MS1.4 - Advances in Computational Structural Dynamics

Manufacturing and metal cutting processes have a rich body of research on the nature and effects emerging from structural dynamics phenomena. It is well established that excessive (and uncontrolled) vibrations in machining operations hinder productivity and quality of the components being made. In these environments it is common to encounter self-excited vibrations originated by the relationship in dynamic response between the cutting tool and workpiece; referred to as regenerative chatter. To supress these effects, and especially in larger scale components, conventional practices provide the workpiece with as much support as possible and therefore commonly require custom-built fixturing bases, several manual interventions and setup stages. In contrast, for modern reduced fixturing approaches, the workpiece is minimally-held, which gives the benefits of reduction of setup times, fixturing costs and inventory, and improves access to the workpiece thereby avoiding multistage setups. However, minimal fixturing reduces support of the workpiece, and so vibration becomes a greater challenge, along with the subsequent detrimental effects to part quality and material removal rate (MRR). This paper sets out to determine an optimization methodology for layout configurations that maximize milling depths of cut whilst achieving dynamic stability; by means of FEA model-based simulations, particle swarm optimization (PSO) methods, and experimental modal analysis (EMA) updating algorithms. The investigation takes a sequential approach for the evaluation of the system’s structural dynamics. First, the accuracy and effectiveness of the optimization algorithm is tested on simplified setups. EMA testing and model updating is then performed before application onto a single workpiece. Finally, a complete doublesided access fixturing assembly is investigated. The optimization program enables analysis of a wide range of possible setup considerations, and through this it is shown that optimal results can differ from standard practice. The comparative reduction in workpiece stiffness to a traditional approach is mostly unavoidable, however careful placement of workholding elements can visibly improve cutting conditions and increase dynamic stability within an unsupported environment. This motivates industrial adoption of the approach.

Condition assessment, model updating, and basic studies of large and complex structures subjected to static and dynamic loadings necessitate establishing a reasonably low order model to enhance computational efficiency. An essential requirement for the development of a low-order model is to preserve the main characteristics of the full-scale model within the frequency range of interest or the desired static and/or dynamic response. In this regard, a novel reduced-order model (ROM) is developed based on a full-scale model (FSM) built using commercial finite element analysis software. Utilizing the common lumped mass matrix can introduce mass modeling errors. Hence, a method is proposed to extract the reduced consistent mass matrix model (RCMM) for use in the ROM. The modeling errors in the proposed ROM is studied for comparison with the static and dynamic responses. It can curtail capability of parameter estimation to capture the physical behavior of the structure using the ROM. Modeling error simulations prior to actual field-testing is highly recommended to determine the feasibility of non-destructive tests for successful system identification. The Milad telecommunication tower is the sixth tallest tower in the world, with a height of 435 meters. Using the proposed method, the consistency of the generated ROM based on the RCMM is verified with the Milad Tower’s FSM. In this regard, displacements due to equivalent static wind loads, natural frequencies, mode shapes, slopes of mode shapes, and time history response for earthquake loading are compared. The proposed ROM assessments utilizing RCMM confirm the accuracy of the static and dynamic characteristics.

A class of underdetermined problems that has received much attention is that where the sparsest solution is assumed to be the most likely. A brute force search for this solution is conceptually straightforward but, except for small problems, computationally prohibitive. Surrogates that allow for efficient solutions include greedy algorithms that look for sparseness in the vicinity of some initial starting point, such as the Iterative Hard Thresholding, the Matching Pursuit or the Orthogonal Matching Pursuit, as well as schemes that relax mini-mum cardinality for solutions with minimum L1 norm. Solution selection based on minimum L1 norm is known to promote sparseness and these solutions can, in the linear case, be extracted efficiently using linear programming. The model updating problem in structural mechanics is nonlinear and the question that arises is whether the performance of linear (sparsity-promoting) techniques may be significantly affected by the deviations from linearity. For small parameter changes one expects that nonlinearity can be appropriately accommodated by denoising, i.e. by relaxing the equality constraints to constraints on the maximum norm of residuals, but small parameter changes are difficult to characterize due to noise and model error so the practical question pertains to parameter changes that are substantial. This paper examines a recently introduced approach known as the Quadratic Basis Pursuit (QBP) that attempts to extend Basis Pursuit (BP) to quadratic nonlinearities and which can be efficiently solved using semi-definite programming. It is found that in contrast with BP the QBP algorithm does not guarantee extraction of the vector with minimum L1 norm from the feasible vector space and is thus, at least in this sense, is not a literal extension of BP to quadratic nonlinearities. The foregoing is shown to be a consequence of the fact that the ordering of any vector space by increasing L1 norm does not generally coincide with the ordering that is realized when this criterion is applied to the rank one matrices formed from these vectors by the lifting operator, which is the way the vectors are represented in the QBP algorithm. A Monte Carlo simulation study using vectors with entries generated from a Gaussian distribution showed that the probability that the vector with the lowest L1 norm maps to the lifted matrix with the lowest L1 is around 40% for vectors with 20 entries and only around 25% when the dimension grows to 60. Reproduction of some previously published results shows that performance claims are limited to the specific conditions considered and can be drastically modified by changes in items that were not in the discussion, for example, changes in the magnitude of the entries of the solution vector. Albeit preliminary, the central observation from this work is that the performance of the QBP in its present form in the updating of underdetermined problems in mechanics is poor.