Modal Technique Research Articles

Modal Parameters Identification of Civil Engineering Structures Based on the Random Decrement Technique

Modal identification technique is an effective measure for building materials health diagnosis, structural optimization design and safety assessment in structural engineering field. The time-domain method can only use the response signals to identify the modal parameters under ambient excitation, which became a wide concern topic in recent years. According to the points above, the theories of random decrement technique, complex exponential method and time-series method are presented. The random decrement technique is combined with the other two methods to become joint algorithms. A numerical simulation model is constructed to verify the feasibility and validity of the two joint algorithms.

Velocity shear effect on the longitudinal wave in a strongly coupled dusty plasma

The characteristics of longitudinal dust acoustic wave (DAW) in presence of velocity shear have been investigated in a strongly coupled dusty plasma using the generalized hydrodynamic (GH) model. In the hydrodynamic regime (ωτ m ≪1), i.e. when characteristic time τ m is slower than inverse of wave frequency, the viscosity in the GH model plays the usual role of wave damping, whereas in the kinetic regime (ωτ m ≫1), i.e. when characteristic time τ m is larger than inverse of wave frequency, viscosity shows energy storing property in the wave. In the kinetic regime, we have studied the longitudinal mode \(\omega^{2}=k^{2} (c_{d}^{2}+c_{l}^{2})\) (where ω is the frequency, k is the wave number, c d is the dust acoustic velocity and c l is the longitudinal velocity that arises due to viscosity) in presence of velocity shear. It is shown that velocity shear can destabilize this mode. Both nonmodal and modal techniques are employed to demonstrate the growth rate of the instability.

A mixed modal-differential quadrature method for free and forced vibration of beams in contact with fluid

A simple and accurate mixed modal-differential quadrature formulation is proposed to study the dynamic behavior of beams in contact with fluid. Both free and forced vibration problems are considered. The proposed mixed methodology uses the modal technique for the structural domain while it applies the differential quadrature method (DQM) to the fluid domain. Thus, the governing partial differential equations of the beam and fluid are reduced to a set of ordinary differential equations in time. In the case of forced vibration, the Newmark time integration scheme is employed to solve the resulting system of ordinary differential equations. The proposed formulation, in general, combines the simplicity of the modal method and high accuracy and efficiency of the DQM. Its application is shown by solving some beam-fluid interaction problems. Comparisons with analytical solutions show that the present method is very accurate and reliable. To demonstrate its efficiency, the test problems are also solved using the finite element method (FEM). It is found that the proposed method can produce better accuracy than the FEM using less computational time. The technique presented in this investigation is general and can be used to solve various fluid-structure interaction problems.

Optimal design of elastic plastic frames accounting for seismic protection devices

The optimal design of elastic perfectly plastic steel frames with or without suitable protection devices and subjected to static as well as seismic loadings is studied. Two minimum volume problem formulations are proposed, on the grounds of the so-called statical approach, accounting for three different resistance limits: the purely elastic limit, the (elastic) shakedown limit and the instantaneous collapse limit. The adopted load combinations are characterized by the presence of fixed loads, of quasi-static perfect cyclic loads and dynamic (seismic) loads. The linear elastic effects of the dynamic actions are studied by utilizing a modal technique. The proposed treatment is referred to the most recent Italian code related to the structural analysis and design. The solution of the optimization problem is reached by using an appropriate linearization iterative technique specialized to the proposed formulations. Flexural frames and cross-braced frames are studied, and the related minimum volume structures are reached for assigned features of the base isolation device. The Bree diagrams of the obtained optimal designs are also determined in order to characterize their structural behaviour.

Experimental Modal Testing of the Elastic Tube Bundle

The elastic tube bundle is a new-style heat exchange element that can enhance heat transfer efficiency and reduce energy consumption. It is difficult to obtain exact analytical solutions because of the complex shape and constraint condition. An experimental modal testing technique is applied to get the dynamic properties. Some issues to which one should pay attention during the experiment are emphasized. Natural frequencies and mode shapes are identified from the test and compared to numerical results. Agreement is found for most frequencies of interest. But, some discrepancies exist for the vibration in-plane due to the inevitable operation error.

