Engineering Mechanics

The transport and mechanical properties of saturated soil drastically change when temperatures drop below the freezing temperature of water. During artificial ground freezing, this change of properties is exploited in order to minimize deformations during construction work and for groundwater control. Whereas for the latter only the size of the frozen-soil body is relevant, which is obtained by solving the thermal problem, the design of the ground-freezing work for support purposes requires information about the mechanical behavior of frozen soil. In addition to the quantification of the improvement of mechanical properties during freezing, information about the dilation associated with the 9% volume increase of water during freezing is required in order to assess the risk of damage to surface infrastructure caused by frost heave. In this paper, a micromechanics-based model for the prediction of both the aforementioned phasechange dilation and the elastic and viscous properties of freezing saturated soil is presented. Hereby, the macroscopic material behavior is related to the behavior of the different constituents such as soil particles, water, and ice. Combined with the solution of the thermal problem, the proposed model provides the basis for predictions of the performance of support structures composed of frozen soil.

Rate-independent monotonic behavior of filled natural rubber and high damping rubber is investigated in compression and shear regimes. Monotonic responses obtained from tests conducted in both regimes demonstrate the prominent existence of the Fletcher-Gent effect, indicated by high stiffness at low strain levels. An improved hyperelasticity model for compression and shear regimes is proposed to represent the rate-independent instantaneous and equilibrium responses including the Fletcher-Gent effect. A parameter identification scheme involving simultaneous minimization of least-square residuals of uniaxial compression and simple shear data is delineated. The difficulties of identifying a unique set of hyperelasticity parameters that hold for both compression and shear deformation modes are thus overcome. The proposed hyperelasticity model has been implemented in a general purpose finite element program. Finite element simulations of experiments have shown the adequacy of the proposed hyperelasticity model, estimated parameters, and employed numerical procedures. Finally, numerical experiments were conducted to further explore the potential of the proposed model, and estimated parameters in analyzing rubber layers of a base isolation bearing subjected either to compression or to a combination of compression and shear.

A large portion of highway bridges in the United States are reaching or have reached their intended design lives. To avoid replacing a large number of bridges simultaneously, methodologies to safely extend their lives are important to help avoid high replacement costs and to schedule bridge replacement over a longer time window. This paper proposes an approach to extend the fatigue life of vulnerable steel bridges through a response modification apparatus, consisting of a mechanical amplifier and a response modification device, which provides supplemental stiffness and damping to the bridge. Because of the relatively small deflections encountered under typical service loads, the use of a mechanical amplifier allows for a smaller apparatus and enables a more efficient device to provide adequate response modification forces to the bridge. Herein, the use of a scissor jack as the mechanical amplifier is proposed for use in bridge applications, and its utility in concert with a passive stiffness device is demonstrated by application to a simple beam structure. Reductions in moment ranges of 37% and safe life extensions of 300% are achieved on a simple beam model with the proposed response modification apparatus.

In the past two decades, meshfree methods have emerged into a new class of computational methods with considerable success. In addition, a significant amount of progress has been made in addressing the major shortcomings that were present in these methods at the early stages of their development. For instance, essential boundary conditions are almost trivial to enforce by employing the techniques now available, and the need for high order quadrature has been circumvented with the development of advanced techniques, essentially eliminating the previously existing bottleneck of computational expense in meshfree methods. Given the proper treatment, nodal integration can be made accurate and free of spatial instability, making it possible to eliminate the need for a mesh entirely. Meshfree collocation methods have also undergone significant development, which also offer a truly meshfree solution. This paper gives an overview of many classes of meshfree methods and their applications, and several advances are described in detail.

