Timoshenko Beam Theory Research Articles

Rounded corner thicken strut re-entrant auxetic honeycomb: Analytical and numerical modeling

An analytical model is formulated for 2-D periodic negative honeycomb thicken strut re-entrant lattice structures and a modified rounded corner negative honeycomb structure that shows negative Poisson’s ratios (NPR). Analytical modeling is done using Castigliano’s second theorem, where each beam is modeled using Timoshenko beam theory, considering bending, stretching, and transverse shearing. Elastic modulus and Poisson’s ratio have been formulated for both structures in the form of non-dimensional geometrical characteristics, such as length ratios, angles of re-entrant arms, shear correction factor, and the material’s Young’s modulus and Poisson’s ratios. Numerical simulations conducted in ABAQUS-CAE explicit solver validate the analytical model. The effect of the non-dimensional parameters on the qualities of the developed structure is demonstrated. It is observed that the structures with a low curvature ratio have a high fluctuation of Poisson’s ratio and Elastic constant when plotted against the other parameters. The slenderness ratio has little impact on Poisson’s ratio but significantly influences elastic modulus. It is shown that various needs can be satisfied by customizing the Poisson’s ratios and elastic constant of both forms of lattice construction over an extensive range by carefully choosing the geometrical parameters and material.

The sub-wavelength focusing of flexural waves achieved by splitting one plane lens into two halves with a controllable angle

The flexural wave focusing in plates and shells is of great importance for energy harvesting and vibration control. Traditional plane lens based on gradient index and metasurface usually exhibits normal focusing, i.e., the focusing spot size is larger than half wavelength. In order to improve its working performance, increase energy at the focal point, reduce the focusing spot size and further achieve subwavelength focusing, a novel design scheme is proposed, i.e., splitting one traditional plane lens into two halves with a controllable inner angle. Firstly, the transmission and phase are calculated by using the Timoshenko beam theory, utilizing which the lens design is finalized via changing beam thickness perpendicular to wave propagation. After that, the working performance of two sub-lenses is compared with that of one single lens via numerical simulations, including the focal position, energy distribution, and spot size, which are further validated through experimental measurements. It is demonstrated that the flexural wave can exhibit subwavelength focusing after traveling across two adjacent halves, with the focusing spot size smaller than half wavelength. Specifically, the subwavelength focusing is broadband, and still occurs in a frequency region centered at the designed frequency. The proposed design scheme is expected to provide an innovative approach for the lens design in acoustics and optics.

Model verification and vibration analysis of the four-disk hollow flexible shaft rotor system

Rotor unbalances failure due to various factors such as manufacturing defects, mounting errors, and material inhomogeneity is inevitable, and will be aggravated by bearing pulse displacement excitation caused by maneuvering flight. Therefore, the purpose of this paper is to study the vibration of the rotor system under disk unbalance forces and bearing pulse displacement excitation. Firstly, the differential equation of motion for four-disk flexible hollow shaft rotor system modeling with a simple finite element model(SFEM) is established by the Lagrangian method in non-inertial systems, and the shaft is modeled using Timoshenko beam theory. Then, the dynamic characteristics of the four-disk flexible hollow shaft rotor are analyzed and compared with the 3D finite element model(3D FEM) to verify the accuracy of the model. To analyze the effects of different disk unbalanced positions and pulse displacement excitation on the vibration characteristics of the rotor, the characteristic vector method and the Runge–Kutta method are used to obtain the steady-state solution and the transient solution, respectively. In addition, the simulation results show that suitable in-shaft damping has a stable effect on the rotor during the start-up. Disk2 and Disk3 are more sensitive to synchronous harmonic excitation and pulse displacement excitation than Disk1 and Disk4. The research of this paper provides an important basis for vibration monitoring and control, and vibration transmission analysis of aero-engine rotor system.

