So far, mathematical modelling of Lamb wave propagation under fluid-structure interaction (FSI) was limited to the case of rigid structure. We extend this concept to account for structural dynamics. Thereby, we provide a model that is suitable for the structural health monitoring (SHM) during the operation of the structure. The model we develop is referred to as the “eXtended Fluid-Structure Interaction” (eXFSI) problem, which is a one-directional coupling of typical FSI problem with an ultrasonic wave propagation in fluid-solid and their interface (WpFSI). Here, the strongly coupled problem of acoustic & elastic wave equations is denoted by WpFSI. Next, we explore the approach to the efficient numerical solution of the problem. We use a combination of Finite Element and Finite Difference methods and employ a dual-loop algorithm to balance the computational cost and quality of the numerical solution. To facilitate our solution algorithm, we rely upon the software library package DOpElib .

For an assembled structure with many bolted joints, predicting its dynamic response with high fidelity is always a difficult problem, because of the nonlinearity introduced by friction contact between jointed interfaces. The friction contact results in nonlinear stiffness and damping to a structure. To realize predictive simulation in structural dynamic design, these nonlinear behaviors must be carefully considered. In this paper, the dynamics of a multi-bolt jointed beam is calculated. A modified IWAN constitutive model, which can consider both tangential micro/macro slip and nonzero residual stiffness at macroslip phase, is developed to model nonlinear contact behaviors due to joint interfaces. A whole interface element integrating the proposed constitutive model is developed. The element is used to model the nonlinear stiffness and damping caused by bolted joints. The interface element is placed between the two contact interfaces. The other part of the beam is modeled by linear beam elements. A Matlab code is developed to realize the proposed nonlinear finite element dynamic analysis method. A hammer impact experiment for the bolt-jointed beam is conducted under different excitation force levels. The calculated nonlinear numerical results are compared with experimental results. It is shown that the effect of joint nonlinearity on structural dynamics can be observed from the response predicted by the proposed method. The numerical results agree well with the experimental results. This work validates the necessary of using nonlinear joint model for dynamic simulation of jointed structures.

This research explores parametric instabilities of the PGT driveline system and a stability-based method for ring gear rim thickness design. Parametric excitation of a planetary gear transmission (PGT) driveline system arises from two sources: 1) gear mesh stiffness variation, 2) Interaction between moving planets, flexible ring gear and boundary struts. Many researchers have studied the parametric instability of planetary gear transmissions due to gear mesh stiffness variation, however, the effect of interaction between moving planets, flexible ring and discrete boundary struts on parametric instabilities has not been fully studied before. Especially, for sufficiently thin ring gears, this kind of effect becomes even more significant. To illustrate the novel PGT rim design proposal, firstly, a structural dynamics model of a complete PGT driveline system with elastic ring gear supported by discrete boundary struts is established. Secondly, by applying Floquet method, the parametric instability behavior due to the second parametric excitation source is fully investigated. Lastly, the design guidelines for planetary gear transmission ring gear rim thickness are proposed based on system stability from a dynamical viewpoint. The analysis and results provide new and important insights into dynamics and design of lightweight planetary gear transmission ring gear rim.

This investigation describes a method for both manufacturing a biomimetic insect-sized wing using the photolithography technique and experimentally analyzing its structural dynamic response. The wing geometry of a crane fly forewing is captured using a micro-computed tomography scanner for its replication. A photomask of the membrane and venation pattern is designed from a computer-aided design model developed from the reconstructed scanned model of the wing. The photolithography process is conducted using the negative photoresist SU-8 and the Kapton film to biomimic the veins and the membrane of the crane fly forewing, respectively. A digital image correlation (DIC) system is used in conjunction to a shaker vibrational setup to determine the natural frequencies of the artificial wing from the fast Fourier transform of the time-varying out-of-plane displacement data. Wind-tunnel experiments are conducted using the DIC system to determine the structural response of the artificial wing under different freestream velocities and angles of attack within the regime of insect flight. The vibration modes are dominated by a bending and torsional deformation response. The deformation along the span of the wing increases nonlinearly from the root to the tip of the wing with Reynolds number.