Abstract: In this paper, the direct differentiation method ͑DDM͒ for finite-element ͑FE͒ response sensitivity analysis is extended to linear and nonlinear FE models with multi-point constraints ͑MPCs͒. The analytical developments are provided for three different constraint handling methods, namely: ͑1͒ the transformation equation method; ͑2͒ the Lagrange multiplier method; and ͑3͒ the penalty function method. Two nonlinear benchmark applications are presented: ͑1͒ a two-dimensional soil-foundation-structure interaction system and ͑2͒ a three-dimensional, one-bay by one-bay, three-story reinforced concrete building with floor slabs modeled as rigid diaphragms, both subjected to seismic excitation. Time histories of response parameters and their sensitivities to material constitutive parameters are computed and discussed, with emphasis on the relative importance of these parameters in affecting the structural response. The DDMbased response sensitivity results are compared with corres...

Floating offshore wind turbines are recently being considered widely for adoption in the wind power industry, attracting interest of several researchers and calling for the development of appropriate computational models and techniques. In the present work, a nonlinear finite element formulation is proposed and applied to the static and dynamic analysis of mooring cables. Numerical examples are presented, and in particular, a mooring cable typically used for floating offshore wind turbines is analyzed. Hydrodynamic effects on the cable are accounted for using the Morison approach. A key enabling development here is an algorithmic tangent stiffness operator including hydrodynamic coupling. Numerical results also suggest that previously empirical hydrodynamic coefficients could be obtained by fully coupled fluidstructure interaction. Convergence rate and energy balance calculations have been used to demonstrate the accuracy of computed solutions. The introduction of the developed cable model in a framework for the study of the global behavior of floating offshore wind turbines is subject of current work. Source code developed for this work is available as online supplemental material with the paper.

The use of self-organizing maps and artificial neural networks for structural health monitoring is presented in this paper. The authors recently developed a nonparametric structural damage detection algorithm for extracting damage indices from the ambient vibration response of a structure. The algorithm is based on self-organizing maps with a multilayer feedforward pattern recognition neural network. After the training of the self-organizing maps, the algorithm was tested analytically under various damage scenarios based on stiffness reduction of beam members and boundary condition changes of a grid structure. The results indicated that proposed algorithm can successfully locate and quantify damage on the structure.

Effective transverse shear moduli of composite honeycomb cores are important material properties in analysis and design of sandwich structures. An analytical approach using a two-scale homogenization technique is presented to predict the effective transverse shear stiffnesses of thin-walled composite honeycomb cores with general configurations. To improve the performance of core transverse shear behavior, a nondimensional index, the so-called efficiency of material (EOM), is introduced to evaluate the optimal design of periodic cellular cores. Explicit formulas of effective transverse shear stiffnesses and the corresponding efficiencies of material are provided for three typical honeycomb cores consisting of reinforced sinusoidal, elliptical, and reinforced hexagonal geometries. It has been shown that the efficiency of material is only determined by nondimensional core geometric ratios. The effects of these ratios on the EOM of effective transverse shear stiffnesses, which are examined in detail in this study, offer insight and guidelines for optimal design and selection of honeycomb cores. The explicit formulas for the effective transverse shear stiffness properties of thin-walled composite honeycomb cores and their related EOMs can be used effectively to predict and optimize the core transverse shear behavior in sandwich structures.

Application of curved beams in special structures requires a special analysis. In this study, the differential quadrature method (DQM) as a well-known numerical method is utilized in the dynamic analysis of the Euler-Bernoulli curved beam problem with a uniform cross section under a constant moving load. DQ approximation of the required partial derivatives is given by a weighted linear sum of the function values at all grid points. A prismatic semicircular arch with simply supported boundary conditions is assumed. The accuracy of the obtained results is corroborated by employing the Galerkin and finite element methods. Finally, the convergence rate of the DQM and Finite Element Method (FEM) in the associated problem is explored. In the structural problems with specific geometry, use of DQM which is independent of domain discretization, is proved to be efficient.

