Modal Force Research Articles

The relationship between irrealis mood and deontic modality in Paresi (Arawak)

This article presents a description and analysis of the deontic modality and its relationship with mood category (realis vs irrealis) in Paresi, a language of the Arawak family, spoken in Brazil. Data were collected from two questionnaires on deontics and texts. For the analysis of the data, we used, as the theoretical framework on mood and modality, the works of Feldman (1986), Hacquard (2006, 2010); Mithun (1995, 1999) and Palmer (2001). First, we show how the realis/irrealis mood marking occurs in Paresi. In the sequence, we describe the Paresi as a language that lexically marks the type of modality, but not the modal force. We present two markers of deontic modality in this language: maika and wa(iye)hena, which indicate both necesssity and possibility. These markers exhibit particle properties and occupy high positions in the sentence structure. Finally, we describe the deontic modality of necessity, showing that there are two types of obligations in Paresi: one indicated by the maika particle; and another, by the particle wa(iye)hena. The first figures, preferably, in contexts in which a participant is directly responsible for the realization of the event and seems to be associated to the realis mood. On the other hand, wa(iye)hena is employed in contexts of laws and general rules, which describe how a state of affairs should be, and co-occurs, predominantly, with the irrealis marker.

Explaining the modal force of natural laws

In this paper, I will defend the thesis that fundamental natural laws are distinguished from accidental empirical generalizations neither by metaphysical necessity (e.g. Ellis 1999, 2001; Bird in Analysis, 65(2), 147–155, 2005, 2007) nor by contingent necessitation (Armstrong 1983). The only sort of modal force that distinguishes natural laws, I will argue, arises from the peculiar physical property of mutual independence of elementary interactions exemplifying the laws. Mutual independence of elementary interactions means that their existence and their nature do not depend in any way on which other interactions presently occur. It is exactly this general physical property of elementary interactions in the actual world that provides natural laws with their specific modal force and grounds the experience of nature’s ‘recalcitrance’. Thus, the modal force of natural laws is explained by contingent non-modal properties of nature. In the second part of the paper, I deal with some alleged counterexamples to my approach: constraint laws, compositional laws, symmetry principles and conservation laws. These sorts of laws turn out to be compatible with my approach: constraint laws and compositional laws do not represent the dynamics of interaction-types by themselves, but only as constitutive parts of a complete set of equations, whereas symmetry principles and conservation laws do not represent any specific dynamics, but only impose general constraints on possible interactions.

Nonlinear mechanical system simulation based on modal coordinates and modal forces

In a project at Beihang University different methods to model, simulate and identify nonlinear mechanical systems are studied. One promising method to simulate forced response in nonlinear mechanical systems is based on modal coordinates and modal forces. The method allows many input forces and many nonlinearities to be handled simultaneously. The method is briefly described here together with a simple example.

Buffeting response evaluation of long-span bridges with emphasis on the three-dimensional effects of gusty winds

A generalized gust loading model applicable to the buffeting response predictions of both slender, line-like long-span bridges and bridges with small aspect-ratios (the ratio of the span to the width of a deck) is established based on the three-dimensional (3D) theory. The spectra of the buffeting forces are determined by the equivalent 3D two-wavenumber aerodynamic admittance function (AAF) to deal with the 3D effects of gusty winds. The mode shape influence function is introduced to take into account the three-dimensionality of the modal force. Since the mode shape influence function involves the aspect-ratio term, the three-dimensionality of modal force therefore shows a dependence on the aspect-ratio of the bridge deck. The gust response analysis can easily be conducted in the frequency domain through the use of the generalized gust loading model. Numerical examples of bridges with different aspect-ratios in service states and construction states are performed to evaluate the discrepancies in the buffeting displacements calculated by both the generalized gust loading model and the traditional gust loading model. The results show that the traditional gust loading model can generally be applied to the buffeting analysis of long-span bridges with large aspect-ratios in both the service and construction states. However, for bridges with small aspect-ratios, such as in the construction stages, the traditional gust model may overestimate the buffeting response of a bridge deck to a larger degree (neglecting any end effect), indicating the invalidation of the strip assumption in these cases.