Slender, lightweight structures are demanded to meet efficiency targets or to enhance vehicle system performance characteristics. Yet, when subjected to static stress for load-bearing purposes, the flexible structural members may buckle. Furthermore, additional dynamic excitations may activate adverse snap-through responses in such post-buckled components, which accelerates fatigue and failure. The severe nonlinearity associated with these phenomena challenges traditional forms of analysis and necessitates studious experimental methods for conclusive system characterization and model validation. This research builds upon state-of-the-art analytical and experimental strategies to examine the complex forced, dynamic behaviors of built-up structures that contain one or more post-buckled members. An analytical modeling and solution formulation is reviewed that is uniquely amenable to the study of multistable structures and permits experimentally-observable measures of impedance to be identified. Through theoretical and experimental studies, the efficacy of the impedance measures is evaluated towards their usefulness in identifying the onset of dynamic bifurcations in the multistable structural dynamics. For moderate amplitudes of input energy, the analysis is found to provide qualitatively accurate prediction of the drive point impedance changes observed prior to dynamic bifurcations from low to high amplitude of displacement.

The modeling of material behavior is an important challenge in structural dynamics. While some materials can be well represented by a linear constitutive law, this becomes more complex when dealing with viscoelastic components. In this paper we investigate a fractional viscoelastic material model and present our results of research, focusing on its parametrical characteristics. We compare the results to a classical linear viscoelastic standard model and highlight advantages of the particular approach: we conduct monofrequent sinusoidal excitations using a DMTA (Dynamic Mechanic Thermal Analysis) machine. We use a viscoelastic TPU (Thermoplastic Polyurethane) sheet as sample and apply varying excitation frequencies and amplitudes. In a first modeling step we reproduce the experimental results with a fractional single degree-of-freedom system with promising results.

The selection of coating or surface treatments is a crucial step in the design of oil and gas equipment to protect against the deterioration caused by wear, corrosion, galling, fatigue, etc. Quench polish quench (QPQ) nitriding is a superior candidate to increase surface hardness for abrasion and galling resistance in carbon or stainless steels. The increased surface hardness improves the wear and corrosion resistance but reduces the surface material ductility. It is generally not recommended for application to V-shaped threads or sharp notches subjected to high stress. During well perforation in cased-hole completion, the detonation of the gun string along with the induced pressure wave in fluids generates a large-magnitude dynamic motion in the gun string. The peak load of a perforating event, from detonation to fluid-structure interaction, happens in the range of microseconds to milliseconds. The coupled wellbore hydrodynamic and structural dynamic shock load may cause an overstress failure in the millisecond scale but is usually overlooked in engineering practice. In this work, we investigated the behavior of QPQ coating under transient dynamic loads, employing both physical test and finite element analysis. We designed a combination of drop test fixture and specimens to simulate a notched specimen subjected to dynamic tensile loads. Two types of specimens were prepared in this study, QPQ-coated specimens and bare metal specimens without coating. The specimens without coating were tested to serve as a baseline for comparison. The methodology in this study provides a generic guideline for design of equipment potentially subjected to transient mechanical shock loads.

Beam-like structure is known as one of crucial engineering structures in practical application of aerospace, vessel, civil and machinery. The damages have a great influence on machine performance and may cause a serious threat for security of mechanical structures and systems. Thus it is very significant to identify the damage of beam-like structures for security of mechanical structures and systems. This paper presents a novel application of wavelet finite element method (WFEM) in Lamb wave propagation of beam-like structures. The WFEM, adopting excellent B-spline wavelet on interval (BSWI) basis as approximating functions, has been verified to possess some superiorities for structural dynamic analysis and damage detection. The motion equations of Lamb wave propagation are derived according to Hamilton’s principle and two-dimensional wavelet-based element is constructed by adopting BSWI scaling functions. The damage, which is modeled as open crack with duplicate nodes, is considered in beam-like structures and corresponding damage model is also added in proposed wavelet finite element model. Then central difference method in time domain is employed for wave propagation simulation. Firstly, the validity and accuracy of proposed WFEM are demonstrated on a beam-like structure without crack by comparing with traditional finite element method (FEM) using 2D plane element. What’s more, the obtained velocities of fundamental S 0 and A 0 mode waves are also compared with Lamb theoretical results to verify the validity and accuracy of proposed model once more. Then the wave propagation in beam-like structures with crack are performed and the process and interaction between Lamb wave and damage are analyzed and discussed in detail. The reflected mode wave and converted mode wave for incident wave interacting with crack are also observed in wave motion snapshots. In summary, this paper presents an accurate but simple and effective numerical method for wave propagation of beam-like structures.