In teaching an introduction to the finite element method at the undergraduate level, a prudent mix of theory and applications is often sought. In many cases, analysts use the finite element method to perform parametric studies on potential designs to size parts, weed out less desirable design scenarios, and predict system behavior under load. In this book, we discuss common pitfalls encountered by many finite element analysts, in particular, students encountering the method for the first time. We present a variety of simple problems in axial, bending, torsion, and shear loading that combine the students' knowledge of theoretical mechanics, numerical methods, and approximations particular to the finite element method itself. We also present case studies in which analyses are coupled with experiments to emphasize validation, illustrate where interpretations of numerical results can be misleading, and what can be done to allay such tendencies. Challenges in presenting the necessary mix of theory and applications in a typical undergraduate course are discussed. We also discuss a list of tips and rules of thumb for applying the method in practice.

Starting from three-dimensional ͑3D͒ continuum mechanics, a simple one-dimensional model aimed at analyzing the whole static behavior of nonhomogeneous curved beams is proposed. The kinematics is described by four one-dimensional ͑unknown͒ functions representing radial, tangential, and out-of-plane displacements of the beam axis, which are due to flexures and extension, and the twist of the cross section due to torsion. The flexural and axial displacements fit with the classical Euler-Bernoulli beam theory of straight beams, and nonuniform torsion is also considered. The relevant elastogeometric parameters have been determined, and the system of governing equilibrium equations is obtained by means of the principle of minimum potential energy. Finally, the general theory is illustrated with examples.

Flow control have been used for many years to control the fluid flow, and some employ different concepts to serve this purpose in last decades. The ability to manipulate a flow passively or actively is of immense technological importance. This paper is more concentrating on modern active flow control methods. These methods are used majorly to achieve transition delay, drag reduction, lift enhancement, turbulence management, separation postponement, noise suppression, etc. The potential benefits of flow control may include improved performance, affordability, fuel consumption economy, and environmental compliance. A review of major techniques used in this context (with more emphasis on experimental methods) is presented along with a brief discussion on each of them.

Flow past a square cylinder placed at an angle to the incoming flow is experimentally investigated using particle image velocimetry, hot wire anemometry, and flow visualization. The Reynolds number based on cylinder size and the average incoming velocity is set equal to 410. Data for four cylinder orientations ͑ = 0, 22.5, 30, and 45°͒ and two aspect ratios ͓AR= 16 and 28͔ are reported. Results are presented in terms of drag coefficient, Strouhal number, time averaged velocity, stream traces, turbulence intensity, power spectra, and vorticity field. In addition, flow visualization images in the near wake of the cylinder are discussed. The shape and size of the recirculation bubble downstream of the cylinder are strong functions of orientation. A minimum in drag coefficient and maximum in Strouhal number is observed at a cylinder orientation of 22.5°. The v-velocity profile and time-average stream traces show that the wake and the separation process are asymmetric at orientations of 22.5 and 30°. The corresponding power spectra show additional peaks related to secondary vortical structures that arise from nonlinear interaction between the Karman vortices. The flow visualization images show the streamwise separation distance between the alternating vortices to be a function of cylinder orientation. Further, the flow approaches three dimensionality early, i.e., closer to the cylinder surface for the 22.5°orientation. The drag coefficient decreases with an increase in aspect ratio, while the Strouhal number is seen to increase with aspect ratio. The turbulence intensity is higher for the large aspect ratio cylinder and the maximum turbulence intensity appears at an earlier streamwise location. The overall dependence of drag coefficient and Strouhal number on orientation is preserved for the two aspect ratios studied.

Negative bending moments acting in the support regions of continuous composite beams generate tensile stresses in the concrete slab and compressive stresses in the lower steel profile. As a result the mechanical behavior of these beams is strongly nonlinear even for low stress levels, due not only to the slip at the beam-slab interface, but also to cracking in the slab. Therefore, an adequate theoretical modeling should take account of the interactions between the structural steel and the concrete slab by shear connectors and ...