Dynamic behavior of upgraded rocking wall-moment frames using an extended coupled-two-beam model

Rocking wall-moment frames (RWMFs), which perform well in controlling the soft-story mechanism, can achieve an enhanced performance by substituting their pinned base by a variable base rotational constraint provided by replaceable self-centering and energy dissipation devices. Rather than experiencing damage inside the moment frames, those upgraded RWMFs show a high potential towards seismic resilience by transferring damage to the replaceable base rotational constraint. The effect of this rotational constraint and the stiffness ratio between the moment frame and rocking wall on the dynamic behavior of upgraded RWMFs is investigated with the aid of an extended coupled-two-beam model proposed in this paper. In this model, the rocking wall and moment frame are represented by a linked flexural beam and a shear beam, respectively. The model replaces the fixed base of the flexural beam by a rotational spring to take the variable base rotational constraint into account. Closed-form solutions for modal displacement shapes, modal drifts, modal shear force and modal moment are derived. The model is verified with finite element analysis, and modal contributions to seismic response and drift concentration factor demand under earthquakes are investigated. It is found that within identified ranges of the rotational constraint and the stiffness ratio between the moment frame and rocking wall, a relatively good uniformity of story drift distribution is obtained and the higher modes effect caused by the full releasing of the rocking wall is mitigated. The model, the derived interstory drift spectra and drift concentration factor spectra can serve as useful tools for preliminary resilience oriented design purpose.

Generalized modal element method: part II—application to eight-node asymmetric and symmetric solid-shell elements in linear analysis

In this paper, two eight-node asymmetric solid-shell elements are firstly presented to illustrate the use of traditional finite element technique in GMEM for constructing new finite element formulations. In these two elements, the analytical method is utilized to derive the displacement functions of the basic in-plane modes, which makes the resulted elements free of mesh distortions for these modes. For out-of-plane modes, the Mindlin plate elements CQUAD4 and QTS4 are integrated to calculate the corresponding modal displacement vectors and modal force vectors of solid-shell elements. As a result, the displacement functions of the plate-bending element range up to three orders of magnitude. On the other hand, since the asymmetric elements cannot be applied to frequency analysis, two symmetric solid-shell elements are proposed by using a modal transformation method, in which the in-plane modes are derived from the previous proposed symmetric solid element S-MEM8S and the out-of-plane modes are constructed by plate elements CQUAD4 and QTS4, respectively. Various benchmarks including linear static and frequency analysis are presented to demonstrate the accuracy and efficiency of the presented elements.

Modified Elastic Dynamic Analysis (EDA) for Seismic Demand on In-Span Hinge Shear Keys in Multi-Frame Bridges

Long concrete box-girder bridges are typically constructed in multiple frames that are separated by in-span hinges. Shear keys, located at the in-span hinges, help preserve the transverse integrity of the bridge frames. To date, no reliable method other than nonlinear time history analysis exists to estimate the seismic force demands on in-span shear keys. Methods such as pushover and elastic dynamic analysis (EDA) do not provide accurate estimations. In this study, a rational and reliable analysis method was developed for obtaining the seismic demand on in-span shear keys of multi-frame bridges. A large number of time history analyses were performed on two- to five-frame bridge models with single- and two-column bents that were designed according to California Department of Transportation (Caltrans) Seismic Design Criteria. The results show that high-frequency modes of vibration of the superstructure significantly contribute to the shear key force demands. These modes may also cause transverse yielding in columns. It was established that a modified EDA method may be used to approximate the shear key force demands. In the proposed modified method, the modal forces are reduced separately by the corresponding modal displacement ductility before performing modal combination. This method accounts for the nonlinear response under high-frequency modes of vibration.