Flexoelectricity includes two effects: the direct flexoelectric effect and the converse flexoelectric effect, which can be respectively applied to flexoelectric sensors and actuators to monitor structural dynamic behaviors or to control structural vibrations. This study focuses on the converse flexoelectric effect and its application to dynamic control of cantilever beams analytically and experimentally. In the mathematical model, a conductive atomic force microscope (AFM) probe with an external voltage is used to generate an inhomogeneous electric field driving the flexoelectric beam. The electric field gradient leads to an actuation stress in the longitudinal direction due to the converse flexoelectric effect. The actuation stress results in a bending control moment to the flexoelectric beam since the stress in the thickness is inhomogeneous. In order to evaluate the actuation effect of the flexoelectric actuator, the flexoelectric induced tip displacement is evaluated when the mechanical force is assumed zero. With the induced control moment, vibration control of the cantilever beam is discussed and the control effect is evaluated. Flexoelectric control effects with different design parameters, such as AFM probe location, AFM probe radius and flexoelectric beam thickness, are evaluated. Analytical results show that the optimal AFM probe location for all beam modes is close to the fixed end. Besides, thinner AFM probe radius and thinner flexoelectric beam enhance the control effects. Laboratory experiments are also conducted with different probe locations to validate the analytical predictions. Experimental results show that the induced tip displacement decreases when the input location moves away from the fixed end, which is consistent with the analytical prediction. The studies provide design guidelines of flexoelectric actuations in engineering applications.

In this paper, we study fully coupled electromagnetic-elastic behaviors present in the structures of smart beams using variational asymptotic beam sections and geometrically exact fully intrinsic beam equations combined in a consistent theory. We present results for smart beams under various oscillatory loads in both the axial and transverse directions and calculate the corresponding deformations. Recovery equations are employed to construct the full 3D stress and strain components in order to complete a full stress / strain analysis. Smart materials change mechanical energy to electrical energy; therefore, changing the structural dynamic behavior of the structure and its stiffness matrix.

To analyze structural dynamic response of rotary ultrasonic motor under high impact load, a theoretical model is established in this paper. A rotary ultrasonic motor includes two main components: stator and rotor. According to structure form and movement principle, they can be simplified as annular plates. When the system is imparted an impact load, dynamic displacement response of stator and rotor can be obtained. The damage to stator and rotor is analyzed in theory. It gave agreement with simulation and experimental result. Finally, influence of various structure parameters on the deformation of stator and rotor is analyzed and some suggestions on improving performance of rotary type ultrasonic motor are proposed.

In this paper, we study fully coupled electromagnetic-elastic behaviors present in the structures of smart beams using variational asymptotic beam sections and geometrically exact fully intrinsic beam equations. We present results for energy harvesting from smart beams under various oscillatory loads in both the axial and transverse directions and calculate the corresponding deformations. The magnitude of these loads are varied to show the generalized trends produced by piezoelectric materials. Smart materials change mechanical energy to electrical energy; therefore, changing the structural dynamic behavior of the structure and its stiffness matrix. A smart structure can be designed to undergo larger loads without changing the surface area of the cross-section.

Structural dynamic and fluid flow analysis of positive displacement piezoelectric micropumps are carried out for microfluidic water transport applications. The micropump consists of trapezoidal prism inlet/outlet elements; the pump chamber; a thin structural layer and a piezoelectric transducer element. Governing equations for the flow fields; the structural-piezoelectric bi-layer membrane motions and electrical variables are considered. Two-way dynamic coupling of forces and displacements between the solid and the liquid domains in the systems are considered. The effects of the structural layer material selection and the thickness of thin structural layer on the structural deformation and fluid flow are investigated. The variation the structural layer material and its thickness enable the selection of the best micropump design among the investigated micropumps made of silicon and Pyrex glass while other parameters are kept unchanged. The change of the structural layer material is considered here through the variation of density, Young’s modulus and Poisson’s ratio. Optimum membrane thickness is also investigated aiming to generate higher rates of time-averaged flow for the selected micropump structural layer material. The present study is useful in the implementation of the micropumps into lab-on-a-chip microfluidic systems.

