Forced Vibration Analysis Research Articles

Free and forced vibration analysis of delaminated FRP composite plate with a circular hole

Free and forced vibration analysis of delaminated FRP composite plate with a circular hole

Free and forced vibration analysis of delaminated FRP composite plate with circular hole

Free and forced vibration analysis of delaminated FRP composite plate with circular hole

Longitudinal Forced Vibration Analysis of a Single-Walled Carbon Nanotube Embedded in an Elastic Medium

Longitudinal Forced Vibration Analysis of a Single-Walled Carbon Nanotube Embedded in an Elastic Medium

Transverse forced nonlinear vibration analysis of a double-beam system with a supporting nonlinearity

To exploit the potential application of supporting nonlinearity in marine engineering, an attempt is made to establish the transverse forced vibration analysis model of a double-beam system supported by a spring-mass system that is nonlinear. This kind of vibration system consists of two beam sections, boundary supports, a coupling component, and a nonlinear spring-mass arrangement. The variational approach and the generalized Hamiltonian concept are used to develop the governing equations of such a double-beam system. The Galerkin truncation method (GTM) is a technique for obtaining the governing equations’ residual equations. By solving the associated residual equations numerically, the nonlinear responses of the double-beam system can be figured out. The GTM has good solidity and correctness in the prediction of the vibration system’s forced transverse vibration. The dynamic responses of the double-beam structure supported by a spring-mass system that is nonlinear are subtle to their initial calculation values. Appropriate parameters of the nonlinear support will subdue the level of vibration at the boundary of the double-beam system. In contrast, unsuitable parameters of the nonlinear support motivate complex dynamic responses of the double-beam system and harmfully influence the vibration repression at the boundary of the vibration system.

A unified analysis model of FGM double-layered submarine type coupled structure with spectral geometry method

The free and forced vibration analysis of the FGM double-layered submarine type coupled structure with elastic boundary conditions and coupled connection conditions is presented by using the spectral geometry method. The displacement variables of substructures are represented in the uniform form, and the displacement components of individual structures are represented by the spectral geometry series. Multiple sets of boundary springs are introduced at the coupling interfaces and end boundaries between the substructures, and the elastic and rigid coupling and boundary conditions can be easily obtained by assigning certain values to the stiffness of the artificial springs. The Rayleigh-Ritz procedure is used to obtain the natural frequencies of the structure as well as the frequency response under forced vibration. The convergence of the method is verified by numerical arithmetic examples, and the results of the natural frequencies and frequency response obtained by comparing the finite element methods are used to demonstrate the good accuracy and reliability of the present method. Finally, some parametric analysis studies are carried out for FGM double-layered submarine type coupled structures with different boundaries, dimensions, and material parameters.

Forced vibration analysis model for pumped storage power station based on the 1D–3D coupling and pipe walls vibration

AbstractHydraulic vibration is a common phenomenon in pumped storage power stations (PSPS) and hydropower plants. Evaluating the performance of the PSPS and water conveyance system under the hydraulic vibration condition is significant for the safety of the electric power and the PSPS system. In this study, the one‐dimensional (1D) and three‐dimensional (3D) coupling model for the entire PSPS system is established based on the open‐source software OpenFOAM and in‐house C++ codes. The coupling data exchange is realized by writing and reading files. The coupling model is validated by comparing the results with the pure 1D method under small load disturbance conditions. The forced vibration source is modeled by the pipe walls vibration method in the 3D region, and the 1D method takes charge of other parts in the PSPS system. The combination of the pipe walls vibration and 1D–3D coupling could fully consider the incident and reflected characteristics of the pressure waves. The established model could evaluate the overall performance of the PSPS system under forced vibration. Sensitive analysis of the vibration magnitude is carried out, and the results are consistent with the theoretical analysis, demonstrating that the established model is applicable for the forced vibration analysis.

Using the Baikal-8 recorders for seismic monitoring of buildings and structures in real time in Seismological Branch of the GS RAS

The paper describes the composition of hardware and software parts of the seismic data transmission complex. The complex has been developed as a variant of a practical approach to the implementation of the method of engineering-seismic monitoring developed in SEB GS RAS. The method is based on spectral and quantitative analysis of the amplitude-frequency components of the signal emitted by the studied sources. Examples of the operation of the complex at industrial facilities and in civil construction are given, various approaches to the analysis of forced vibrations caused by the operation of large industrial equipment and normal oscillations of structures are shown.