Modal contributions to sound radiated from a fluid loaded cylinder

A modal decomposition technique to compute the individual modal contributions to the sound radiated from a cylindrical shell submerged in water is presented. The wet structural modes are calculated by means of a polynomial approximation and symmetric linearization of the underlying nonlinear eigenvalue problem. A Krylov subspace technique is used to reduce the model size of the structural domain, while the fluid domain remains unchanged. Results for the radiated sound power and sound pressure directivity are presented for groups of circumferential modes with common mode number. Under axial and transverse excitation, the cylinder breathing and bending modes are respectively the major modes contributing to the radiated sound at low frequencies. The contribution of the rigid body modes to the radiated sound is also observed.

Optimal design of steel frames accounting for buckling

A formulation of a special design problem devoted to elastic perfectly plastic steel frame structures subjected to different combinations of static and dynamic loads is presented. In particular, a minimum volume design problem formulation is presented and the structure is designed to be able to elastically behave for the assigned fixed loads, to elastically shakedown in presence of serviceability load conditions and to prevent the instantaneous collapse for suitably chosen combinations of fixed and ultimate seismic loadings as well as of fixed and wind actions. The actions that the structure must suffer are evaluated by making reference to the actual Italian seismic code. The dynamic response of the structure is performed by utilizing a modal technique. In order to prevent other undesired collapse modes further constraints are introduced in the relevant optimization problem taking into account the risk of element buckling. Different applications devoted to flexural frames conclude the paper. The sensitivity of the structural response has been investigated on the grounds of the determination and interpretation of the Bree diagrams of the obtained optimal structures.

Equivalent Representation of Mutual Coupling in Transmission Lines by Discrete Element

This paper describes a computational model based on lumped elements for the mutual coupling between phases in transmission lines without the explicit use of modal transformation matrices. The self and mutual parameters and the coupling between phases are modeled using modal transformation techniques. The modal representation is developed from the intrinsic consideration of the modal transformation matrix and the resulting system of time-domain differential equations is described as state equations. Thus, a detailed profile ofthe currents and the voltages through the line can be easily calculated using numerical or analytical integration methods. However, the original contribution of the article is the proposal of a time-domain model without the successive phase/mode transformations and a practical implementation based on conventional electrical circuits, without the use of electromagnetic theory to model the coupling between phases.

Dynamic Characteristics of a Wood Frame Structure: (II) the Effect of Artificial Damage

A full-scale, three-storey wood frame structure had been tested in-situ to investigate the changes of dynamic properties due to artificial damage. Beams and braces of the test structure were removed, to simulate damage, and then reassembled, to simulate rehabilitation. Free vibration tests were performed during every stage of the tests. The natural frequencies and damping ratios were obtained using modal parameter identification technique based on the Hilbert-Huang Transform. It is shown that, when the structure is damaged or rehabilitated, the natural frequency changes in accord with the structural stiffness in general while the damping ratio varies irregularly.

Component Mode Synthesis Method Applied to Two-Dimensional Acoustic Analysis in Ducts

This paper presents a modal approach to calculate the acoustic normal modes in complex ducts. In this study, the component modal synthesis (CMS) method in two dimensions for application in large duct with acoustic propagation in order to obtain a reduced acoustic model will be developed. The proposed technique is based on division of the acoustic system in well-known modal model subdomains and uses a CMS procedure to obtain a reduced acoustic modal model of the large system. In this paper, the applicability of the CMS Craig-Chang's method was adapted for acoustics CMS, considering only acoustic fluid interaction. In the modal synthesis technique developed originally for structural purpose, displacements and forces were coupled at the boundary of the substructures by dynamic constraint equations. The methodology developed here is based on residual flexibility, using residual inertia relief attachment modes in place of simply residual attachment modes to couple sound pressure and flow rates at the substructures interfaces. The approach leads to a versatile method with a low computational cost. To validate the proposed CMS approach, comparison with acoustic ducts models using finite element methodology (FEM) and analytical solutions were made. The differences between the analytical and numerical results as well as the limitations and advantages of each method were discussed.

