Use Of Mode Shapes Research Articles

Damage identification using vibration monitoring techniques

Damages can originate in engineering structures due to various detrimental and hostile conditions that leads to calamitous occurrences. Structural damage monitoring has been formally established in the past few decades and is critical for sustaining and upholding the integrity of structures in its designated service life. Real time condition monitoring and damage detection needs to be necessitated for the appropriate functioning of the concerned entity. Vibration intensive damage identification techniques have been reviewed for identifying the actual material properties such as stiffness and damping for assessing authentic health condition of machine elements as well as structures. Acceleration, velocity and displacement-based signals are measured and processed further using vibration monitoring hardware and software. The structural dynamic responses are studied and analyzed to be correlated to the presence of damages. This paper reviews the use of mode-shapes, modal strain energy, wavelet transform, waveform fractal dimension and finite element model updating in damage identification. The challenges encountered with each technique are discussed and the proposed methodology for overcoming them. Propositions have also been made with respect to the current scenario and downsides of respective technique. The paper will be helpful for practicing engineers and researchers working in structural damage identification and control related field for conceiving novel, reliable, effective, robust, and practical methods.

Similitudes for the structural response and radiated sound power of simply supported plates

This communication investigates exact and distorted similitudes and the related scaling laws for the analysis of both dynamic response and radiated power of rectangular plates. The response of a given panel in similitude from another one is determined from a generalization of the modal approach, allowing the use of mode shapes, natural frequencies and finally radiation functions in order to establish appropriate scaling laws. Analytical models of simply supported rectangular plates are used to produce both original and replica model responses under point mechanical excitation. Emphasis is then especially put on laboratory experiments which are performed on baed simply supported aluminum panels under mechanical excitations. All the six possible scaling directions, i.e., predicting a plate vibroacoustic reponse from another plate, are reported. All obtained results show that structural response or radiated sound power of a given plate can be both recovered with satisfactory accuracy by using the related scaling laws, even if parent models are used.

Expansion of experimental mode shape from operational modal analysis and virtual sensing for fatigue analysis using the modal expansion method

Offshore structures are exposed to fatigue damage due to fluctuating environmental and operational forces. The actual stress history of structures in operation is an important parameter for the remaining fatigue lifetime. Unfortunately, the fatigue critical locations are often difficult to reach for inspection of cracks or installation of sensors and these direct locations lead to corruption of sensors due to the environmental effects. Virtual sensing enables full-field stress/strain estimation that facilitates fatigue analyses of offshore structures in operation. In the literature, various virtual sensing methods exist but this paper focuses on modal expansion. This technique uses the mode shapes (the linear subspace) of the structure to transform the measured system response into the full-field stress/strain response. The applied mode shapes either hail from a finite element model or an expansion of experimental mode shapes from an operational modal analysis. This paper compares the use of mode shapes from a finite element model to the use of expanded experimental mode shapes. Modal expansion is applied to a scaled offshore platform in the laboratory to estimate the strain response using the finite element mode shapes and expanded experimental mode shapes using different expansion techniques: System Equivalent Reduction Expansion Process (SEREP), local correspondence principle, and the new leave-p-out cross validation implementation of the local correspondence principle introduced in this paper. The results are analysed with different metrics and this paper introduces a new quality measurement – the normalised error of fatigue damage – for strain estimation intended for fatigue analysis. Based on this study, expansion of experimental mode shapes has the potential to reduce errors in stress/strain estimation. The expansion is, however, a fitting process and, thus, it contains fitting error dependent on the case. In this study, the finite element mode shapes outperform some of the mode shape expansion techniques due to this fitting errors. Therefore, expansion of experimental mode shapes can improve stress/strain estimation but it should be used with care to avoid an overfit.

Component Mode Synthesis Approach for Micro End Mill Dynamics Considering Machine Tool Compliance