Evaluating actuator distributions in simply supported truncated thin conical shell with embedded piezoelectric layers

In this investigation, distributed modal actuator forces of simply supported truncated conical shell embedded by a piezoelectric layer are studied. Piezoelectric layer is distributed on the conical shell surface as actuators. Three types of distributions are considered: longitudinal, circumferential, and diagonal distributions. First, electromechanical equations of the conical shell with embedded piezoelectric actuator layer are extracted. Then modal expansion method is used to define independent modal characteristics of the conical shell. For each kind of distribution, three case studies are considered and evaluated. Results showed that in the longitudinal and diagonal distributed actuator, membrane force in the longitudinal direction is the dominant force and in the circumferential distributed actuator, the membrane force in the circumferential direction is the dominant force. The effects of cone angle, piezoelectric thickness, and piezoelectric layer segmentation on modal forces of each distributed actuator are also studied. In circumferential distributed actuator, modal forces increase as the cone angle increases. This phenomenon in the longitudinal and diagonal distributed actuator is almost reversed. The piezoelectric layer segmentation effect on the modal forces distribution is also evaluated, and it showed that this phenomenon has a critical effect on the modal forces distribution.

Multi-parameter optimization of piezoelectric actuators for multi-mode active vibration control of cylindrical shells

A novel technique for the multi-parameter optimization of distributed piezoelectric actuators is presented in this paper. The proposed method is designed to improve the performance of multi-mode vibration control in cylindrical shells. The optimization parameters of actuator patch configuration include position, size, and tilt angle. The modal control force of tilted orthotropic piezoelectric actuators is derived and the multi-parameter cylindrical shell optimization model is established. The linear quadratic energy index is employed as the optimization criterion. A geometric constraint is proposed to prevent overlap between tilted actuators, which is plugged into a genetic algorithm to search the optimal configuration parameters. A simply-supported closed cylindrical shell with two actuators serves as a case study. The vibration control efficiencies of various parameter sets are evaluated via frequency response and transient response simulations. The results show that the linear quadratic energy indexes of position and size optimization decreased by 14.0% compared to position optimization; those of position and tilt angle optimization decreased by 16.8%; and those of position, size, and tilt angle optimization decreased by 25.9%. It indicates that, adding configuration optimization parameters is an efficient approach to improving the vibration control performance of piezoelectric actuators on shells.

Modal energy analysis for mechanical systems excited by spatially correlated loads

Abstract MODal ENergy Analysis (MODENA) is an energy-based method, which is proposed to deal with vibroacoustic problems. The performance of MODENA on the energy analysis of a mechanical system under spatially correlated excitation is investigated. A plate/cavity coupling system excited by a pressure field is studied in a numerical example, in which four kinds of pressure fields are involved, which include the purely random pressure field, the perfectly correlated pressure field, the incident diffuse field, and the turbulent boundary layer pressure fluctuation. The total energies of subsystems differ to reference solution only in the case of purely random pressure field and only for the non-excited subsystem (the cavity). A deeper analysis on the scale of modal energy is further conducted via another numerical example, in which two structural modes excited by correlated forces are coupled with one acoustic mode. A dimensionless correlation strength factor is proposed to determine the correlation strength between modal forces. Results show that the error on modal energy increases with the increment of the correlation strength factor. A criterion is proposed to establish a link between the error and the correlation strength factor. According to the criterion, the error is negligible when the correlation strength is weak, in this situation the correlation strength factor is less than a critical value.