The following is meant to be a review of sailboat mast design methods and their practical application. In the first portion, the Euler‐Bernoulli beam theory, the P‐Δ method, Skene’s method and the Nordic Boat Standard are summarised and evaluated as design methods for masts. It was found that the Nordic Boat Standard represents the state of the art available in the public domain. In the second portion, the practical case of the Ultimate 20 racing yacht is reviewed. The Ultimate 20 has shown a tendency for the mast failing by buckling at a stress concentration on the bottom of the mast, and several solutions have been brought forward to solve this issue. In order to quantitatively establish which configuration is best, this boat’s mast was modelled according to Euler‐Bernoulli beam theory and practically tested using strain gauges. The results of both the mathematical model and the practical testing show consistent results and trends. It was found that the best single solution to reduce the chances of mast failure was the addition of baby stays.

An idea of passive base isolation of buildings is explored, using inclined rubber base isolators or inclined ''soft'' first-story columns. Such a system behaves as a physical pendulum, ''pivoted'' above center of mass, and is more stable than the standard system. Another advantage of the inclination is that the inertia forces of the structure due to rotation about the pivot point cancel to some degree the inertia forces due to the base translation. This is expected to result in smaller relative deformations of the building and smaller internal forces. In this paper, the consequences of this concept are illustrated on a simple model (base isolated single-degreeof-freedom oscillator), but also considering the soil flexibility and the wave nature of strong earthquake shaking (these are associated with additional rotations of the system and also affect the system period). A frequency domain solution is presented for small deformations, rigid foundations embedded in a homogeneous elastic halfspace, and horizontal in-plane and Rayleigh wave foundation driving motion.

Eurocode 4 is the European design code for composite construction ; in its so-called ENV version (ENV 1994) (Eurocode 4 1992), the scope is limited to "non-sway buildings" with efficient bracing systems. Therefore, it gives mainly rules to analyze and to check structural elements like beams, columns, slabs and joints. However, in the last years, the construction of taller buildings and larger industrial halls without wind bracing systems is susceptible to make global instability a relevant failure mode, which is not covered by Eurocode 4 ENV 1994. For three years, in the framework of a European research project funded by the European Community for Steel and Coal (ECSC), in which the university of Liège was deeply involved, intensive experimental, numerical and theoretical investigations have been carried out. The latter aimed at improving the knowledge in the field of sway composite frames and at developing appropriate design rules. The rotational behavior of the beam-to-column composite joints is one of the key aspects of the problem to which a special attention has been paid.

To understand the behavior of concrete material in ambient water, a series of triaxial compressive tests of concrete cylindrical specimens ͑ 100ϫ 200 mm͒ was conducted on a large scale triaxial machine. The acting pattern of water, confining pressure, loading strain rate, and moisture content were chosen as test parameters. The water acting patterns on concrete were directly divided into mechanical loading and real water loading according to whether the specimens were directly exposed to water or not. The confining pressure ranged from 0-8 MPa and the strain rate included 10 −5 / s, 10 −3 / s, and 10 −2 / s. By testing dry and saturated specimens, the effect of moisture on concrete strength was also examined. The test results indicated that the compressive strengths of both dry and saturated concrete increase obviously with the confining pressure under mechanical confining pressure. However, the effect on the strengthened dry concrete specimens is more significant. The strength of dry concrete under real water loading decreased remarkably, even less than its uniaxial strength, whereas the compressive strength of the saturated concrete specimen under real water loading is close to its uniaxial compressive strength. The strength of concrete increases with strain rate, and this phenomenon becomes more apparent under water loading.