Transversely heterogeneous nonlocal Timoshenko beam theory: A reduced-order modeling via distributed-order fractional operators

Nonlocal effects are widely identified in micro/nano systems and have been studied extensively in recent decades. Nevertheless, existing studies mostly focus on the modeling of homogeneous nonlocal systems and as a result, cannot model micro/nanostructures with heterogeneously distributed nonlocal effects. This study introduces a reduced-order nonlocal Timoshenko beam model that facilitates precise modeling of micro-elastic beams with layer-wise heterogeneous nonlocal effects. First, a fully-resolved two-dimensional (2D) plane-strain fractional-order nonlocal elastic framework is developed to provide reference solutions for 2D nonlocal beam problems. Building upon this general nonlocal elasticity theory, an equivalent one-dimensional (1D) nonlocal Timoshenko model is then developed. The layer-wise heterogeneous nonlocal information is captured by using distributed-order (DO) operators, and the impacts arising from the nonlocal heterogeneity are further characterized by introducing two auxiliary parameters. Both 1D and 2D approaches are applied to simulate the mechanical responses of nonlocal beams. Direct comparisons of numerical simulations produced by either the 1D or the fully-resolved 2D model confirm that the DO Timoshenko beam formulation (together with the two auxiliary parameters) can capture not only the overall beam deflection but also the additional shear effect induced by the heterogeneous nonlocality. Computational cost assessment also indicates the proposed approach’s superior performance. The proposed DO Timoshenko model enables model-order reduction without compromising the heterogeneous nonlocal description of the material hence leading to an efficient and accurate reduced-order nonlocal modeling approach that addresses the limitations of prior nonlocal microstructural theories and extends applicability to a broader range of heterogeneous nano/microstructures.

Vibration and sound radiation of acoustic black hole beams on Pasternak foundation by the Riccati transfer matrix method

This paper aims to study the vibration and sound radiation of the acoustic black hole (ABH) beams on Pasternak foundations. We focus on the influences of the foundations on the ABH effect because foundations are essential and common parts of mechanical systems. To this end, we derive the exact transfer matrix of the ABH beam on the viscoelastic Pasternak foundation based on the Timoshenko beam theory. Using the presented method, we explore the influences of Pasternak foundations on the natural frequencies, modal damping factors, and mode shapes of ABH beams. In addition, the sound radiation behavior of ABH beams on Pasternak foundations is also investigated. Several case studies are presented to demonstrate the effects of nonuniform foundations on wavenumber-domain properties and the vibroacoustic response of ABH beams. The results suggest that viscoelastic Pasternak foundations can greatly influence vibration characteristics and increase the modal damping factors due to the shear effect of the Pasternak foundation, which enriches the physical understanding of the ABH structures. Finally, the experimental results are used to validate the presented model.

Investigating the Sommerfeld effect in the rotating shaft with internal and external damping using the Timoshenko beam theory

The Sommerfeld effect is a destructive phenomenon in rotating systems with a non-ideal electrical source, which causes instability in the system by applying a dynamic jump around critical speeds. In this article, the Sommerfeld effect has been investigated for the first time using the Timoshenko beam theory for an eccentric continuous shaft with internal and external damping. After deriving the governing equations and finding displacement functions using the semi-analytical method, the Sommerfeld effect near the critical speeds is detected using the instantaneous power balance method. As confirmation of the correctness of the derived relations, it has been shown that for thin shafts, there is a good consistency between the results obtained from the Euler–Bernoulli and Timoshenko theories in the early modes. However, it was observed that at higher critical speeds, the jump amplitude decreases, and the unstable speed range increases significantly, so the probability of entering the vicinity of the instability range in the next mode is not unexpected. Since no effect has been ignored in this study, the dynamic analysis of the Sommerfeld jump in thick shafts is also possible. Despite the common belief that Timoshenko beam theory is only considered suitable for studying thick shafts, it has been shown that the effects of shear deformation are significant in high-speed systems, even for non-thick shafts, and regardless of them in higher modes, it causes a calculation error in determining the point of occurrence of the Sommerfeld phenomenon.