Panel Flutter Emulation Using a Few Concentrated Forces

The objective of this paper is to study the feasibility of panel flutter emulation using a few concentrated forces. The concentrated forces are considered to be equivalent to aerodynamic forces. The equivalence is carried out using surface spline method and principle of virtual work. The structural modeling of the plate is based on the classical plate theory and the aerodynamic modeling is based on the piston theory. The present approach differs from the linear panel flutter analysis in scheming the modal aerodynamics forces with unchanged structural properties. The solutions for the flutter problem are obtained numerically using the standard eigenvalue procedure. A few concentrated forces were considered with an optimization effort to decide their optimal locations. The optimization process is based on minimizing the error between the flutter bounds from emulated and linear flutter analysis method. The emulated flutter results for the square plate of four different boundary conditions using six concentrated forces are obtained with minimal error to the reference value. The results demonstrated the workability and viability of using concentrated forces in emulating real panel flutter. In addition, the paper includes the parametric studies of linear panel flutter whose proper literatures are not available.

An energy-based pushover-analysis with torque-effects in assessment of the structures with asymmetric plan

The current paper aims to investigate the pushover schemes for buildings with asymmetric plan in nonlinear static procedures (NSPs). Moreover, this paper will propose an extension of the energy-based adaptive pushover analysis (EAPA) procedure for the seismic design/assessment of 3D irregular structures, which will be denoted as energy-based pushover-analysis with torque-effects (EPT). This innovative single-run adaptive method is proposed based on the work done produced by modal force in each step of analysis; and is validated on 3D steel structures with asymmetric plan composed from moment-resisting frames. EPT uses the concepts of energy to produce an incremental, adaptive load pattern that takes into account the effects of structural deterioration due to seismic loads, the higher modes of vibration, and the characteristics of the frequency content of the excitations. Also, an innovative MDOF-to-SDOF transformation method is proposed based on energy concept, removing the ambiguity of choosing a controlling point in asymmetric plan buildings. The seismic response obtained from nonlinear analyses under 20 earthquake excitations are plotted over the height of the structures. The results of the analytical studies of these buildings show that the EPT method provides a good prediction of maximum inter-story drifts and displacements over the height of the structures.

Response Spectrum Method for integrated and differential spatial seismic ground motions

The Response Spectrum Method (RSM) is a widely known method for solving linear dynamic problem in earthquake engineering. However, it is often believed that the RSM can only be applied to the integrated (or averaged over the base of the building) seismic ground motion, when a ground base moves like a rigid body. In this paper we show how to apply spectral technique not only to the integrated six-component seismic motion that is included three translational and three rotational components, but also to the differential seismic motion, when each support point of structure makes individual spatial motion.The RSM is a quasistatic modal method, in which the modal seismic forces are defined as static loads that depend on spectral accelerations. To use the RSM for the differential seismic motion it is necessary to solve two key problems: firstly, correctly define the relative motion of a structure about the moving points of the ground and, secondly, determine the spatial distribution of spectral accelerations. These problems are solved by introducing an influence matrix (it relates the generalized coordinates of the support points and the generalized coordinates of the structure) and a matrix of spatial variations of intensity. The use of these matrices allows to obtain the equations of relative differential motion which are similar to the equations of the integrated seismic ground motion. Therefore, it's easy to apply the RSM to them.This article presents a theory of spectral technique for the general cases of the integrated and differential ground motions. To illustrate the application of the RSM, we consider a simple spatial structure (a rigid plate with shifted flexural center on four steel columns under two-component seismic action, the m-file with solution is attached in the Appendix) for the integrated and differential ground motions.

Seismic effectiveness of top-story mass dampers for inelastic two-way asymmetric-plan buildings

Self-mass dampers, which use intrinsic parts of structures as tuned mass dampers, are economically advantageous in terms of the materials and space required. Previous research proposed using the top story of a two-way asymmetric-plan building as a self-mass damper, referred to as a top-story mass damper (TSMD), for suppressing the seismic response of an elastic building. In light of the promising results of that research, this study further explores the seismic effectiveness of TSMDs when two-way asymmetric-plan buildings become inelastic under earthquake loads. Furthermore, this study explores the possibility of using a pair of elastic TSMDs to alleviate the detuning effects caused by yielding of the main structure. One TSMD of the pair is designed according to the previous research and is responsible for suppressing the vibrations of the target building in elastic states. The other TSMD is designed based on the properties of collective force–deformation relationships and is responsible for suppressing the vibrations of the target building in inelastic states. The collective force–deformation relationships are the pushover curves of the target building when subject to the collective modal inertia force vectors of the first triplet of vibration modes of the building. This study looks at one single-story building and one 20-story building, which are shaken into various damage states, as the numerical examples for evaluating the seismic effectiveness of TSMDs for inelastic two-way asymmetric-plane buildings.