 Abstract— Theory of Eight Palaces (八宫) or Eight Veins (八 脉) is useful in understanding economic disease. By using mathematical reasoning based on Yin Yang Wu Xing Theory in Traditional Chinese Economics (TCE), this paper demonstrates the treatment principle: " Even if all changed, it is hard to change one's nature " (江山易改，本性难移). It means that for the economic society, there is the mathematical structure of Eight Palaces or Eight Veins as the second physiological system of a steady multilateral system. It can be used to determine the root-cause of the sick system by using the six indexes of comprehensive judgment as the Eight palaces or Eight veins. The six indexes are PPI (the Producer Price Index), AAF (the total output value of Agriculture forestry Animal husbandry and Fishery), CPI (the Consumer Price Index), GBR (the General Budget Revenue), GDP (the Gross Domestic Product), and GDP (the right of making money), simple namely PACGGF. The six indexes of PACGGF inflation rates which can be used as diagnostic subsystem of disease. The first or second transfer law of economic society energies of Eight Palaces or Eight Veins changes according to the different PACGGF inflation rates of an economic society whether in the normal range or not. Assume that the range of one of PACGGF inflation rates is divided into four parts from small to large. Both second and third are for a healthy economy. The treating works are the treatment directly for a root-cause and the prevention indirectly for a more serious relation economic disease as symptoms. Both the root-cause and symptoms come from the first transfer law of economic society energies. And both first and fourth are for an unhealthy economy. The treating works are the treatment directly for a root-cause or the prevention indirectly for a more serious relation economic disease as symptoms. Both the root-cause and symptoms come from the second transfer law of economic society energies. An economic disease treatment should protect and maintain the balance of two incompatibility relations: the loving relationship and the killing relationship.Economic disease treatment should protect and maintain the balance of two incompatibility relations: the loving relationship and the killing relationship. As an application, the Chinese Finance inflation rate can be used for the jun-fire subsystem how to do works based on to diagnose the root-cause of steady multilateral systems by using Eight palaces.

Transfer Function is a Simple Pole and Functional Signal.Using MATLAB for the Pole Gain Function with the s transfer function.The Controller is compile the Degree of Freedom in Mechanics as the advance fluid mechanics and the mechanism linkage.The Vehicle is also function of Dynamics and Gain.

 Abstract— Theory of Sixty JiaZi (60 甲子) is useful in understanding economic disease. By using mathematical reasoning based on Yin Yang Wu Xing Theory in Traditional Chinese Economics (TCE) , this paper demonstrates the treatment principle: " seize the momentum of development， hasten lucky avoids disaster " (顺势而为,趋吉避凶). It means that for the economic society, there is the mathematical structure of Sixty JiaZi as the second physiological system of a steady multilateral system. It is used to predict the development of the corresponding subsystem based on 60 Jiazi numbers. People should be according to its momentum of development, hasten lucky avoids disaster. Theory of Eight palaces is to determine both the root-cause and symptoms of the sick system based on the six indexes of comprehensive judgment. It is the base of Six Jiazi. The six indexes are PPI (the Producer Price Index), AAF (The total output value of Agriculture forestry Animal husbandry and Fishery), CPI(the Consumer Price Index), GBR(the General Budget Revenue), GDP (the Gross Domestic Product), and Finance (the right of making money), simple namely PACGGF. The first or second transfer law of economic society energies of Sixty JiaZi changes according to the different PACGGF inflation rates of economic society whether in the normal range or not. Assume that the range of one of PACGGF inflation rates is divided into four parts from small to large. Both second and third are for a healthy economy. The treating works are the treatment directly for a root-cause and the prevention indirectly for a more serious relation economic disease as symptoms. Both the root-cause and symptoms come from the first transfer law of economic society energies. And both first and fourth are for an unhealthy economy. The treating works are the treatment directly for a root-cause or the prevention indirectly for a more serious relation economic disease as symptoms. Both the root-cause and symptoms come from the second transfer law of economic society energies. An economic disease treatment should protect and maintain the balance of two incompatibility relations: the loving relationship and the killing relationship.As an application, the Chinese GDP inflation rate can be used for the water subsystem how to do works based on to predict the root-cause of steady multilateral systems by using Sixty Jiazi.

