, the sliding mode control algorithm is put forward to trajectory tracking of the end-effector on a vertical constrained surface to obtain actual values of the unknown constraint force. Moreover, model order reduction method is innovatively used in the Udwadia–Kalaba approach and sliding mode controller to reduce variables and simplify the complexity of the calculation. Based on the demonstration of this novel method, a detailed robot system example is finally presented.

Numerical Decision of Problems of Structural Mechanics with Nonideal Unilateral Constraints

Here computational models of contact of elastic systems with the contact finite elements (CFE) in a 2D or 3D frame-rod systems are reviewed. The solution is based on the method of the step-by-step analysis taking into account the character of loading, the complicated conditions of the contact and other factors consideration of which approaches the calculation circuit of the task to the real operating conditions of any structures or construction

Motion of mechanical systems with non-ideal constraints

In the paper a new method to consider a mechanical system with non-ideal constraints is presented. It is proved that a mechanical system subjected to physical non-ideal constraints cannot be determined purely by theoretical analysis because the reaction forces depend on the physical parameters of interactive environment, which are defined only by measurement. The Principle of Compatibility is shown to be an effective tool in combination with experience for investigating such a problem. For illustration the dynamics of a digging machine are investigated.

Equilibrium and stability of tensegrity structures: A convex analysis approach

In this paper, tensegrity structures are modeled by introducing suitable energy convex functions. These allow to enforce both ideal and non-ideal constraints, gathering compatibility, equilibrium, and stability problems, as well as their duality relationships, in the same functional framework. Arguments of convex analysis allow to recover consistently a number of basic results, as well as to formulate new interpretations and analysis criterions.

Simulation of Constrained Mechanical Systems — Part I: An Equation of Motion

This paper presents an equation of motion for numerical simulation of constrained mechanical systems with holonomic and nonholonomic constraints. In order to avoid the error accumulation typically experienced in such simulations, the standard equation of motion is enhanced with embedded force and impulse terms which perform continuous constraint and energy correction along the numerical solution. To avoid interference between the kinematic constraint correction and the energy correction terms, both are derived by taking the geometry of the constrained dynamics rigorously into account. In this light, enforcement of the (ideal) holonomic and nonholonomic kinematic constraints are performed using ideal forces and impulses, while the energy conservation law is considered as a nonideal nonlinear nonholonomic constraint on the simulated motion, and as such it is enforced with nonideal forces. As derived, the equation can be directly discretized and integrated with an explicit ODE solver avoiding the need for expensive implicit integration and iterative constraint stabilization. Application of the proposed equation is demonstrated on a representative example. A more elaborate discussion of practical implementation is presented in Part II of this work.

Sensitivity of freedom spaces during flexure stage design via FACT

► Identified the sensitivity of freedom spaces as an area of concern for designers. ► Showed via a case study of how a 1-DOF system may emulate a 3-DOF system. ► Quantified the sensitivity of the freedom space for the 1-DOF case study. ► Identified the design space for the 1-DOF case study. The theoretical kinematic design of flexure stages using exact constraint methods is well known. These methods, however, do not take into account practical design considerations such as non-ideal constraint behavior. It is shown via a case study that the freedom space of a one degree-of-freedom (DOF) translation stage is extremely sensitive to both the arrangement and the elastomechanic behavior of the flexural constraints. The results of the case study show that certain combinations of constraint properties and layout yield a 1-DOF system that is more accurately modeled as a 3-DOF system. A non-dimensional constraint quality metric, CQ , is introduced in this paper to help classify the system in the case study as a 1-DOF system, a 3-DOF system, or a combination thereof. This paper is a first step in showing how practical design considerations may negatively influence the kinematics of systems that were previously assumed to have been designed “correctly” using exact constraint methods.

Modeling for dynamics of rigid-body systems with friction by linear complementary problem (LCP)

The purpose of this paper is to study the modeling method for nonholonomic systems with friction by linear complementary problem (LCP). Firstly, the dynamic equation with multipliers for the nonholonomic system with friction is given. Secondly, a standard linear complementary model is established, which describes the normal and tangential characteristics for a nonholonomic system. Thirdly, by using LCP theory, a general criterion is obtained, which can identify the singularity induced by nonideal geometrical constraints in a nonholonomic system. By a typical example of a nonholonomic system with friction, it is revealed how the problem solving for the constraint reaction forces can be transformed into the standard linear complementary problem. The research work may provide reliable theoretical basis for the dynamical simulation of a nonholonomic system with non-smooth factors.

Variational Method for Percussion Motion of a Non-Ideal Constraint System

The purpose is to study the variational method for impact problem of a non-ideal constraint system. Compared to an ideal constraint system, a non-ideal constraint system has more practical engineering background, but it contains unknown non-ideal constraint forces, which usually can be written as the function of ideal constrained forces. The existing analytical method on ideal constraint systems does not contain constraint forces. The non-ideal constraint forces are considered for impact problems in the variational principle, and then by method of Lagrange multipliers, equations for impact motion of a holonomic system and an expression of the kinetic energy variation during the impact motion are obtained.

Curve squealing of trains: Measurement, modelling and simulation

Curve squealing of railway wheels occurs erratically in narrow curves with a frequency of about 4 kHz . Squealing is caused by a self-excited stick-slip oscillation in the wheel–rail contact. The mechanism which activates squeal is still unexplained and will be analyzed in the paper at hand. The squeal model consists of the first modal forms of an elastic wheel and is equipped with a three-dimensional hard Coulomb contact. Based on this model, a linear stability analysis of the stationary run through a curve is performed for the four wheels of the investigated bogie. The results show that in particular the front inner wheel tends to squeal. A numerical simulation of the system's differential inclusions performed on the unstable states shows the existence of a self-excited stick-slip oscillation. The computed frequency of the limit cycle agrees well with the measurements. The design of the squeal model, the steps necessary to perform the stability analysis on systems with non-ideal constraints, as well as the non-smooth dynamics code used to perform the simulations are explained in detail.

Dynamics of Mechanical Systems and the Generalized Free-Body Diagram—Part I: General Formulation

In this paper, we generalize the idea of the free-body diagram for analytical mechanics for representations of mechanical systems in configuration space. The configuration space is characterized locally by an Euclidean tangent space. A key element in this work relies on the relaxation of constraint conditions. A new set of steps is proposed to treat constrained systems. According to this, the analysis should be broken down to two levels: (1) the specification of a transformation via the relaxation of the constraints; this defines a subspace, the space of constrained motion; and (2) specification of conditions on the motion in the space of constrained motion. The formulation and analysis associated with the first step can be seen as the generalization of the idea of the free-body diagram. This formulation is worked out in detail in this paper. The complement of the space of constrained motion is the space of admissible motion. The parametrization of this second subspace is generally the task of the analyst. If the two subspaces are orthogonal then useful decoupling can be achieved in the dynamics formulation. Conditions are developed for this orthogonality. Based on this, the dynamic equations are developed for constrained and admissible motions. These are the dynamic equilibrium equations associated with the generalized free-body diagram. They are valid for a broad range of constrained systems, which can include, for example, bilaterally constrained systems, redundantly constrained systems, unilaterally constrained systems, and nonideal constraint realization.

Dynamic-model reduction for a multimass system with nonideal constraint in a seismic damper

A dynamic model for a multimass system with a seismic damper as a nonlinear inertial component is reduced via balancing. The seismic damper is subject to a nonideal constraint. As an example, the order of the system of differential equations is reduced by one for a dynamic three-mass system. A comparison of the processes in the original and reduced systems confirms that it is possible to use balancing to simplify such models