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Showing papers in "Journal of Vibration and Acoustics in 1995"


Journal ArticleDOI
TL;DR: The Method of Imprecision (MoI), a formal method, based on the mathematics of fuzzy sets, for representing and manipulating imprecision in engineering design, can provide formal information upon which to base decisions during preliminary engineering design and can facilitate set-based concurrent design.
Abstract: The decisions with the greatest importance and potential cost (if wrong) are made early in the engineering design process. A method for representing and manipulating imprecise and vague information in design is described, particularly focused on the preliminary phase when the (fuzzy) imprecision and uncertainty in the descriptions of the design artifact are high. The preferences of designers and customers are captured with fuzzy sets. Formal methods for including noise, trade-off strategies and design iteration are included. Increasing the information available to a designer will reduce the risk of making design decisions incorrectly. Providing (fuzzy) set-based information to engineers can facilitate concurrency in design.

292 citations


Journal ArticleDOI
TL;DR: In this paper, a time domain model of linear viscoelasticity is developed based on a decomposition of the total displacement field into two parts: one elastic, the other anelastic.
Abstract: A time domain model of linear viscoelasticity is developed based on a decomposition of the total displacement field into two parts: one elastic, the other anelastic. The anelastic displacement field is used to describe that part of the strain that is not instantaneously proportional to stress. General coupled constitutive equations for (1) the total and (2) the anelastic stresses are developed in terms of the total and anelastic strains, and specialized to the case of isotropic materials. A key feature of the model is the absence of explicit time dependence in the constitutive equations. Apparent time-dependent behavior is described instead by differential equations that govern (1) the motion of mass particles and (2) the relaxation of the anelastic displacement field. These coupled governing equations are developed in a parallel fashion, involving the divergence of appropriate stress tensors. Boundary conditions are also treated: the anelastic displacement field is effectively an internal field, as it is driven exclusively through coupling to the total displacement, and cannot be directly affected by applied loads. In order to illustrate the use of the method, model parameters for a commonly-used high damping polymer are developed from available complex modulus data.

198 citations


Journal ArticleDOI
TL;DR: In this article, the state-of-the-art methods for solving systems of polynomial equations, viz., Dialytic Elimination, Polynomial Continuation, and Grobner bases, are reviewed.
Abstract: Problems in mechanisms analysis and synthesis and robotics lead naturally to systems of polynomial equations. This paper reviews the state of the art in the solution of such systems of equations. Three well-known methods for solving systems of polynomial equations, viz., Dialytic Elimination, Polynomial Continuation, and Grobner bases are reviewed. The methods are illustrated by means of simple examples. We also review important kinematic analysis and synthesis problems and their solutions using these mathematical procedures.

112 citations


Journal ArticleDOI
TL;DR: In this paper, the authors present a review of the procedures used to formulate component modes for substructures and to assemble substructure models to form reduced-order models of the original system.
Abstract: When the response of a structural system to dynamic excitation must be analyzed, a substructure coupling method (or component-mode synthesis method) is frequently employed to reduce the order of the finite element model of the structure. This paper reviews procedures used to formulate component modes for substructures and to assemble substructure models to form reduced-order models of the original system. A brief literature survey covering several applications of substructure coupling is also presented.

93 citations


Journal ArticleDOI
TL;DR: In this paper, the nonlinear modes and natural frequencies of a simply supported Euler-Bernoulli beam resting on an elastic foundation with distributed quadratic and cubic nonlinearities were determined.
Abstract: We use two approaches to determine the nonlinear modes and natural frequencies of a simply supported Euler-Bernoulli beam resting on an elastic foundation with distributed quadratic and cubic nonlinearities. In the first approach, we use the method of multiple scales to treat the governing partial-differential equation and boundary conditions directly. In the second approach, we use a Galerkin procedure to discretize the system and then determine the normal modes from the discretized equations by using the method of multiple scales and the invariant manifold approach. Whereas one- and two-mode discretizations produce erroneous results for continuous systems with quadratic and cubic nonlinearities, all methods, in the present case, produce the same results because the discretization is carried out by using a complete set of basis functions that satisfy the boundary conditions.