Forced vibration analysis of inhomogeneous quasicrystal coating in a thermal environment

The tremendous attention of researchers has been attracted to the unusual properties of quasicrystals in coatings. In this paper, the exact solutions of the functionally graded multilayered two-dimensional quasicrystal coating structures in a thermal environment are derived for advanced boundary-value problems with mixed boundary conditions. The state space method is formulated to the thermal coupling with quasicrystal linear elastic theory that derives the state equations for functionally graded quasicrystal coating structures along the thickness direction. The mixed supported boundary conditions in the x-direction and the simply supported boundary conditions in the y-direction are subjected to time-harmonic temperature loadings, which are represented by means of the differential quadrature technique and Fourier series expansions, respectively. Traction on both the bottom and top surfaces is free, and perfect thermal and mechanical contacts between constituents are incorporated at the internal interfaces. A global propagator matrix, which connects the field variables at the top interface to those at the bottom interface for the whole coating structure, is further completed by joint coupling matrices to overcome the numerical instabilities. Finally, three application examples are proposed to throw light on various effects of the power law index, frequency, and different boundary conditions on the field variables in three-layer coating structures. The present solution can serve as a benchmark for the modeling of functionally graded quasicrystal coating structures based on various numerical methods.

Forced vibration analysis of isogrid-stiffened composite plates using VAM-based equivalent plate model

The dynamic behaviors of isogrid-stiffened composite plates (SCPs) exhibit new dynamic characteristics as a result of the introduction of composite materials. To accurately and quickly characterize the forced vibration characteristics of the isogrid SCP, its equivalent plate properties were determined by homogenizing over the unit cell and input to a two-dimensional equivalent model (2D-EPM) obtained from the framework of the variational asymptotic approach. Experiments of free and forced vibrations, as well as numerical examples of free vibration under various boundary conditions and frequency-/time-domain forced vibration under single-/multi-point excitation, were performed to validate the accuracy and efficiency of the proposed model. The effects of structural parameters and stiffening schemes on dynamic characteristics were also investigated. Compared to traditional finite element models, the novelty of cell tailoring is a very important feature that significantly facilitates the investigation of the effect of geometric parameters on the dynamic performance of isogrid SCPs. The results showed that the dynamic performance of the antisymmetric angle-ply SCP was significantly better than that of the unidirectional SCP. The stiffener height had a stronger impact on the forced vibration response, and the inclined stiffeners could significantly improve the dynamic performance of stiffened composite plates. The modeling method has high accuracy and efficiency in forced vibration analysis, which is helpful in predicting the fatigue life of an isogrid SCP under a periodic load.

Static and forced vibration analysis of layered piezoelectric functionally graded structures based on element differential method

A novel strong-form numerical algorithm, piezoelectric vibration element differential method (PVEDM), is proposed for simulating the static deflection and forced vibration of the structure integrated with piezoelectric layers, with the host structure being homogeneous or functionally graded materials. A unified manner for the steady-state and dynamic responses of piezoelectric structures is set up by the proposed method, which draws on the merits of the finite element method and collocation method. In the whole process of assembling the system of equations, variational principle and integration are not required. Furthermore, the influence of boundary conditions on static deflection, and static shape control are investigated. Three examples of static and dynamic responses from one-layer structure, bimorph structure to the structure bonded with piezoelectric layers are given in turn. By comparing with analytical solution or ABAQUS, precise results are achieved, which verifies the the accuracy of the method.

Free and forced vibration analysis of general multiple beam systems

As typical structural elements, multiple beam systems exist widely in many practical engineering applications. Existing research usually makes some simplifications in the systems and cannot analyze the actual structures very precisely. This paper focuses on studying both free and forced transverse vibrations of general multiple beam systems, which are a set of parallel Euler-Bernoulli beams joined by viscoelastic connections. In particular, the to-be-solved models are very generalized and it enables one to simultaneously consider (1) arbitrary number of beams, (2) any boundary conditions, (3) different beam lengths, (4) variable cross sections, (5) axial loads, and (6) various types of viscoelastic connections. Single uniform beams are introduced to modify the original governing equations to a set of inhomogeneous differential equations. Defining some mode-shape coefficients and state variables, a state-space approach is proposed to transfer these differential equations into a state-space equation. Natural frequencies and forced vibration responses are obtained through the state-space equation. With the obtained natural frequencies and a modal Rayleigh-Ritz method, the differential equations about mode shapes are transformed into several algebraic equations that are easily solved. The accuracy of the proposed methods is validated by numerical examples from previous literature and the finite element method. Finally, the requirements for the mode number in the developed methods are presented. This study is of great significance in analyzing and designing multiple beam systems in engineering practices.

Free and Forced Vibration Analyses of Functionally Graded Graphene-Nanoplatelet-Reinforced Beams Based on the Finite Element Method.