Wave propagation in beams with functionally graded porosity distribution under highly transient axial and transverse impacts

Recent advances in the manufacturing process provide a possibility of fabricating a new generation of porous materials denoted by functionally graded porous materials (FGPM). This paper aims to present a time domain analysis of wave propagation through the porous structures with functionally graded porosity distribution, which has not been completely studied before. For this purpose, the beams with different functionally graded porosity distributions subjected to both axial and transverse tip impact loads with a high-frequency content are investigated. The shear deformable cantilevered functionally graded porous beams with various porosity distributions through the beam thickness are studied. The governing differential equations are derived using the Hamiltonian principle based on the Timoshenko beam theory. A locking-free first-order shear deformable beam element is used to derive the finite element formulation of the equations. The Newmark time integration method is used to perform a time domain analysis of the equations of motion and to investigate the transient response of the beams. The axial and transverse wave propagation characteristics through functionally graded (FG) porous beams are found using time domain analysis of the results. Deflection and velocity time histories of the tip and each point of the beam, reflection time, and variation of support reactions are obtained. The influences of the porosity magnitude and porosity distribution on the wave propagation characteristics and overall time responses are investigated. The results reveal that porosity distribution has a significant effect on the wave amplitude, wave speed, and reflection from the boundary. Also, this study can help in a better understanding of porous structures' behavior subjected to high-transient impact loads in different engineering applications.

Vibration damping by periodic additive acoustic black holes

Embedded acoustic black holes (ABHs) have demonstrated significant efficiency in vibration mitigation. However, their practical application is limited due to their inherent low strength. To address this issue, this paper introduces an alternative approach of additive ABHs, which are periodically mounted on the host structure to simultaneously enhance structural rigidity and damping effects. The Gaussian expansion method (GEM) is employed to model the ABH beam and base beam within the framework of Timoshenko beam theory. The coupling between the two substructures is achieved using the nullspace method (NSM) based on the interface coupling condition. Additionally, the wave and Rayleigh–Ritz method (WRRM) is utilized to handle the Bloch-Floquet periodic boundary conditions. The complex dispersion curves are obtained using the k(ω) method, where the imaginary part represents the attenuating waves in space. The accuracy of the proposed model is validated against finite element simulations for the unit cell modes and dispersion curves. The results indicate that local resonance dominates the behavior, overshadowing the Bragg scattering effect. Furthermore, the inclusion of a damping layer results in a strong damping effect across a wide frequency band. Parametric studies reveal that larger lattice constant and increased uniform portion thickness of the ABH contribute to better damping performance, albeit with an associated increase in the added mass of the ABH component. Finally, the damping capability of finite periodic beams with 5 cells is investigated, assessing modal loss factor (MLF), transmissibility, and forced vibration shapes. The findings demonstrate that the proposed additive ABH approach opens up new possibilities for engineering applications.

Fluid-structure interaction characteristics between natural gas fluid and tubing string in high-pressure high-temperature high-production gas wells

The transient internal flow in high-pressure high-temperature high-production (three-high) gas wells may bring about serious fluid-structure interaction (FSI) between natural gas fluid and tubing string. Then, fatigue failure, wear and leakage of tubing string can easily be caused to threaten the wellbore safety and integrity. However, it is difficult to directly adopt the existing FSI model owing to particularity environment of the three-high gas wells. Based on water hammer, FSI and Timoshenko beam theory, a mathematical model expounding FSI phenomenon of the three-high gas wells is established by Poisson, friction and junction coupling, which considers unsteady friction effect, centrifugal and Coriolis force to make FSI characteristics more consistent with the engineering practice. Then, the improved method of characteristics (MOC) is applied into combination solution of the model. Later, the model and solution method is verified by comparing the results with different reference's ones respectively. On this basis, the effects of shut-in time, well depth position, unsteady friction on FSI characteristics are analyzed and discussed systematically. The calculation results are shown that shut-in time and well depth position have a more significant influence on FSI characteristics in three-high gas wells. In addition, FSI characteristics under action of unsteady friction decay faster, the time of the peak value also is delayed accordingly, and cumulative attenuation and cumulative delayed time of FSI characteristics increases with decrease of shut-in time. The FSI model, solution method proposed in this paper and results can provide theoretical basis and reference for the research on FSI and the formulation of shut-in operation for three-high gas wells, and even for highly deviated or horizontal gas wells.