Various structural health monitoring (SHM) techniques utilizing vibration signals have been developed for identification of damages in a structure. Many of these studies are based on sensitivity analysis, finite element model (FEM) updating, and optimization techniques. FEM updating technique is one of the major techniques that iteratively minimizes the difference between the modal parameters measured from the real structure and the corresponding analytical predictions. This method would be more beneficial for typical continuous systems such as beams, plates, and shells which cannot be reasonably discretized. One of the drawbacks of these techniques is the large number of unknowns to be estimated. These techniques in the literature that use FEM updating to estimate perturbed parameters for all elements in the model can be time-consuming and ill-conditioned, even for relatively simple structures. The technique also requires a full and accurate finite element model for each monitored structure. A new method to identify damages in a structure using embedded sensitivity functions and optimization algorithms is described and its performance is demonstrated in this paper. The perturbed frequency response function (FRF) is calculated using Taylor series expansion in terms of the baseline system and the embedded sensitivity functions. The optimization process minimizes the difference between the measured FRFs of the damaged structure and the perturbed FRFs calculated from the baseline structure. Structural damages are often characterized by changes in mechanical parameters such as stiffness, mass, and damping. Embedded sensitivity functions offer a means of determining the path that is followed from the baseline to the perturbed FRF of the structure. The robustness and efficiency of suggested structural health monitoring method are discussed in this paper. The accuracy of damage estimation is investigated with respect to various types and values of damages, objective functions, frequency ranges, scale factors, procedures, and noise levels. Precise measurement and monitoring of vibration signals are critical for accurate detection of the location, type, and level of damage. However, in most practical mechanical systems, vibration tests may result in noise on the input or output measurements. Noise on the measurement affects the accuracy of the FRFs and identification of damages in a structure. Based on the results of the study, several parameters and factors in the optimization process and structural dynamics are suggested to enhance the efficiency and robustness of damage identification process. It is shown that the iteration number of the optimization process is significantly reduced. Accurate estimate of damages can be obtained within the range of 2∼5% error with various enhancements applied to the technique.

The aerodynamics of a wind turbine is governed by the flow around the rotor, where the prediction of air loads on rotor blades in different operational conditions and its relation to rotor structural dynamics is one of the most important challenges in wind turbine rotor blade design. Because of the unsteady flow field around wind turbine blades, prediction of aerodynamic loads with high level of accuracy is difficult and increases the uncertainty of load calculations. A free vortex wake method, based on the potential, inviscid and irrotational flow, is developed to study the aerodynamic loads. Since it is based on the potential, inviscid and irrotational flow, it cannot be used to predict viscous phenomena such as drag and boundary layer separation. Therefore it must be coupled to the tabulated airfoil data to take the viscosity effects into account. The results are compared with the Blade Element Momentum (BEM) [1] method and the GENUVP code [2] (see also the acknowledgments).

Dielectric elastomers hold much promise as smart materials that could rapidly adapt to changes in environmental conditions due to their mechanical response to an electrical input. They belong to the group of electroactive polymers which have unique mechanical properties such as flexibility, light-weight, and electrical field-induced deformation. These characteristics make dielectric elastomers suitable candidates as actuators, sensors, or energy converter media. The objective of this study is to characterize the structural dynamic response of a dielectric elastomer membrane exposed to stagnant air environment and steady airflow at different angles of attack. A simulation of the fluid-structure interaction of the membrane is performed by coupling an electromechanical finite element model of the membrane with a computational fluid dynamics model representing the external flow. From the fluid-structure interaction simulation, the vibration frequencies and mode shapes, the time-varying out-of-plane deformation, and the coefficients of lift and drag are determined. Furthermore, a convergence study and mesh refinement are performed to guarantee mesh independence of the calculations from the fluid-structure interaction simulation. Results indicate that the stiffness of the electroactive membrane decreases nonlinearly with an increase of the applied voltage. The electrostatic force from the applied voltage adds compressive stress to the membrane, effectively softening the membrane, increasing the out-of-plane deformation, and reducing the resonance frequency.