The finite element method (FEM) is used to investigate the free and forced vibration characteristics of functionally graded graphene-nanoplatelet-reinforced composite (FG-GPLRC) beams. The weight fraction of graphene nanoplatelets (GPLs) is assumed to vary continuously along the beam thickness according to a linear, parabolic, or uniform pattern. For the FG-GPLRC beam, the modified Halpin–Tsai micromechanics model is used to calculate the effective Young’s modulus, and the rule of mixture is used to determine the effective Poisson’s ratio and mass density. Based on the principle of virtual work under the assumptions of the Euler–Bernoulli beam theory, finite element formulations are derived to analyze the free and forced vibration characteristics of FG-GPLRC beams. A two-node beam element with six degrees of freedom is adopted to discretize the beam, and the corresponding stiffness matrix and mass matrix containing information on the variation of material properties can be derived. On this basis, the natural frequencies and the response amplitudes under external forces are calculated by the FEM. The performance of the proposed FEM is assessed, with some numerical results obtained by layering method and available in published literature. The comparison results show that the proposed FEM is capable of analyzing an FG-GPLRC beam. A detailed parametric investigation is carried out to study the effects of GPL weight fraction, distribution pattern, and dimensions on the free and forced vibration responses of the beam. Numerical results show that the above-mentioned effects play an important role with respect to the vibration behaviors of the beam.

Free and forced vibration analysis of a Z-shaped structure with multi-span elastic supports

In this paper, an in-plane Z-shaped structure with multi-span elastic supports is proposed to investigate the natural frequency and transmission response through employing in-plane governing equation and transfer matrix method. Based on the solutions of transverse vibration and torsional vibration, the total transfer matrix for the Z-shaped structure with multi-span elastic supports is derived. Furthermore, natural frequencies and mode shapes of the Z-shaped structure are calculated. Finite element simulation method (FEM) is conducted here to verify the theoretical results. In order to effectively evaluate the vibration reduction performance, transmission response of the Z-shaped structure under different boundary supports and multi-span elastic supports is analyzed. This work is significant for the vibration reduction of in-plane Z-shaped structure, especially the multi-span elastic support case in engineering applications.

Refined 1D–3D Coupling for High-Frequency Forced Vibration Analysis in Hydraulic Systems

High-Frequency Pressure Fluctuation (HFPF) is an extensively observed hydraulic phenomenon in pumped-storage power stations and water conveyance projects. The investigation of the propagation characteristics of the pressure perturbation is of great significance for the safe operation of hydraulic facilities. In this study, a one-dimensional (1D)–three-dimensional (3D) coupling model is established based on the combination of the Method of Characteristics (MOC) and Computational Fluid Dynamics (CFD) and implanted in the open source software OpenFOAM. The established model in this study implants the dynamic mesh module into the original OpenFOAM solver sonicLiquidFoam and presents the complete solution procedure of the CFD model with the dynamic mesh considered. The vibration of the pipe walls modeled by the mesh motion is employed to numerically generate the HFPF in the hydraulic system, which could not be implemented in the traditional MOC model. The independence of the pressure perturbation in the pipeline system is validated by the time-domain pressure variation. The graphical method is applied to describe the multiple reflection and superposition characteristics of the traveling wave in a simplified hydraulic system. Based on this, the mechanism of the superimposed characteristic of the traveling and standing pressure waves in the hydraulic system are analyzed, and the theoretical superimposed time-domain processes and the variations of the pressure oscillation magnitude are analyzed and presented. The 1D–3D coupling method and the theoretical analysis method could be referenced by other complex hydraulic systems.

Free and forced vibration analysis of uniform and stepped combined conical-cylindrical-spherical shells: A unified formulation

The free and forced vibration characteristics of uniform and stepped coupled shell structures with arbitrary boundary conditions is investigated in this paper. The coupled structure is comprised of typical conical shell, spherical shell and stepped cylindrical shell. The first-order shear deformation theory (FSDT) is applied to establish the analytical model, together with the domain decomposition method (DDM). Then the Jacobi orthogonal polynomials and standard Fourier series are introduced to express the displacement functions along axial direction and circumferential orientation, respectively. The free and forced vibration characteristics of uniform and stepped conical-cylindrical-spherical shells can be obtained by utilizing Ritz method, besides, the Newmark-β integration method is utilized to accomplish time-domain (transient) analysis of the structure. The reliability of the presented method is validated by comparing with the Finite Element Method (FEM) results, the free and forced vibration characteristics of the structure with different boundary conditions, structural scale parameters and damping parameters are analyzed by presenting several numerical examples, numerous new results obtained by present method may serve as reference values for other researches.