88 citations


Journal ArticleDOI
TL;DR: In this article, a non-linear formulation of the second-order terms in the strain-displacement relationship is proposed to represent axial displacement along the deformed (instead of undeformed) axis.
Abstract: In this paper, the equations of motion of flexible multibody systems are derived using a nonlinear formulation which retains the second-order terms in the strain-displacement relationship. The strain energy function used in this investigation leads to the definition of three stiffness matrices and a vector of nonlinear elastic forces. The first matrix is the constant conventional stiffness matrix, the second one is the first-order geometric stiffness matrix ; and the third is a second-order stiffness matrix. It is demonstrated in this investigation that accurate representation of the axial displacement due to the foreshortening effect requires the use of large number or special axial shape functions if the nonlinear stiffness matrices are used. An alternative solution to this problem, however, is to write the equations of motion in terms of the axial coordinate along the deformed (instead of undeformed) axis. The use of this representation yields a constant stiffness matrix even if higher order terms are retained in the strain energy expression. The numerical results presented in this paper demonstrate that the proposed new approach is nearly as computationally efficient as the linear formulation. Furthermore, the proposed formulation takes into consideration the effect of all the geometric elastic nonlinearities on the bending displacement without the need to include high frequency axial modes of vibration.

87 citations


Journal ArticleDOI
TL;DR: In this paper, the authors examine how engineering models can be used to develop robust designs-designs that can tolerate variation, defined in terms of tolerances which bracket the expected deviation of model variables and/or parameters.
Abstract: This paper examines how engineering models can be used to develop robust designs-designs that can tolerate variation. Variation is defined in terms of tolerances which bracket the expected deviation of model variables and/or parameters. Several methods for robust design are discussed. The method of transmitted variation is explained in detail and illustrated on a linkage design problem and a check valve design problem.

79 citations


Journal ArticleDOI
TL;DR: A detailed discussion of the typology of decomposition in mechanical design is provided in this paper, and examples are provided to illustrate the need for decomposition of products, problems, and processes in design.
Abstract: The broad interest in concurrent engineering has inspired research in the area of decomposition in mechanical design. Much of the research reported in the literature falls into one of three categories : (1) product decomposition, (2) problem decomposition, or (3) process decomposition. This paper provides a detailed discussion of the typology of decomposition in mechanical design. Related work is described and examples are provided to illustrate the need for decomposition of products, problems, and processes in design. Representation techniques and methodologies for decomposition are outlined. Finally, future research issues in decomposition in mechanical design are identified.

79 citations


Journal ArticleDOI
TL;DR: The theory predicts that the fuzzy internal structure can be approximated by a statistical average in which the only relevant property is a function m F (Ω) which gives a smoothed-out total mass, per unit plate area, of all those attached oscillators which have their natural frequencies less than a given value Ω.
Abstract: Fundamental issues relative to structural vibration and to scattering of sound from structures with imprecisely known internals are explored, with the master structure taken as a rectangular plate in a rigid baffle, which faces an unbounded fluid medium on the external side. On the internal side is a fuzzy structure, consisting of a random array of point-attached spring-mass systems. The theory predicts that the fuzzy internal structure can be approximated by a statistical average in which the only relevant property is a function m F (Ω) which gives a smoothed-out total mass, per unit plate area, of all those attached oscillators which have their natural frequencies less than a given value Ω. The theory also predicts that the exact value of the damping in the fuzzy structure is of little importance, because the structure, even in the limit of zero damping, actually absorbs energy with an apparent frequency-dependent damping constant proportional to dm F (ω)/dω incorporated into the dynamical description of the master structure. A small finite value of damping within the internals will cause little appreciable change to this limiting value.