A modal approach to the numerical calculation of primordial non-Gaussianities

We propose a new method to numerically calculate higher-order correlation functions of primordial fluctuations generated from any early-universe scenario. Our key-starting point is the realization that the tree-level In-In formalism is intrinsically separable. This enables us to use modal techniques to efficiently calculate and represent non-Gaussian shapes in a separable form well suited to data analysis. We prove the feasibility and the accuracy of our method by applying it to simple single-field inflationary models in which analytical results are available, and we perform non-trivial consistency checks like the verification of the single field consistency relation. We also point out that the iϵ prescription is automatically taken into account in our method, preventing the need for ad-hoc tricks to implement it numerically.

Wideband generalized admittance matrix representation for the analysis and design of waveguide filters with coaxial excitation

A very efficient technique for the full‐wave analysis and design of complex passive waveguide filters, including rectangular cavities with metallic cylindrical posts and coaxial excitation, is presented. This novel technique provides the wideband generalized admittance matrix representation of the whole structure in the form of pole expansions, thus extracting the most expensive computations from the frequency loop. For this purpose, the structure is properly segmented into its key building blocks, all of them characterized in terms of wideband admittance matrices. Then, an efficient iterative algorithm for combining these matrices, and finally providing the wideband generalized admittance matrix of the complete structure, is followed. In order to validate the accuracy and efficiency of this full‐wave modal technique, four different waveguide filters have been considered. In particular, the design of a compact four‐pole in‐line filter with tuning screws and of an evanescent‐mode filter, both operating in the X‐band and including a standard (vertical) coaxial excitation, are first presented. Finally, two C‐band six‐resonator comb‐line filters, one of them with a cross‐coupling configuration, and both excited with a collinear end‐launcher transition based on a disc‐ended coaxial, are also designed. Numerical data from a commercial software, as well as measurements of a manufactured prototype, are included for verification purposes.

Parametric study of the influence of the structure dimensions and the material properties on the global behavior of plates made of composite materials

This paper considers the effect of the damage caused by transverse stresses due to a low velocity impact loading on composite plates. The dynamic response of a plate is calculated using the modal superposition technique based on the classical plate theory of sandwich plates (stratified) taking into account transverse shear effects. An indentation law, based on the Hertz theory and verified experimentally, governs the behavior of the plate subsequent to impact. The numerical time integration scheme is used to calculate the contact force at any instant by combining the indentation and the dynamic response of the structure. The obtained results show a good correlation between the shock results and their prediction. This method is equally applied to the contact force as well as to the deformation of the plate. The simulation permits a parametric study of the structure dimensions and the material properties on the global behavior of the plate.

A Nonlinear Dynamic Finite Element Analysis of Drilling Shaft including Multispan Auxiliary Supports in Deep-Hole Machining

This paper presents a method to enhance computational efficiency of the nonlinear dynamic analysis of the large-scale deep-hole drilling machine. Based on finite element model, the drilling shaft system is constructed into Timoshenko beam element on the basis of flexible rotary shaft so as to increase the accuracy of numerical calculation. In order to save the calculation time and resources, modal synthesis technique is adopted to reduce the feature modal of linear freedom degrees of drilling shaft system. As a result, the accuracy required by the non-linear analysis will not be loss. On the basis of these, the whirling characteristics of drilling shaft system are studied under the conditions of different shaft lengths, and simultaneously, the stability patterns of drilling shaft motion and its stability region are obtained in the selected drilling depth and cutting speed parameters while drilling intersection holes.