Static, dynamic and buckling behavior of functionally graded beams with tunable inclusions

The introduction of microstructurally tunable materials endorses functionally graded (FG) beams with distinctly inspiring functionalities and mechanical properties. In order to facilitate the multiscale design of FG beams and evaluations of corresponding mechanical behavior, analytical solutions are developed in the present research on the static, dynamic and buckling responses of FG beams reinforced with graphene platelets, porosity or origami inclusions, etc. To facilitate the analytical derivation as well as numerical extension, this paper establishes a theoretical framework, firstly formulating the principle of virtual work and reciprocal theorem of work for the FG beams, and then deriving and proving the principles of minimum potential and complementary energies, the former of which is used for the establishment of the variational principles for the static bending, free vibration and buckling phenomenon in the present work. Following the proposed variational principles and considering Timoshenko beam theory, the strong-form partial differential governing equations as well as the corresponding boundary conditions can be obtained for static bending, free vibration and buckling responses of FG beams. The Ritz method is finally employed to obtain the explicit expressions of transverse bending and rotation as well as the frequencies and critical loads for FG beams with different boundary conditions. What’s more, it should be noted that the FG of the beams is achieved through tailoring micromechanical parameters, such as volume fraction and distribution of reinforcement, which are usually unevenly distributed. The mechanical responses of FG beams are also predicted through micromechanics approaches, such as Halpin-Tsai expression. Conventional GPL distributions as well as graphene origami (GOri) distributions with negative Poisson's ratios (NPR) are also presented to validate the analytical derivation and solutions. Finally, the proposed solutions are employed to investigate the effect of the microstructural parameters on the effective behavior of FG beams.

Dynamic Analysis of Isotropic Homogeneous Beams Using the Method of Initial Functions and Comparison with Classical Beam Theories and FEM

The main aim of this study is the dynamic analysis of isotropic homogeneous beams using the method of initial functions (MIFs) and comparison with classical beam theories and FEM. Also, this research employs the state space methodology, with a special emphasis on isotropy, to analyse simply supported beam systems. A mathematical model for the dynamic response of beams is constructed using the method of initial functions. The novelty of this study lies in its approach to dynamic analysis, where isotropic homogeneous beams are explored without making assumptions, thus ensuring increased precision using the method of initial functions. Importantly, the approach remains free from restrictive assumptions and relies solely on mathematical formulations, yielding results superior to classical beam theories such as Euler–Bernoulli, Timoshenko, and Rayleigh beam theories. In this work, the application of MIFs of various orders (4th, 6th, 8th, and 10th) to calculate natural frequencies is explored, enabling a thorough examination of the beam’s dynamic characteristics. In addition, parameters such as normal stresses, shear stresses, and deflections in different directions are considered to provide a comprehensive understanding of beam behaviour. To validate the findings, a detailed comparison with a finite element method (FEM) is conducted, achieving excellent agreement between the analytical results and FEM solutions. Furthermore, the influence of Poisson’s ratio (μ) on natural frequencies is investigated by varying its value from 0.18 to 0.30. The research also explores the deviation of plane stress values of the beam section from those estimated using the FEM for the corresponding components.