The analysis and design of fluid-filled structures is a common problem in mechanical engineering. The fluid will add mass, stiffness, and damping properties to the structure that are not present in the dry configuration, and that alter the dynamic response of the structure. Understanding the fluid-structure dynamics can be an essential part of designing a fluid container, particularly if large structural deflections or dynamic motion are expected. For many structures, it is important to appreciate the modal harmonics of the structure and how the fluid will influence them. For instance, the modal frequencies of the tank change with the fluid level, requiring a study of frequency response for different fluid levels. Actual testing to confirm these effects can be expensive and impractical so it is useful to have an accurate model to supplement or replace physical data. Finite element analysis (FEA) codes are well suited to modeling the hydroelastic coupling between the fluid and container. FEA is commonly used to model the structural dynamics of complex systems and to generate the modal frequencies and shapes. One such application is the design of the fuel tank on a flight vehicle, where pressure fluctuations in the fuel line can lead to oscillations in thrust at the engine and high vibrations in the structure. If the frequency of these vibrations matches a natural frequency of the fluid-tank structure, a feedback loop forms coupling the structural response to the fluid oscillations through the engine thrust. This phenomenon is often referred to as “pogo” instability in flight vehicles. The resulting vibrations can cause the vehicle to break apart. The fuel tank must be designed to avoid natural frequencies in the range likely to be excited vehicle vibrations. This report describes the use and verification of hydroelastic modeling capabilities using FEA software to model a fluid-filled fuel tank. Test data from previous experimental work is used to validate the natural frequencies and mode shapes of the tank at different fluid fill levels. The FEA model compares very well to experimental data and theoretical calculations, providing good validation for the modeling technique. The FEA modeling method is thus authenticated as a valuable tool for predicting the dynamics of fluid-tank systems.

Work presented in this paper describes the formulation for implementation of a concurrent multiple-time-scale integration method with improved numerical dissipation capabilities. This approach generalizes the previous Multiple Grid and Multiple Time-Scale (MGMT) Method [ 1 ] implemented for the Newmark family of algorithms. The framework is largely based upon the fundamental principles of Lagrange multipliers used to enforce workless nonholonomic constraints and Domain Decomposition Methods (DDM) to obtain coupled equations of motion for distinct regions of a continuous domain. These methods when combined together systematically yield constraint forces that not only ensure conservation of energy but also enforce continuity of velocities across the interfaces. Multiple grid connections between (non-conforming) sub-domains are handled using Mortar elements whereas coupled multiple-time-scale equations are derived for the Generalized-α Method [ 2 ]. We show that MGMT Method can be easily extended to incorporate the Generalized-α family of time integration algorithms, hence allowing selective discretization in space and time along with controlled numerical dissipation for distinct grids. We also show that interface energy across connecting sub-domains is identically zero, further assuring global energy balance and continuity of velocities across connecting sub-domains.

An accurate finite element model of a structure is essential for predicting reliably its dynamic characteristics. Such a model can be used to predict the effects of structural modifications for dynamic design of the structure. These structural modifications may be imposed by design alterations for operating reasons. Most of the model updating techniques neglect damping and so these updated models can’t be used for accurate prediction of vibration amplitudes. This paper deals with the basic formulation of finite element model updating method having identified structural damping matrix, and its use for structural dynamic modifications. A case involving actual measured data for the case of F-shaped test structure, which resembles the skeleton of a drilling machine is used to evaluate the effectiveness of FE model updating method incorporating identified structural damping matrix for accurate prediction of the vibration levels and thus its use for structural dynamic modifications. Design modifications in terms of mass and stiffener modifications are introduced to evaluate the effectiveness updated model incorporating damping matrices for structural dynamic modifications. It has been concluded that the FE model updating incorporating identified structural damping matrix can be used for structural dynamic modifications with confidence.

Certification process is one of the crucial procedures for safety in the design of a new aerial platform. Flight flutter testing is the most critical component for the certification process. Usually a flutter analysis is performed beforehand for the planning of flight flutter testing of an aircraft which mostly requires the Finite Element Model (FEM) together with Ground Vibration Testing (GVT) to construct the structural dynamic model of the complete aircraft for the flutter analyses. GVT is not only required for new aircraft design but also when considerable changes are made to an existing aircraft or when new external load configurations are introduced. Experimental methods require high effort, high budget, long time, and much repetition. Therefore, the computational and theoretical studies seem more applicable in the early phase. However, GVT of an available fighter aircraft in defense projects becomes an issue for the designers if a detailed FEM of the aircraft is not available prior to test. Hence, planning of the GVT in early stage is vital for project leaders. In this study, a rough FEM of a fighter aircraft is developed and correlated to available GVT data for planning purpose. The representative mode shapes are evaluated by estimation of the several sections of the aircraft. It is also shown that a rough FEM of the aircraft can be utilized for determination of the measurement and excitation points on the aircraft in planning stage. The geometrical properties, physical limitations and basic requirements of GVT are also taken into account for an efficient planning.