Dynamic Performance Test and Analysis of Spindle System of High Speed Grinding Machine Tools

The high speed machine tool spindle plays an important role in machining operations. Based on modal test techniques and rotating machinery signature techniques, the research focused on the test and analysis of the dynamic characteristics of spindle system of high speed grinder. First, an experimental modal analysis (EMA) is performed in the spindle system; then, the frequency response characteristics and the FRFs of the system should be considered. Furthermore, rotating machinery signature techniques are used to analyze the dynamic behavior of the spindle system in process due to the limitation of modal test techniques, and the theoretical proof is given to explain the spindle system order. The results show that it requires the machine tool to avoid the use of vibration-sensitive speed in the production process and the machine production process, especially bearing manufacturing to improve its accuracy.

A-posteriori error estimation for second order mechanical systems

One important issue for the simulation of flexible multibody systems is the reduction of the flexible bodies degrees of freedom. As far as safety questions are concerned knowledge about the error introduced by the reduction of the flexible degrees of freedom is helpful and very important. In this work, an a-posteriori error estimator for linear first order systems is extended for error estimation of mechanical second order systems. Due to the special second order structure of mechanical systems, an improvement of the a-posteriori error estimator is achieved. A major advantage of the a-posteriori error estimator is that the estimator is independent of the used reduction technique. Therefore, it can be used for moment-matching based, Gramian matrices based or modal based model reduction techniques. The capability of the proposed technique is demonstrated by the a-posteriori error estimation of a mechanical system, and a sensitivity analysis of the parameters involved in the error estimation process is conducted.

Applying a modal technique on a planar lens based on nanoscale slit arrays

A planar lens structure based on an array of nanoscale slits in a metallic film is modeled using a waveguide modal technique. The structure is modeled as a one dimensional lens followed by free space propagation. The obtained results are compared to published experimental results as well as numerical simulations using either the finite difference frequency domain or the transmission line method. A good agreement has been obtained with significant simulation time reduction.

Finite Element Analysis and Vibration Control of a Deep Composite Cylindrical Shell Using MFC Actuators

A four-node composite facet-shell element is developed, accounting for electromechanical coupling of Macrofiber Composite (MFC) and conventional PZT patches. Further a warping correction is included in order to capture correctly the induced strain of conformable MFC, surface bonded on a cylindrical shell. The element performance to model the relations between in-plane electric field to normal strains is examined with the help of experiment and ANSYS analysis. In ANSYS, a simple modeling scheme is proposed for MFC using a parallel capacitors concept. The independent modal space control technique has been revisited to address the control of combination resonances through a selective modal space control scheme, where two or more modes can be combined to form the vibrating system or plant in modal domain. The developed control schemes are implemented in a digital processor using DS1104 and the closed-loop vibration control experiments are conducted on a CFRP shell structure. The influence of directionally induced actuation of MFC actuators on elastic couplings of composite shell is studied theoretically and is subsequently demonstrated in experiments. MFC actuators provide the much needed optimization domain for achieving the vibration control of combination resonances of elastically coupled deep-shell structure.

Modeling of subwavelength problems using modal techniques

A modal technique is used for modeling the problem of light propagation through masks with subwavelength features. Different approaches for the proper treatment of the excitation and the finite window are discussed. Results obtained using the technique are compared to those obtained by the volume integral equation method and the finite difference time domain method. The proposed technique shows very good agreement with both methods as well as significant reduction in the simulation time compared to the finite difference time domain method.

Calculation of Coupled Modes for Vibro-Acoustic Problems

A new numerical method for the study of elasto-acoustic structures coupled with fluid-filled cavities has been developed. This method essentially consists of solving the eigenvalue problem for the determination of elasto-acoustic modes. The Numerical methods commonly used for its resolution is based on the mass coupling. However, this approach requires for it is resolution the inversion of a singular matrix, "the stiffness matrix of the fluid". We then propose a new numerical method based on stiffness coupling by using modal superposition techniques through a change of variable which shows a symmetric and regular problem in terms of displacement of the elastic structure and in terms of fluid pressure in the cavity.