Exact vibration solution for three versions of Timoshenko beam theory: A unified dynamic stiffness matrix method

This paper introduces a unified and exact method for the vibration solution of three versions of Timoshenko beam theory, namely the classical Timoshenko beam theory (TBT), truncated Timoshenko beam theory (T-TBT), and slope inertia Timoshenko beam theory (S-TBT). The proposed unified method enables the free vibration analysis of these three beam theories performed by only one equation, which avoids separate modeling and solution with different beam theories. Firstly, the comparison of three beam theories is conducted with a special focus on deriving the governing differential equation of T-TBT based on Hamilton’s principle. Then, two parameters are introduced to unify the three governing differential equations. The dynamic stiffness matrix is derived in a unified form by reducing the order of inverse matrix operation from 2 n to n, allowing the dynamic properties of three beam theories to be characterized with only a single model. Additionally, this paper also derives the unified frequency-dependent mass and stiffness matrices based on the unified dynamic stiffness matrix, which eliminates the limitation of DSM in studying the independent influence of the structure's mass and stiffness characteristics. Finally, the discrepancies of the three beam theories are discussed under different boundary conditions and aspect ratios.

Modeling and analysis of radial throw of micro-milling tool based on tool-attachment errors in high-speed rotating

In the process of micro-milling complex structures, radial throw is likely to cause lower dimensional/form accuracy, which will severely affect the performance of the components. Therefore, it is necessary to investigate the source contributing to the radial throw. According to the kinematic process of the radial throw arising from the attachment errors of the micro milling cutters, a mathematical model considered the attachment errors and the variable section geometry of the micro milling cutters was established to predict the radial throw on the basis of the principle of minimum total potential energy and the Timoshenko beam theory. In comparison to the mathematical model, the proposed finite element model (FEM) presetting the attachment errors shows the effect of modal vibration and the variation of radial throw with attachment errors. To further investigate the environmental factors influencing the radial throw, a measurement method based on the laser measurement system is presented to achieve the on-machine measurement of runout, and a specific extraction method of attachment errors was proposed to help validate the mathematical model. The difference between the results of the mathematical model, FEM, and the experiment is not exceeding 10 % within 3 μm of the maximum runout. Radial throw varies strongly with attachment errors, and the high rotation speed will aggravate the system instability caused by the attachment errors. The main contributor among experimental factors to the variation of runout is the form accuracy of micro milling cutters, accounting for 4.7 % at the highest. This method can provide a theoretical basis for the sources of unbalanced cutting force analysis and the improvement of dimensional/form accuracy.

Experimental Investigations of Damage Identification for Aluminum Foam Sandwich Beams Using Two-Step Method

In the experiment, strain gauges and dynamic signal acquisition instruments are used to collect and record data, and the stochastic subspace algorithm is used to extract the first three strain modal parameters of each case. The damage amount identified by the second natural frequency based on the modified Timoshenko beam theory is more in line with the actual situation. The damage depth of case 2 and case 4 is 2 mm, and the identified damage amount is 10% and 9%, respectively. The damage depth of case 3 and case 5 is 4 mm, and the identified damage amount is 16% and 23%, respectively. The damage location information of case 6 is well identified by using the normalized strain modal shape difference index and the enhanced strain modal shape difference index. Taking the strain response signal of case 6 as an example, it is proved that the stochastic subspace strain modal parameter identification algorithm has strong anti-interference ability under the action of 1.5 times, 4 times, and 9 times noise. In addition, the method is verified by theoretical calculation and numerical simulation, and the damage law has a high degree of coincidence with the test. The experimental results show that this method expands the theoretical basis of foam metal damage degree information identification and improves the accuracy of damage location information identification and the anti-interference of parameter identification.