Chatter in machining can be avoided by machining at stable process parameters obtained from the stability lobe diagram. The accuracy of the stability lobe diagram depends on the accurate determination of micro-endmill dynamics. It is not trivial to experimentally determine the tool tip dynamics of a micro-endmill due to relatively small diameters (10μm to 500μm). There are different approaches to estimate the micro-endmill dynamics, however, one of the most widely used techniques is the receptance coupling method. It combines the frequency response functions for the two substructures (machine tool with a portion of shank and the micro-endmill) to determine the tool-tip dynamics. There are certain issues with the receptance coupling which uses only two locations for determining the FRF one at the coupling and other at tip unlike the component mode synthesis which allows use of mode shapes at multiple points in the substructures. Another limitation for receptance coupling method is that the FRF for both substructures must be sampled at same frequency for coupling but the first non-rigid modal frequency for free-free substructure of micro-endmill can exceed 50kHz which would require a high bandwidth sensor with a sampling frequency in excess of 100kHz. Consequently, the component mode synthesis approach has been used to couple the substructures. The mode synthesis approach adopted in the present work contains the position dependent modes along the length of substructures. In order to ensure that the component mode synthesis yields accurate results, a test case of a micro-endmill as a fixed cantilever beam has been analyzed. Note that the actual micro-end mill dynamics is affected by the machine tool compliance which needs to be accounted for. Hence, a component mode synthesis of the two substructures, machine-tool/shank and the micro-endmill is carried out. The mode shapes of machine-tool shank substructure are determined experimentally whereas the micro-endmill mode shapes are determined via finite element method (FEM). The predicted micro-endmill dynamics with machine tool compliance has been experimentally validated.

Detection of damage location using mode shape deviation: Numerical study

This study presents the use of mode shapes for the identification of damage location. The residual values from curve fitting procedure on mode shape vectors with Chebyshev standard rational series were used to detect the damage along the beam length. The results showed that all the mode shapes for the damaged cases deviated from that of the undamaged case, where the deviation was towards the damage location. The results also showed that the residual from curve fitting procedure for all mode shapes have higher values around the damaged element along the beam length which made it a good indicator for damage location.

Influence of Reference Conditions on the Analysis of Impact-Induced Elastic Waves

Impact problems involving flexible bodies that undergo largerotations and translations were solved by using the floating frame ofreference approach. Analytically defined modes were selected to describedeformation. Different mode shapes can be used depending on the type ofattachment between the body frames of reference and the flexible bodies.Evaluating the kinematic coefficient of restitution during impactentails using the equivalent rigid body velocities of the flexiblebodies. In general, however, such velocities cannot be identified withreference velocities. When the colliding bodies can undergo large translations, freeattachments allow the use of mode shapes that possess zero totalmomentum. In this case, reference motion coincides with the equivalentrigid body motion of the flexible bodies and is not coupled to elasticmotion. When the colliding solids can rotate freely, the use of modeshapes with a zero angular momentum does not uncouple reference andelastic motion. However, if small deformation occurs during freerotation of the flexible body, the derivative of the reference angleremains roughly constant. Such a derivative can be interpreted as theequivalent angular velocity of the flexible body. When using a rigidattachment between the body frames of reference and the flexible bodies,reference motion does not coincide with the equivalent rigid bodyvelocity of the flexible bodies, which leads to non-constant referencevelocities when the bodies move freely. As a result, the equivalentrigid body velocities must be evaluated as linear combinations ofreference and elastic velocities. As shown in this paper, the use of free or rigid attachments asreference conditions, and their corresponding mode shapes allows theaccurate description of impact-induced elastic waves. However, theevaluation of elastic efforts with rigid attachments provides spuriouselastic forces at the attachment point. Such forces decrease as thenumber of modes increases.

Frequency dependent ritz vectors

AbstractIn order to reduce the size of problems involving analysis of the dynamic response of structural systems, a transformatio based on appropriately selected Ritz shapes is commonly employed. The lower mode shapes may at times serve a effective Ritz shapes. However, the computation of mode shapes is a time consuming task; in addition, the mode shapes may not form the best basis for representing the spatial distribution of loads. The recently developed load dependent vectors, which are derived from a static solution for the applied loads, address some of the problems inherent in the use of mode shapes. However, both the natural mode shapes and the load dependent vectors fail to account for the frequency content of the loading, a parameter that may influence strongly the response, particularly for loading with a high frequency content. A procedure is presented here for the generation of frequency dependent vectors. A combination of load dependent and frequency dependent vectors will often form a very efficient basis for the representation of the response, as illustrated by several examples presented here.

The role of median surface curvature in large amplitude flexural vibrations of thin shells

General conclusions regarding the non-linear vibration of structural components like curved beams, rings and thin shells are derived from the study of two specific examples, the circular ring and shallow spherical shell. It is shown that whereas the non-linear behaviour of flat plates and straight bars is generally of a hardening type, the behaviour of thin structural elements that have a finite curvature of the undeformed median surface in one or both principal axis directions may be of the hardening or softening type, depending on the structural parameters as well as on whether the shell is open or closed. It is seen that with careful judgment in the use of mode shapes of one or more terms, the resulting modal equations help one to appreciate much better the physics of the problem, whereas sophisticated mathematical models tend to obscure this.