77 citations


Journal ArticleDOI
TL;DR: In this paper, a time-domain method was proposed to identify a state space model of a linear system and its corresponding observer/Kalman filter from a given set of general input-output data.
Abstract: This paper presents a time-domain method to identify a state space model of a linear system and its corresponding observer/Kalman filter from a given set of general input-output data. The identified filter has the properties that its residual is minimized in the least squares sense, orthogonal to the time-shifted versions of itself, and to the given input-output data sequence. The connection between the state space model and a particular auto-regressive moving average description of a linear system is made in terms of the Kalman filter and a deadbeat gain matrix. The procedure first identifies the Markov parameters of an observer system, from which a state space model of the system and the filter gain are computed. The developed procedure is shown to improve results obtained by an existing observer/Kalman filter identification method, which is based on an auto-regressive model without the moving average terms. Numerical and experimental results are presented to illustrate the proposed method.

77 citations


Journal ArticleDOI
TL;DR: In this paper, an improved inverse eigensensitivity method, which avoids the existing problems of classical inverse eigen sensitivity method, has been developed, which employs both analytical and experimental modal data to calculate the required eigenensitivity coefficients which are very close to their true values.
Abstract: In order to update analytical models of practical engineering structures, inverse eigensensitivity method (IEM) has been developed. Though it has nowadays been widely accepted, the classical inverse eigensensitivity method does have some drawbacks such as the assumption of small error magnitudes and slow speed of convergence due to the fact that the sensitivity coefficients are calculated purely based on modal data of analytical model. In the present paper, an improved inverse eigensensitivity method, which avoids the existing problems of classical inverse eigensensitivity method, has been developed. The improved method employs both analytical and experimental modal data to calculate the required eigensensitivity coefficients which are very close to their true values. The method has been further extended to the case where measured coordinates are incomplete. Practical applicability of the method has been assessed by its application to the updating of the finite element model of a plane truss structure

Journal ArticleDOI
TL;DR: In this paper, two approaches for determination of the nonlinear planar modes of a cantilever beam are compared and the results show that both approaches yield the same nonlinear modes because the discretization is performed using a complete set of basis functions, namely, the linear mode shapes.
Abstract: Two approaches for determination of the nonlinear planar modes of a cantilever beam are compared. In the first approach, the governing partial-differential system is discretized using the linear mode shapes and then the nonlinear mode shapes are determined from the discretized system. In the second approach, the boundary-value problem is treated directly by using the method of multiple scales. The results show that both approaches yield the same nonlinear modes because the discretization is performed using a complete set of basis functions, namely, the linear mode shapes.

Journal ArticleDOI
TL;DR: In this paper, the dynamic stability of the steady frictional sliding of a linear elastic or viscoelastic half-space compressed against a rigid plane which moves with a prescribed nonvanishing tangential speed is investigated.
Abstract: This paper presents a study on the dynamic stability of the steady frictional sliding of a linear elastic or viscoelastic half-space compressed against a rigid plane which moves with a prescribed nonvanishing tangential speed. The system of differential equations and boundary conditions that govern the small plane oscillations of the body about the steady-sliding state of deformation is established. It is shown that for large coefficient of friction and large Poisson's ratio the steady-sliding of the elastic body is dynamically unstable. This instability manifests itself by growing surface oscillations which necessarily propagate from front to rear and which in a short time lead to situations of loss of contact or stick. Similarly to what has been found with various finite dimensional frictional systems, these flutter type surface instabilities result from the intrinsic nonsymmetry of dry friction contact laws. The effect of viscous dissipation within the deformable body is also assessed : when viscous dissipation is present larger coefficients of friction are required for the occurrence of surface solutions propagating and growing from front to rear.