Rolling Shear Strength of Cross Laminated Timber (CLT)—Testing, Evaluation, and Design

Cross laminated timber (CLT), with its typical orthogonal layering and exposure to out-of-plane bending, develops inherent rolling shear stresses. These stresses need to be checked during the ultimate limit state design process. With the ongoing revision of Eurocode 5, a discussion regarding the characteristic value of the rolling shear strength of CLT has arisen. One obstacle in the discussion is seen in the lack of harmonized regulations concerning how to determine rolling shear properties. This circumstance manifests in the greatly diverging test results of different institutions testing the rolling shear strength. The paper at hand aims to propose a candidate for such harmonized regulations. To achieve this, the most common test setups, such as the inclined shear test, three- and four-point bending tests, etc., were numerically and experimentally investigated. Within the numerical investigations, a comparison of the most common calculation methods (Timoshenko beam theory, modified γ-method, Shear Analogy Method, and Finite Element Analysis) for evaluating rolling shear stresses was included. In the experimental program, parameters such as the specimen width, number, and thickness of the cross layer(s), shear length, optional reinforcement against the stresses perpendicular to the grain, and the overall test setup were varied. It was found that the used test setups themselves and the area of the cross layer(s) (shear length, number, and thickness of the cross layer(s)) have a major impact on the rolling shear strength. In contrast, no effect was found from the calculation methods. Based on these findings and on a database of approx. 300 four-point bending rolling shear tests on CLT specimens from five well-established CLT manufacturers, a model for the regulation of the rolling shear strength of CLT is proposed, in combination with a corresponding four-point bending test setup. Afterwards, with two additionally conducted four-point bending test series, the proposed model is successfully validated. The conclusions and recommendations in respect to the test setup (four-point bending), evaluation procedure (Timoshenko beam theory), reference characteristic rolling shear strength, and the model, which allows adapting the reference rolling shear strength to individual conditions, are seen as a worthy basis for a more objective discussion on this topic.

Lateral Dynamic Response of Helical Pile in Viscoelastic Foundation Considering Shear Deformation

Helical piles are a new type of pile that has good application prospects, and researchers have carried out an in-depth investigation into their vertical uplift and compressive bearing capacity. However, there is relatively little research on the dynamic bearing characteristics of helical piles. Therefore, the lateral vibration of a helical pile embedded in the viscoelastic foundation is systematically studied in this article. Utilizing the equivalent stiffness method to transform a helical pile into a cylindrical pile of special diameter, the lateral vibration model of the helical pile considering shear deformation is established based on the Winkler foundation model and the Timoshenko beam theory. The analytical solutions for the lateral dynamic displacement, bending moment, and shear force of the helical pile are strictly derived, and the rationality of the present solutions is also verified by comparing them with existing solutions. Based on the present solutions, a parametric study is carried out to investigate the influence of the pile and soil properties on the lateral dynamic response of the helical pile. It is found that the load excitation frequency and pile–soil stiffness ratio have a significant influence on the lateral dynamic displacement, bending moment, and shear force of the helical pile with space and time response.

Novel hybrid-controlled graded metamaterial beam for bandgap tuning and wave attenuation

In this paper, a tunable functionally graded metamaterial beam is designed for flexural wave attenuation by integrating piezomagnetic shunt damping system and inertial amplification mechanism. The proposed piezomagnetic shunt damping system is a complex mechanic–magnetic–electrical coupling system, which aims to transform and consume the vibration energy through local resonance to form a bandgap with tunable and strong wave attenuation ability. Based on Timoshenko beam theory, the wave equation and transmission spectrum of the metamaterial beam are derived by using transfer matrix method. The theoretical results are compared with the numerical simulation results. The results show that the resonance characteristics of piezomagnetic shunt circuit lead to negative group velocity and strong wave attenuation(−30 dB) at frequency defined by inductance and capacitance in shunt circuit. In varying frequency regimes, the coupled bandgap width can be maximized to 1925 Hz by tuning the external capacitance and coil turns. The superposition of double attenuation peaks caused by inertial amplification mechanism and local resonance coupling can be generated in the bandgap, allowing wave attenuation up to −94 dB. Subsequently, the attenuation capability of locally resonant bandgap can be significantly enhanced without changing the frequency by introducing the negative resistance into shunt circuit. Furthermore, the initiation and termination frequencies of bandgap can be flexibly designed by important material and structural parameters. This work is expected to provide valuable research ideas for the application of advanced intelligent materials in the field of vibration and noise reduction.

