Finite Element Modal Analysis Research Articles

Active Damping Design of Flexible Structures Based on SISO and SIMO Noncollocated Sensor-Actuator Velocity Feedback

An active damping design technique based on single input velocity feedback is presented in this paper. The stability conditions for each individual mode in SISO and SIMO velocity feedback are demonstrated. Since these stability conditions are derived using modal information, it is appropriate to incorporate this technique with the commonly used dynamic analysis techniques, such as experimental modal analysis and finite element analysis, for active damping design. Based on these stability conditions, two active damping design algorithms are proposed: 1) Constrained Least Squares Feedback Gain Computation, and 2) Optimal Feedback Gain Computation With Flexible Damping Factors. The first algorithm is a straightforward method to find the feedback vector for the given damping factors and the modal frequencies. The second algorithm is based on an optimization process which allows freedom in chosing the desired damping factors. The problem of locating the actuator and sensors is also discussed in this paper. The stability theory and active damping design technique are verified by an experimental example.

Transient response of piezoelectric discs to applied voltage pulses

Most of the techniques commonly used to analyse the vibration characteristics of piezoelectric discs are one-dimensional and assume that the piezoelectric disc vibrates in the thickness direction only (piston-like motion). They are applicable to discs with either very large diameter to thickness (D/T) ratios or very small D/T ratios. However, at intermediate D/T ratios, other vibration modes are significant, particularly in the transient motion when the disc is excited by voltage pulses. In this paper, finite element methods and modal analysis techniques have been used to predict the transient mechanical displacement over the surface of piezoelectric discs when they are excited by voltage pulses across electrodes on their top and bottom surfaces. Although many modes are predicted, and no one of them has the piston-like motion assumed by the one-dimensional model, the predicted transient response shows that the disc may display piston-like motion over the first few periods of the major through thickness mode due to high modal density and modal coupling effects. The surface motion then becomes complicated since other lower frequency modes come into effect. Finally the surface motion tends to that of the first radial mode, which is the last mode to be damped out.

Stability analysis of constraints in flexible multibody systems dynamics

Automated algorithms for the dynamic analysis and simulation of constrained multibody systems assume that the constraint equations are linearly independent. During the motion, when the system is at a singular configuration, the constraint Jacobian matrix possesses less than full rank and hence it results in singularities. This occurs when the direction of a constraint coincides with the direction of the lost degree of freedom. In this paper the constraint equations for deformable bodies are modified for use in the neighborhood of the singular configuration to yield the system inertia matrix which is nonsingular and also to take the actual generalized constraint forces into account. The procedures developed are applicable to both the augmented approach and the coordinate reduction methods. For the modeling of the constrained flexible multibody systems, a general recursive formulation is developed using Kane's equations, finite element method and modal analysis techniques. The system may contain revolute, prismatic, spherical or other types of joints, as well as geometrical nonlinearities; the rotary inertia is also automatically included. Simulation of a two-link flexible manipulator is presented at a singular configuration to demonstrate the utility of the method.

EXPERIMENTAL. MODAL. ANALYSIS OF REINFORCED CONCRETE STRUCTURES

Summary Experimental modal analysis techniques have been shown to be applicable to both laboratory test specimens and in situ test structures made of reinforced concrete. These techniques, in general, apply only to linear structures; however, many concrete structures are designed to remain in the linear, uncracked response region during dynamic excitation (nuclear power plant structures, for example). Data from the experimental analyses agreed well with finite-element modal analysis results, and the numerical models were further refined based on the experimental results. Because of the relatively low excitation levels required, these methods provide engineers with techniques for assessing the as-built condition of a structure without introducing damage into the structure. If a concrete structure is damaged, the experimental modal analysis methods could possibly be used to monitor its deterioration. Further investigations are needed to evaluate the sensitivity to damage of the experimentally determined modal properties. Also, methods must be found to determine, without prior modal data, if an in-situ structure is in a damaged state. These topics are being pursued by other researchers in the experimental modal analysis field.6 In its current form, experimental modal analysis methods can provide both practicing and research engineers with a valuable tool for verifying dynamic properties of reinforced concrete structures.