Journal ArticleDOI
TL;DR: An overview of the recent development of tuned vibration absorbers (TVAs) for vibration and noise suppression is presented in this article, which summarizes some popular theory for analysis and optimal tuning of these devices, discusses various design configurations, and presents some contemporary applications of passive TVAs.
Abstract: An overview of the recent development of tuned vibration absorbers (TVAs) for vibration and noise suppression is presented. The paper summarizes some popular theory for analysis and optimal tuning of these devices, discusses various design configurations, and presents some contemporary applications of passive TVAs. Furthermore, the paper also presents a brief discussion on the recent progress of adaptive and semi-active TVAs along with their on-line tuning strategies, and active and hybrid fail-safe TVAs.

Journal ArticleDOI
TL;DR: In this article, the authors present a method which utilizes substructure normal modes to predict the vibration properties of a cantilever beam with a breathing transverse crack, where the two segments of the beam, separated by the crack are related to one another by time varying connection matrices representing the interaction forces.
Abstract: The paper presents a method which utilizes substructure normal modes to predict the vibration properties of a cantilever beam with a breathing transverse crack. The two segments of the cantilever beam, separated by the crack are related to one another by time varying connection matrices representing the interaction forces. The connection matrices are expanded in a Fourier series leading to a classical eigenvalue problem. Subsequently, the initial formulation is extended to avoid interference of the crack interfaces with a time domain formulation. The Lagrange multipliers, used to enforce the exact continuity constraints when the crack is closed, produce the interfaces forces needed for the modelling of interface dry friction.

Journal ArticleDOI
TL;DR: In this article, the authors present a number of specific techniques that are applicable for evaluating either the total mechanical-thermal noise or the spectral distribution of that noise for simple or complex sensors, and a summary of other noise components is given in the context of design guidelines for high-sensitivity sensors.
Abstract: Recent technological advances in microfabrication and fiber optics have made practical the construction of very small, sensitive sensors for acoustic or vibration measurements. As the sensitivity is increased or the size is decreased, a sensor becomes more susceptible to mechanical noise resulting from molecular agitation. Traditional noise analysis is often focused exclusively on electrical or optical noise ; consequently, mechanical-thermal noise may not be considered in new types of sensors until the prototype testing reveals an unexpectedly high noise floor. Fortunately, mechanical-thermal noise is relatively easy to estimate early in the design process because the equivalent noise force is only a function of the temperature and the mechanical losses in the sensor. There are a number of specific techniques that are applicable for evaluating either the total mechanical-thermal noise or the spectral distribution of that noise for simple or complex sensors. These techniques are presented and, in addition, a summary of other noise components is given in the context of design guidelines for high-sensitivity sensors.

Journal ArticleDOI
TL;DR: In this article, a feedback control of free field structural radiation is considered and two experimental implementations of feedback control strategies using shaped piezoelectric polymer film sensors to measure the transformed system states are described.
Abstract: Feedback control of free field structural radiation is considered. State equations are formulated with a transformation which decouples the acoustic power error criterion. Using the resultant equations, expressed in terms of “transformed mode” states, the order of the state equations can be significantly reduced at low frequencies. Two experimental implementations of feedback control strategies using shaped piezoelectric polymer film sensors to measure the transformed system states are described. The first of these is a simple analog implementation. The second implementation is in discrete time, where an adaptive algorithm for optimizing the weights of IIR filters for practical use is described. It is shown that by using the outlined control approach significant levels of low frequency acoustic power attenuation can be obtained with no control spillover and subsequent increase in higher frequency acoustic power output.