An analytical approach for the analysis of stress wave transmission and reflection in waveguide systems based on Timoshenko beam theory

The paper presents an analytical continuous solution for the analysis of wave refraction and transmission/reflection caused by arbitrarily complex waveguide subsystems. It allows analyzing the way stress wave components are altered as they go through a substructure. The method is new in that it investigates the wave phenomena which govern the dynamic behavior of a structural system explicitly and studies the effectiveness of different serrated and fractal subsystem designs functioning as wave content filters. Timoshenko beam theory is used to model stress wave propagation in waveguides because of its accuracy and consistency over a wide range of vibration frequencies. The versatility of the method is demonstrated using a number of numerical examples characterizing stress wave refraction in single input/single output and single input/multiple output subsystems to study periodic, fractal, and serrated forms. The low computation cost and stable accuracy of the method over a very wide range of frequencies, make it an effective tool for metaheuristic optimization approaches which require massive calculations over many generations. The method is demonstrated to perform seamlessly in coupling with a genetic algorithm optimization framework to determine the optimal serrated configuration of a wave filter.

Nonlinear modeling and analysis of spatial pipeline with arbitrary shapes supported by clamps considering displacement-dependent characteristic

Considering the displacement-dependent characteristics of the clamp, a general nonlinear semi-analytical modeling method for the spatial pipeline with arbitrary shapes supported by multiple clamps is proposed to study the vibration characteristics of the pipeline-clamp system. The coupling of the complex spatial pipeline is realized by introducing the connecting springs at the connection region of the straight pipe and curved pipe. The equation of motion for spatial pipeline structure is established based on the Lagrange energy equation and Timoshenko beam theory. High-order polynomials are used to characterize the stiffness and damping characteristics of the clamp, and the simple straight pipe is used as the basic model to reverse the clamp parameters. The influence of clamps on pipeline vibration is skillfully introduced into the nonlinear dynamic model of the spatial pipeline. According to the Newton-Raphson method, the nonlinear equation of motion is solved. Taking the spatial pipeline supported by double clamps as an example, the related experiment tests and ANSYS simulation are carried out, and the effectiveness of the established model is verified by comparing the results. Finally, the nonlinear vibration mechanism of the pipeline-clamp system is analyzed. The modeling method proposed in this paper can provide positive guidance for modeling and vibration analysis of the aero-engine pipeline with arbitrary shapes.

Electro-mechanical transfer matrix modeling of piezoelectric actuators and application for elliptical flexure amplifiers

Mechanically amplified piezoelectric actuators (APAs) can be found in many scenarios of precision engineering and instrumental devices. However, the electro-mechanical design of curvilinear APAs is difficult due to the existence of curved flexure beams and multi-domain electro-elasto dynamics. In this paper, the electro-mechanical behavior of elliptical APAs is studied by exploiting a novel electro-mechanical transfer matrix method. The motivation is to facilitate both the static and dynamic analyses of such a complex APA with curvilinear flexure beams by considering the multi-domain dynamics of piezoelectric stacks and compliant mechanisms from an electro-mechanical viewpoint. To this end, an analytical electro-elasto transfer matrix of piezoelectric stacks operating at the d33 mode is derived in the form of Taylor's series based on Timoshenko beam theory. The dynamic response spectrum of displacement and impedance for elliptical APAs are insightfully captured by such an electro-mechanical model. Different topologies of elliptical APAs are also compared and the optimal configuration is suggested. At last, a proof-of-concept prototype is fabricated and tested with a special focus on experimental evaluation of the electro-mechanical coupling model.