Component failures due to the hydrogen embrittlement (HE) were observed in different industrial systems, including high-pressure hydrogen storage tanks, aircraft components, high-strength alloy components, and high-strength steel fasteners [1,2]. The contemporary approach in studying the effects of hydrogen on the mechanical properties of steels at different scales is based on the implementation of various multiscale (macro, micro-meso, and nano-atomic) modeling approaches and the applications of advanced multiscale experimental methods, Fig. 1 [3]. Simultaneous action in a cooperative manner of the hydrogen-enhanced localized plasticity (HELP) and the hydrogen-enhanced decohesion (HEDE) mechanism of HE, according to the HELP + HEDE model [4] of HE, were confirmed to be active, depending on the local concentration of hydrogen in steel [2-5], Table 1 [2]. Further investigations of the mechanical properties of steels at different length scales exposed to hydrogen damage should open a new window in the research related to the simultaneous action of HE mechanisms. It will also provide improved maintenance and the accurate service life prediction of various industrial components exposed to multiple active HE mechanisms [5,6].

A new electromechanical finite element modelling of a vibration power harvester and its validation with experimental studies are presented in this paper. The new contributions for modelling the electromechanical finite element piezoelectric unimorph beam with tip mass offset under base excitation encompass five major solution techniques. These include the electromechanical discretization, kinematic equations, coupled field equations, Lagrangian electromechanical dynamic equations and orthonormalized global matrix and scalar forms of electromechanical finite element dynamic equations. Such techniques have not been rigorously modelled previously by other researchers. There are also benefits to presenting the numerical techniques proposed in this paper. First, the proposed numerical techniques can be used for applications in many different geometrical models, including micro-electro-mechanical system power harvesting devices. Second, applying tip mass offset located after the end of the piezoelectric beam length can result in a very practical design, which avoids direct contact with piezoelectric material because of its brittle nature. Since the surfaces of actual piezoelectric material are covered evenly with thin conducting electrodes for generating single voltage, we introduce the new electromechanical discretization, consisting of the mechanical and electrical discretized elements. Moreover, the reduced electromechanical finite element dynamic equations can be further formulated to obtain the series form of new multimode electromechanical frequency response functions of the displacement, velocity, voltage, current and power, including optimal power harvesting. The normalized numerical strain node and eigenmode shapes are also further formulated using numerical discretization. Finally, the parametric numerical case studies of the piezoelectric unimorph beam under a resistive shunt circuit show good agreement with the experimental studies.

Despite the increased use of laminated glass ͑two monolithic layers of glass joined with an elastomeric interlayer-usually PVB-to form a unit͒ as a cladding material for architectural glazing applications and by now as a structural material, the mechanical properties and the structural capabilities of PVB laminated glass are not well known. This paper presents an analytical model that predicts stress development and ultimate strength of laminated glass beams involving a multilayered system that allows displacements in the shear flexible interlayer. The model may be applied to laminates of arbitrary shape and size under prevailing uniaxial bending. No specific simplifying assumption is made in formulating the procedure, so the modeling inaccuracy is marginal, as proved by comparing theoretical model predictions with test results. The model was then used for assessing the safety and predicting the failure strength of laminated glass products available in the architectural glass marketplace, in order to identify the basis for rational design with glass-polymer laminates. The closed form of the model permits us to both explain the behavior of laminated glass, and correlate the structural performance with the geometrical and mechanical parameters.

An analytical solution for the dynamic response of an infinite beam resting on a viscoelastic foundation and subjected to arbitrary dynamic loads is developed in this paper. Fourier and Laplace transforms are utilized to simplify the governing equation of the beam to an algebraic equation, so that the solution can be conveniently obtained in the frequency domain. The convolution theorem is employed to convert the solution into the time domain. Final solutions of beam responses investigated are deflection, velocity, acceleration, bending moment, and shear force. The validation of the proposed solution is verified by considering the solutions of several special dynamic loads and comparing the degraded solution to the known results. Further complicated dynamic loads, such as impulsive loads and time-lag loads, are also discussed and analytical solutions are presented. These relationships can be an effective tool for practitioners.