Journal ArticleDOI
TL;DR: The axiomatic approach to design provides a general theoretical framework for all these design fields, including mechanical design as discussed by the authors, which can be used as design rules or guidelines for designers and can be applied to all design fields.
Abstract: Design is done in many fields. Although the design practices in different fields appear to be distinct from each other, all fields use a common thought process and design principles. Consequently, the true differences between these fields are minor, often consisting of the definitions of words, the specific data, and knowledge. In comparison, larger differences can exist within a given field between simple systems and large systems due to the size and the time dependent nature of functional requirements. The axiomatic approach to design provides a general theoretical framework for all these design fields, including mechanical design. The key concepts of axiomatic design are : the existence of domains, the characteristic vectors within the domains that can be decomposed into hierarchies through zigzagging between the domains, and the design axioms (i.e., the Independence Axiom and the Information Axiom). Based on the two design axioms, corollaries and theorems can be stated or derived for simple systems, large systems, and organizations. These theorems and corollaries can be used as design rules or guidelines for designers. The basic concepts are illustrated using simple mechanical design examples. When design is viewed axiomatically, not only product design but all other designs, including design of process, systems, software, organizations, and materials, are amenable to systematic treatment.

Journal ArticleDOI
TL;DR: In this paper, a numerical model of the acoustic radiated field from a turbofan engine inlet in the presence of a mean flow has been constructed with conventional finite elements in near field and wave envelope elements in far field.
Abstract: Improvements have been made in the finite element model of the acoustic radiated field from a turbofan engine inlet in the presence of a mean flow. The problem of acoustic radiation from a turbofan engine inlet is difficult to model numerically because of the large domain and high frequencies involved. A numerical model with conventional finite elements in the near field and wave envelope elements in the far field has been constructed. By employing an irrotational mean flow assumption, both the mean flow and the acoustic perturbation problem have been posed in an axisymmetric formulation in terms of the velocity potential; thereby minimizing computer storage and time requirements. The finite element mesh has been altered in search of an improved solution. The mean flow problem has been reformulated with new boundary conditions to make it theoretically rigorous. The sound source at the fan face has been modeled as a combination of positive and negative propagating duct eigenfunctions. Therefore, a finite element duct eigenvalue problem has been solved on the fan face and the resulting modal matrix has been used to implement a source boundary condition on the fan face in the acoustic radiation problem. In the post processing of the solution, the acoustic pressure has been evaluated at Gauss points inside the elements and the nodal pressure values have been interpolated from them. This has significantly improved the results. The effect of the geometric position of the transition circle between conventional finite elements and wave envelope elements has been studied and it has been found that the transition can be made nearer to the inlet than previously assumed.


Journal ArticleDOI
TL;DR: In this paper, necessary and sufficient conditions for Lyapunov stability, semistability and asymptotic stability of matrix second-order systems are given in terms of the coefficient matrices.
Abstract: Necessary and sufficient conditions for Lyapunov stability, semistability and asymptotic stability of matrix second-order systems are given in terms of the coefficient matrices. Necessary and sufficient conditions for Lyapunov stability and instability in the absence of viscous damping are also given. These are used to derive several known stability and instability criteria as well as a few new ones. In addition, examples are given to illustrate the stability conditions.

Journal ArticleDOI
TL;DR: In this paper, a theoretical approach to study breathing vibrations of cylindrical shells with horizontal axis, partially filled with liquid, is delineated and the results of some modal tests conducted on an industrially-manufactured tank are presented and discussed.
Abstract: A theoretical approach to study breathing vibrations of cylindrical shells with horizontal axis, partially filled with liquid, is delineated and the results of some modal tests conducted on an industrially-manufactured tank are presented and discussed. The good agreement between theoretical and experimental results is preliminarily verified in the case of both an empty and completely full shell, in order to confirm that it is possible to apply the theoretical approach to real structures. The modal properties of a partially-filled shell as a function of liquid level are then experimentally studied, the mode shapes are compared using the Modal Assurance Criterium and a qualitative explanation of the dynamic behavior is proposed