An investigation of ball-on-ball impact

The Bureau of Mines, U.S. Department of the Interior, has used a shock accelerometer to measure deceleration in ball-on-ball impact. The accelerometer signal was analyzed by a fast-Fourier-transform (FFT) technique, and signal components were identified from the accelerometer characteristics, solid mechanics, and finite-element modal and spectral analysis. Following frequency-domain digital filtering to remove extraneous frequencies, the remaining signal was reconstituted by an inverse FFT. Supporting Hertzian quasistatic and elastic and elastic-plastic dynamic finite-element calculations were carried out. All calculations predicted similar peak decelerations and contact times. The former agreed well with experiment. However, stress-wave effects make it difficult to use deceleration measurements to define contact times, even at an impact velocity of 8 ms−1. Such an impact must be analyzed as dynamic rather than static.

Nonlinear Modeling of Flexible Multibody Systems Dynamics Subjected to Variable Constraints

This paper presents the geometric stiffening effects and the complete nonlinear interaction between elastic and rigid body motion in the study of constrained multibody dynamics. A recursive formulation (or direct path approach) of the equations of motion based on Kane’s equations, finite element method and modal analysis techniques is presented. An extended matrix formulation of the partial angular velocities and partial velocities for flexible (elastic) bodies is also developed and forms the basis for our analysis. Closed loops and kinematical constraints (specified motions) are allowed and their corresponding Jacobian matrices are fully developed. The constraint equations are appended onto the governing equations of motion by representing them in a minimum dimension form using an innovative method called the Pseudo-Uptriangular Decomposition method. Examples are presented to illustrate the method and procedures proposed.

Finite element method applied to modeling crosstalk problems on printed circuit boards

In modeling crosstalk on printed circuit boards, the distributed parameter transmission line model is applied to include the effects of electromagnetic coupling between tracks. Starting with a finite element approach, a computer model for predicting crosstalk voltages and currents in a general n+1 multiconductor configuration is outlined. After the currents on each track are calculated by using the finite element method and modal analysis, a simple radiation model is used to calculate the radiated field produced by the printed circuit boards for a frequency range of 30-1000 MHz. The algorithm presented was implemented in a series of Fortran programs, and the results obtained using this procedure compare very well with available theoretical and experimental data.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Development of isometic force action programmed for weight during a lifting task with precision grip

Automated algorithms for the dynamic analysis and simulation of constrained multibody systems assume that the constraint equations are linearly independent. During the motion, when the system is at a singular configuration, the constraint Jacobian matrix possesses less than full rank and hence it results in singularities. This occurs when the direction of a constraint coincides with the direction of the lost degree of freedom. In this paper the constraint equations for deformable bodies are modified for use in the neighborhood of the singular configuration to yield the system inertia matrix which is nonsingular and also to take the actual generalized constraint forces into account. The procedures developed are applicable to both the augmented approach and the coordinate reduction methods. For the modeling of the constrained flexible multibody systems, a general recursive formulation is developed using Kane's equations, finite element method and modal analysis techniques. The system may contain revolute, prismatic, spherical or other types of joints, as well as geometrical nonlinearities; the rotary inertia is also automatically included. Simulation of a two-link flexible manipulator is presented at a singular configuration to demonstrate the utility of the method.

Determination of elastic constants of orthotropic plates by a modal analysis/Rayleigh-Ritz technique

The first part of this paper describes a computer programme in which equations derived by the Rayleigh-Ritz technique are used to model the vibrations of rectangular orthotropic plates. The characteristic functions of vibrating beams were used as the assumed functions for plates with boundary conditions consisting of clamped and free edges. Natural frequencies and mode shapes from the programme were verified by finite element analysis and modal analysis for square aluminium and graphite/epoxy plates. The plate vibration model was then incorporated into a second computer programme which was desgned to use the measured natural frequencies of orthotropic plates to determine the four apparent elastic constants. Natural frequencies measured by an impulse technique were used to determine two Young's moduli, the in-plane shear modulus, and a Poisson ratio for each plate.