An improved EMD method for modal identification and a combined static-dynamic method for damage detection

Empirical mode decomposition (EMD) is a highly adaptable signal processing method. However, the EMD approach has certain drawbacks, including distortions from end effects and mode mixing. In the present study, these two problems are addressed using an end extension method based on the support vector regression machine (SVRM) and a modal decomposition method based on the characteristics of the Hilbert transform. The algorithm includes two steps: using the SVRM, the time series data are extended at both endpoints to reduce the end effects, and then, a modified EMD method using the characteristics of the Hilbert transform is performed on the resulting signal to reduce mode mixing. A new combined static-dynamic method for identifying structural damage is presented. This method combines the static and dynamic information in an equilibrium equation that can be solved using the Moore-Penrose generalized matrix inverse. The combination method uses the differences in displacements of the structure with and without damage and variations in the modal force vector. Tests on a four-story, steel-frame structure were conducted to obtain static and dynamic responses of the structure. The modal parameters are identified using data from the dynamic tests and improved EMD method. The new method is shown to be more accurate and effective than the traditional EMD method. Through tests with a shear-type test frame, the higher performance of the proposed static-dynamic damage detection approach, which can detect both single and multiple damage locations and the degree of the damage, is demonstrated. For structures with multiple damage, the combined approach is more effective than either the static or dynamic method. The proposed EMD method and static-dynamic damage detection method offer improved modal identification and damage detection, respectively, in structures.

Fluid structure interaction analysis: vortex shedding induced vibrations

Fluid Structure Interaction (FSI) numerical modelling requires an efficient workflow to properly capture the physics involved. Computational Structural Mechanics (CSM) and Computation Fluid Dynamics (CFD) have to be coupled and at the moment there is a lack of monolithic solvers capable to tackle industrial applications that involves high fidelity models which mesh can be comprised of hundred millions of cells. This paper shows an efficient approach based on standard commercial tools. The FEM solver ANSYS® Mechanical™ is used to extract a given number of eigenmodes. Then the modal shapes are imported in the CFD solver Fluent® using the Add On RBF Morph™. Updating the modal coordinates it is possible to adapt the shape of the model by taking into account the elasticity of the CFD model. Transient analysis is faced using a time marching solution by updating the shape of the mesh at each time step (weak coupling, evaluated as single DOF systems and integrating modal forces over the CFD grid). Numerical performances and solution accuracy of this approach are analyzed on a practical application (NACA0009 Hydrofoil) for which experimental data are available. A comparison between proposed method and experiment is provided. Transient coupled solver is used for the computation of eigenvalues in water by post processing the free vibration response in calm fluid.

Vibration suppression of flexible spacecraft during attitude maneuver using CMGs

In this paper, control moment gyroscope (CMG) system is employed to suppress vibration of flexible spacecraft during attitude maneuver. Direct modal force generated by CMGs is exerted to elastic dynamics due to interaction between CMGs and flexibilities of structure. A novel control strategy based on a modal force compensator is proposed, which is simple and efficient to reduce vibration during attitude maneuver. The proposed modal force compensator avoids exciting vibration by the means of canceling out disturbance input to elastic dynamics using modal force generated by CMGs. No modal information is required in the modal force compensator. A concept named as modal force singularity is introduced and analyzed in depth. A restriction on gimbal angles is developed to avoid modal force singularity. Subsequently, a steering logic based on pseudo-inverse is proposed to allocate modal force commands without introducing force errors. Numerical simulations are presented to show the effectiveness of the proposed approaches.