Mantari’s Higher-Order Shear Deformation Theory of Sandwich Beam with CNTRC Face Layers with Porous Core Under Thermal Loading

In the dynamic study of sandwich structures, the analysis of forced vibrations of these structures is particularly important. Also, no exact solution can be found from the forced vibrations of sandwich beams, and mainly by numerical methods, the dynamic response of sandwich beams has been obtained. Also, there is no coupling solution for this type of structure with an exact solution. Therefore, the present work aims to present a method by which an accurate solution to the dynamic response of sandwich beams can be obtained to eliminate the computational error in numerical methods. Hence, the model is a five-layer sandwich beam with a constant moving load. Carbon nanotubes (CNTs) are used as functionally graded (FG) distributions as reinforcements for the core. Mantari’s higher-order shear deformation theory is also used for displacement fields. The governing equations were derived using the Hamilton principle. The Laplace method is used to obtain the exact solution of the dynamic response of the sandwich beam in both longitudinal and transverse directions. For validation, the natural frequency is compared with previous research. In the following, parameters such as voltage, thickness ratio, the volume fraction of CNTs, and velocity of moving load on the dynamic response of piezoelectric sandwich beams in transverse and axial displacement are investigated.

Vibration-Based Fatigue Analysis of Octet-Truss Lattice Infill Blades for Utilization in Turbine Rotors.

Vibration fatigue characteristics are critical for rotating machinery components such as turbine rotor blades. Lattice structures are gaining popularity in engineering applications due to their unique ability to reduce weight and improve the mechanical properties. This study is an experimental investigation of octet-truss lattice structure utilization in turbine rotor blades for weight reduction and to improve vibration fatigue characteristics. One completely solid and three lattice infilled blades with variable strut thickness were manufactured via additive manufacturing. Both free and forced experimental vibration analyses were performed on the blades to investigate their modal and vibration fatigue characteristics. The blades were subjected to random vibration using a vibration shaker. The response was measured using a triaxial accelerometer in terms of vibration acceleration time histories in the X, Y, and Z directions. Results indicate a weight reduction of up to 24.91% and enhancement in the first natural frequency of up to 5.29% were achieved using lattice infilled blades. The fatigue life of the blades was investigated using three frequency domain approaches, namely, Lalanne, Dirlik and narrow band. The fatigue life results indicate that the 0.25 mm lattice blade exhibits the highest fatigue life, while the solid blade exhibits the lowest fatigue life of all four blades. The fatigue life of the 0.25 mm lattice blade was 1822-, 1802-, and 1819- fold higher compared to that of the solid blade, using the Lalanne, Dirlik, and narrow-band approaches, respectively. These results can serve as the first step towards the utilization of lattice structures in turbine blades, with thermal analysis as the next step. Therefore, apart from being light weight, the octet-truss lattice infilled blades exhibited superior vibration fatigue characteristics to vibration loads, thereby making them a potential replacement for solid blades in turbine rotors.

Free and Forced Vibration Analysis of Moderately Thick Functionally Graded Doubly Curved Shell of Revolution by Using a Semi-Analytical Method

Free and Forced Vibration Analysis of Moderately Thick Functionally Graded Doubly Curved Shell of Revolution by Using a Semi-Analytical Method

A local meshless numeric method applied in free and forced vibration analyses for elastic problems

A local meshless numeric method applied in free and forced vibration analyses for elastic problems

A full-textile triboelectric nanogenerator with multisource energy harvesting capability

This study develops a full-textile triboelectric nanogenerator to harvest energy from multiple sources, such as sound, human motion, and wind, individually. The textile device consists of three layers, an elastic electrically conductive fabric knitted by silicone-coated yarn as the negative component and electrode, a commercial silk fabric as the positive component, and a conductive fabric as the second electrode. Under the mechanical impact (force ∼50 N, frequency 3 Hz), the device can generate 888.08 ± 4.75 V peak-to-valley voltage, 2.01 ± 0.50 μA short-circuit current, and 138.55 mW/m2 maximum instantaneous power density. It can also convert low-frequency sound (e.g., 75 Hz) into 174.66 ± 2.59 V peak-to-valley voltage (short-circuit current 6.62 ± 0.13 μA, maximum instantaneous power density 19.4 mW/m2). We also used the forced vibration analysis and the intrinsic output characteristics to model the acoustoelectric conversion. The modeling showed good agreement with the experiment results. We further demonstrated the ability to harvest energy from multisource individually, such as airborne noise generated by a working machine, human motion, and wind. The electrical power generated can run commercial electronic devices (e.g., 37 LEDs) or accumulate in a capacitor. In addition, the device has high air permeability and good softness. It may be useful for developing wearable energy generators for various high-tech applications.