Engineering Mechanics is one of the
important subject which deals with
mechanics of various structures and
components. The results determined at
laboratories ensure about safety, strength,
rigidity, reliability and behaviors of
mechanical beams, trusses, struts, joints and
other technological aspects. It is thus
significant to acquire sound theoretical
knowledge coupled with practical inputs
observed at laboratories

Stability equations that evaluate the elastic critical load of columns in any type of construction with sidesway uninhibited, partially inhibited, and totally inhibited including the effects of bending and shear deformations are derived in a classical manner. The "modified" shear equation proposed by Timoshenko and Gere is utilized in the derived equations which can be applied to the stability of frames ("unbraced," "partially braced," and "totally braced") with rigid, semirigid, and simple connections. The complete column classification and the corresponding three stability equations overcome the limitations of current methods. Simple criteria are presented that define the concept of minimum lateral bracing required by columns and plane frames to achieve nonsway buckling mode. Four examples are presented that demonstrate the effectiveness and accuracy of the proposed stability equations and the importance of shear deformations in columns with relatively low shear stiffness A s G such as in built-up metal columns or columns made of laminated composites (fiber-reinforced polymers).

This paper focuses on the primary development of novel numerical and analytical techniques of the modal damped vibration energy harvesters with arbitrary proof mass offset. The key equations of electromechanical finite element discretisation using the extended Lagrangian principle are revealed and simplified to give matrix and scalar forms of the coupled system equations, indicating the most relevant numerical technique for the power harvester research. To evaluate the performance of the numerical study, the analytical closed-form boundary value equations have been developed using the extended Hamiltonian principle. The results from the electromechanical frequency response functions (EFRFs) derived from two theoretical studies show excellent agreement with experimental studies. The benefit of the numerical technique is in providing effective and quick predictions for analysing parametric designs and physical properties of piezoelectric materials. Although analytical technique provides a challenging process for analysing the complex smart structure, it shows complementary study for validating the numerical technique.

A state space linear mathematical model oriented to the design of passive and active mass dampers for tall buildings and bridges subjected to the wind action is presented in this paper. The model accounts for an arbitrary number of passive and/or active damping devices positioned at arbitrary points of the structure, as well as for an arbitrary number of structural modes of vibration. The aerodynamic terms of the stiffness and damping matrices are considered following a linearized quasisteady approach. A general discussion on the application of H 2 /H ϱ control techniques to the synthesis of the active mass dampers control law is carried out. For the tuning of the mechanical parameters of passive devices, the problem is reformulated in terms of a decentralized static output feedback control law design problem.

This paper presents an electromechanical dynamic modelling of the partially smart pipe structure subject to the vibration responses from fluid flow and input base excitation for generating the electrical energy. We believe that this work shows the first attempt to formulate a unified analytical approach of flow-induced vibrational smart pipe energy harvester in application to the smart sensor-based structural health monitoring systems including those to detect flutter instability. The arbitrary topology of the thin electrode segments located at the surface of the circumference region of the smart pipe has been used so that the electric charge cancellation can be avoided. The analytical techniques of the smart pipe conveying fluid with discontinuous piezoelectric segments and proof mass offset, connected with the standard AC–DC circuit interface, have been developed using the extended charge-type Hamiltonian mechanics. The coupled field equations reduced from the Ritz method-based weak form analytical approach have been further developed to formulate the orthonormalised dynamic equations. The reduced equations show combinations of the mechanical system of the elastic pipe and fluid flow, electromechanical system of the piezoelectric component, and electrical system of the circuit interface. The electromechanical multi-mode frequency and time signal waveform response equations have also been formulated to demonstrate the power harvesting behaviours. Initially, the optimal power output due to optimal load resistance without the fluid effect is discussed to compare with previous studies. For potential application, further parametric analytical studies of varying partially piezoelectric pipe segments have been explored to analyse the dynamic stability/instability of the smart pipe energy harvester due to the effect of fluid and input base excitation. Further proof between case studies also includes the effect of variable flow velocity for optimal power output, 3-D frequency response, the dynamic evolution of the smart pipe system based on the absolute velocity-time waveform signals, and DC power output-time waveform signals.