Journal ArticleDOI
TL;DR: In this paper, a set of jointed structures consisting of simple round rods and simple beam blocks of rectangular cross-section was idealized to simplify the analysis of the three-dimensional vibrations of automobile engine crankshafts under firing conditions.
Abstract: To simplify the analysis of the three-dimensional vibrations of automobile engine crankshafts under firing conditions, the crankshaft was idealized by a set of jointed structures consisting of simple round rods and simple beam blocks of rectangular cross-section. The front pulley, timing gear, and the fly-wheel were idealized by a set of masses and moments of inertia. The main journal bearings were idealized by a set of linear springs and dash-pots. For each constituent member, the dynamic stiffness matrix was derived (in closed form) from the transfer matrix. Then the dynamic stiffness matrix for the total crankshaft system was constructed, and the natural frequencies and mode shapes were calculated. The modeling and analysis procedures were aplied to the analysis of free vibrations of four kinds of crankshafts: single cylinder, three-cylinder in-line, four-cylinder in-line, and V-six engines. The different coupling behavior of the three-dimensional vibrations in the planar-structure and the solid-structure crankshaft is discussed, and the influence of the bearing oil film stiffness on the crankshaft natural frequency is also analyzed

Journal ArticleDOI
TL;DR: A high speed damper test rig has been assembled at Texas A&M University to develop rotordynamic dampers for rocket engine turbopumps that operate at cryogenic temperatures, such as those used in the space shuttle main engines.
Abstract: A high speed damper test rig has been assembled at Texas A&M University to develop rotordynamic dampers for rocket engine turbopumps that operate at cryogenic temperatures, such as those used in the space shuttle main engines (SSMEs). Damping is difficult to obtain in this class of turbomachinery due to the low temperature and viscosity of the operating fluid. An impact damper has been designed and tested as a means to obtain effective damping in a rotorbearing system. The performance and behavior of the impact damper is verified experimentally in a cryogenic test rig at Texas A&M. Analytical investigations indicate astrong amplitude dependence on the performance of the impact damper. An optimum operating amplitude exists and is determined both analytically and experimentally. In addition, the damper performance is characterized by an equivalent viscous damping coefficient. The test results prove the impact damper to be a viable means to suppress vibration in a cryogenic rotorbearing system.

Journal ArticleDOI
TL;DR: In this article, the performance of an active vibration isolator consisting of a fluid mount and an electromagnetic actuator is discussed, where the active isolator is modeled using bond graphs to gain insight into the active mount's performance.
Abstract: The performance of an active vibration isolator consisting of a fluid mount and an electromagnetic actuator is discussed. The electromagnetic actuator augments the inertia effects of the fluid mount to reduce the dynamic stiffness of the mount at the vibrational disturbance frequencies of the engine. The active isolator is modeled using bond graphs. Dynamic stiffness, blocked force, and free displacement transfer functions are developed from the bond graph model to gain insight into the active mount’s performance. A mount effectiveness analysis shows that reducing the mount’s dynamic stiffness results in better dynamic isolation. Numerical simulations along with laboratory testing of the active isolator are used to evaluate the performance of the mount. A simple laboratory experiment shows that an active mount can be controlled to have a dynamic stiffness that is 100 times (40 dB) lower than a passive mount, without sacrificing static stiffness.

Journal ArticleDOI
TL;DR: In this article, a general formulation to obtain the analytical expressions for the sensitivity of the acoustic power radiated by a vibrating structure to one of its design variables is described, which is applied to both single frequency and broad band harmonic excitation of plates.
Abstract: A general formulation to obtain the analytical expressions for the sensitivity of the acoustic power radiated by a vibrating structure to one of its design variables is described. The formulation, which is based on finite elements, is applied to both single frequency and broad band harmonic excitation of plates. The sensitivity coefficients indicate the effect of changing various design or modeling parameters on the acoustic power and can be used to optimize the structure for minimum sound radiation. Analytical sensitivity estimates are compared with finite difference values. Results show that analytical sensitivity analysis is important from both computational time and accuracy points of view