Magnetic resonance in schizophrenia: A multiplanar approach to brain morphology : A. Rossi, P. Stratta, M. Gallucci, R. Passariello, A. Splendiani, V. Di Michele and M. Casacchia Chair of Clinical Psychiatry, MR Unit, Department of Radiology, University of L'Aquila, Italy

Dental implants are ideally placed in an orientation that allows vertical transfer of occlusal forces along their long axis. Nevertheless, optimal situations for implant placement are seldom encountered resulting in implants placement in angulated positions, which may affect their long-term success. The resonance frequency (RF) is an objective tool used to monitor stability of the implant tissue integration; however, little is known of the effect of the implant orientation in bone on the RF and its potential significance. The purpose of this research was to determine the relation between the dental implant orientation and the corresponding RF of implant. Three-dimensional (3D) modelling software was used to construct a 3D model of a pig mandible from computed tomography (CT) images. The RF of the implant was analysed using finite element (FE) modal analysis in software ANSYS (v.12). In addition, a cubical model was also developed in MIMICS to investigate the parameters affecting the relationship between RF and implant orientation in a simplified environment. The orientation angle was increased from 0 to 10 degrees in 1 degree increments and the resulting RF was analysed using correlation analysis and one-way ANOVA. Our analysis illustrated that the RF fluctuation following altering implant orientation was strongly correlated (r = 0.97) with the contacting cortical to cancellous bone ratio (CCBR) at the implant interface. The most extreme RF change (from 9.81 kHz to 10.07 kHz) occurred when the implant was moved 0.5 mm in positive z-direction, which resulted in the maximum change of CCBR from 52.9 to 54.8.

DYNAMIC CRACK PROPAGATION IN ELASTIC SOLID

The dynamic crack propagation in finite elastic solid is analyzed by using the combination of finite element method and modal analysis. It is proved analytically and numerically that the global energy release rate equals the local energy release rate. Energy release rate is employed as a fracture criterion so that the crack speed is determined as function of time for a given dynamic loading.

Optimal design of damped dynamic structures

AbstractA method of optimal design of damped structures under dynamic loads is developed, and several illustrative problems for minimum‐weight design of planar frame structures under impulsive external forces or ground accelerations are studied. In order to analyse dynamic structures, the finite element method and modal analysis technique are used, and structural damping is included in terms of modal damping ratios. For numerical optimization, a gradient‐type algorithm based on the state‐space approach in optimal control is utilized.

Comparative perturbation studies of the elastica

Continuum, harmonic and finite-element perturbation studies of the elastica are presented and compared, each study yielding the first four post-buckling path derivatives from an exact non-linear energy formulation. In the exact continuum analysis the boundary conditions demand the “suppression of secular terms” and the four path derivatives are obtained in closed form. The discrete harmonic and finite-element modal analyses are based on a recently developed general branching theory and a concise and extended version of this is presented. In the harmonic analysis and corresponding to the form of the continuum solution the initial infinite series are found to be progressively truncated by certain orthogonality conditions and closed-form solutions agreeing with those of the continuum analysis are obtained. The solutions of the finite-element study are seen to converge rapidly to those exact values as the number of elements is increased. The exact post-buckling load derivatives are used to construct approximate series solutions for the post-buckling equilibrium path of the strut, and these are shown to converge to the complete solution for values of the lateral deflexion up to about one-quarter of the length of the strut. The continuum and discrete perturbation schemes are seen to have identical patterns and it is observed that the suppression of secular terms in the continuum theory plays precisely the same role as the contraction of the equilibrium equations in the discrete theory.