Distributed microscopic actuation analysis of paraboloidal membrane shells of different geometric parameters

Abstract Paraboloidal membrane shells of revolution are commonly used as key components for advanced aerospace structures and aviation mechanical systems. Due to their high flexibility and low damping property, active vibration control is of significant importance for these in-orbit membrane structures. To explore the dynamic control behavior of space flexible paraboloidal membrane shells, precision distributed actuation and control effectiveness of free-floating paraboloidal membrane shells with piezoelectric actuators are investigated. Governing equations of the shell structronic system are presented first. Then, distributed control forces and control actions are formulated. A transverse mode shape function of the paraboloidal shell based on the membrane approximation theory and specified boundary condition is assumed in the modal control force analysis. The actuator induced modal control forces on the paraboloidal shell are derived. The expressions of microscopic local modal control forces are obtained by shrinking the actuator area into infinitesimal and the four control components are investigated respectively to predict the spatial microscopic actuation behavior. Geometric parameter (height-radius ratio and shell thickness) effects on the modal actuation behavior are explored when evaluating the micro-control efficiency. Four different cases are discussed and the results reveal the fact that shallow (e.g., antennas/reflectors) and deep (e.g., rocket/missile fairing) paraboloidal shells exhibit totally different modal actuation behaviors due to their curvature differences. Analytical results in this paper can serve as guidelines for optimal actuator placement for vibration control of different paraboloidal structures.

Design and implementation of a novel modal space active force control concept for spatial multi-DOF parallel robotic manipulators actuated by electrical actuators

Robotic spine brace based on parallel-actuated robotic system is a new device for treatment and sensing of scoliosis, however, the strong dynamic coupling and anisotropy problem of parallel manipulators result in accuracy loss of rehabilitation force control, including big error in direction and value of force. A novel active force control strategy named modal space force control is proposed to solve these problems.Considering the electrical driven system and contact environment, the mathematical model of spatial parallel manipulator is built. The strong dynamic coupling problem in force field is described via experiments as well as the anisotropy problem of work space of parallel manipulators. The effects of dynamic coupling on control design and performances are discussed, and the influences of anisotropy on accuracy are also addressed. With mass/inertia matrix and stiffness matrix of parallel manipulators, a modal matrix can be calculated by using eigenvalue decomposition. Making use of the orthogonality of modal matrix with mass matrix of parallel manipulators, the strong coupled dynamic equations expressed in work space or joint space of parallel manipulator may be transformed into decoupled equations formulated in modal space. According to this property, each force control channel is independent of others in the modal space, thus we proposed modal space force control concept which means the force controller is designed in modal space. A modal space active force control is designed and implemented with only a simple PID controller employed as exampled control method to show the differences, uniqueness, and benefits of modal space force control. Simulation and experimental results show that the proposed modal space force control concept can effectively overcome the effects of the strong dynamic coupling and anisotropy problem in the physical space, and modal space force control is thus a very useful control framework, which is better than the current joint space control and work space control.

The Expression of Modality in Tlingit: A Paucity of Grammatical Devices

This paper provides an in-depth description of the expression of modal categories in Tlingit (Na-Dene; Alaska). Epistemic, deontic, and circumstantial modal statements are examined, and for each I examine statements with strong and weak modal force. A notable feature of the Tlingit system is that—relative to other languages of the Pacific Northwest—Tlingit exhibits a striking paucity of grammaticalized modal expressions, and only a limited subset of the aforementioned modal categories can be expressed by the conventionalized, truth-conditional semantics of a statement. Nevertheless, speakers employ a variety of pragmatic strategies to communicate information about other modal categories. This situation is rather similar to that reported for Nez Perce, but different from cases such as St’át’imcets or Washo, in which modals exhibit a context-dependent meaning, allowing for a small set to denote all logically possible modal categories.