Journal ArticleDOI
TL;DR: In this article, a decomposition of gear motion and related dynamic measurements for the condition monitoring and fault diagnosis of gearboxes is described, where the motion error signal is separated according to fundamental frequencies into the harmonic error and the residual error, which are used to quantify the gear condition.
Abstract: The decomposition of gear motion and the related dynamic measurements for the condition monitoring and fault diagnosis of gearboxes are described. The motion error signal is separated according to fundamental frequencies into the harmonic error and the residual error, which are used to quantify the gear condition. High-order accelerations, such as jerk, are considered and shown to be more sensitive to some classes of early damage to gear teeth. Analysis of the time domain average of a gearbox casing vibration signal enables early detection of gear damage. Several methods to represent and enhance the fault information in the signal are introduced, based on the representation of different forms of the motion errors

Journal ArticleDOI
TL;DR: In this paper, the importance of extensional effects in the core and its effect on the loss factor is brought out in the study of cylindrical shells with a constrained damping layer treatment.
Abstract: Cylindrical shells with a constrained damping layer treatment are studied using three theories The finite element method is made use of in the study The nondimensional frequencies and loss factors predicted by the three theories are compared and the theories are evaluated The importance of inclusion of the extensional effects in the core and its effect on the loss factor is brought out in this study

Journal ArticleDOI
TL;DR: In this paper, the bending stress singularities that occur in the two opposite, obtuse corner angles of simply supported rhombic plates undergoing free, transverse vibration are explicitly considered, and the analysis is carried out by the Ritz method using a hybrid set consisting of two types of displacement functions.
Abstract: This is the first known work which explicitly considers the bending stress singularities that occur in the two opposite, obtuse corner angles of simply supported rhombic plates undergoing free, transverse vibration. The importance of these singularities increases as the rhombic plate becomes highly skewed (i.e., the obtuse angles increase). The analysis is carried out by the Ritz method using a hybrid set consisting of two types of displacement functions, e.g., (I) algebraic polynomials and (2) corner functions accounting for the singularities in the obtuse corners. It is shown that the corner functions accelerate the convergence of solution, and that these functions are required if accurate solutions are to be obtained for highly skewed plates. Accurate nondimensional frequencies and normalized contours of the vibratory transverse displacement are presented for simply supported rhombic plates with skew angles ranging to 75 deg. (i.e., obtuse angles of 165 deg.). Frequency and mode shapes of isosceles and right triangular plates with all edges simply supported are also available from the data presented.

Journal ArticleDOI
TL;DR: First-order Taylor and half-quadratic series approximation optimization approaches were compared to traditional local minimization methods (Modified Method of Feasible Directions and Broydon-Fletcher-Goldfarb-Shanno).
Abstract: This study investigates the applicability of various approximation methods to broadband radiated noise design optimization problems. Low-order series approximations of dynamic response may be used to replace full numerical system solutions to effect significant computer cost savings during design iterations. Also, the ease of evaluating the approximate functions may be further exploited by using global optimization search methods, such as simulated annealing, at individual design iterations. The combination of approximating radiated noise spectra and evaluating the approximate spectra for all possible design alternatives greatly increases the possibility of finding a truly optimal design. The effectiveness of the approximation is measured by considering optimization accuracy, evaluated by the algorithm's ability to find a global or near-global minimum independent of the initial design; computational efficiency, based on the number of numerical design analyses required for convergence; and generality, where the method should be relatively independent of the problem type. Finite element models of three test cases with varying performance goals and design parameters were used to evaluate the optimization methods. Shell thicknesses, shell loss factors, and rib stiffener locations were varied to minimize structural weight and manufacturing costs while lowering broad-band radiated noise levels below a specified goal. First-order Taylor and half-quadratic series approximation optimization approaches were compared to traditional local minimization methods (Modified Method of Feasible Directions and Broydon-Fletcher-Goldfarb-Shanno). For all test cases, the approximation approaches found the global optimum design more frequently than the local minimization methods. Also, the half-quadratic method converged using fewer design evaluations than the first-order Taylor method for most test cases