Performance analysis and material distribution optimization for sound barriers using a semianalytical meshless method

With the increase in car ownership,traffic noise pollution has increased considerably and is one of the most severe types of noise pollution that affects living standards.Noise reduction by sound barriers is a common protective measure used in this country and abroad.The acoustic performance of a sound barrier is highly dependent on its shape and material.In this paper,a semianalytical meshless Burton-Miller‐type singular boundary method is proposed to analyze the acoustic performance of various shapes of sound barriers,and the distribution of sound‐absorbing materials on the surface of sound barriers is optimized by combining a solid isotropic material with a penalization method.The acoustic effect of the sound‐absorbing material is simplified as the acoustical impedance boundary condition.The objective of optimization is to minimize the sound pressure in a given reference plane.The volume of the sound‐absorbing material is used as a constraint.The density of the nodes covered with the sound‐absorbing material is used as the design variable.The method of moving asymptotes was used to update the design variables.This model completely avoids the mesh discretization process in the finite element method and requires only boundary nodes.In addition,the approach also does not require the singular integral calculation in the boundary element method.The method is illustrated and validated using numerical examples to demonstrate its accuracy and efficiency.

Swelling-induced finite bending of functionally graded pH-responsive hydrogels:a semi-analytical method

Recently, pH-sensitive hydrogels have been utilized in the diverse applications including sensors, switches, and actuators. In order to have continuous stress and deformation ?elds, a new semi-analytical approach is developed to predict the swelling induced?nite bending for a functionally graded(FG) layer composed of a pH-sensitive hydrogel,in which the cross-link density is continuously distributed along the thickness direction under the plane strain condition. Without considering the intermediary virtual reference,the initial state is mapped into the deformed con?guration in a circular shape by utilizing a total deformation gradient tensor stemming from the inhomogeneous swelling of an FG layer in response to the variation of the pH value of the solvent. To enlighten the capability of the presented analytical method, the ?nite element method(FEM) is used to verify the accuracy of the analytical results in some case studies. The perfect agreement con-?rms the accuracy of the presented method. Due to the applicability of FG pH-sensitive hydrogels, some design factors such as the semi-angle, the bending curvature, the aspect ratio, and the distributions of deformation and stress ?elds are studied. Furthermore, the tangential free-stress axes are illustrated in deformed con?guration.

The semi-analytical modeling and vibration reduction analysis of the cylindrical shell with piezoelectric shunt damping patches

By considering electromechanical coupling, a unified dynamic model of the cylindrical shell with the piezoelectric shunt damping patch(PSDP) is created. The model is universal and can simulate the vibration characteristic of the shell under different states including the states in which PSDP cannot be connected, partially connected, and completely connected to the shunt circuit. The equivalent loss factor and elastic modulus with frequency dependence are proposed to consider the electrical damping effect of resistance shunt circuits. Moreover, the semi-analytical dynamic equation of the cylindrical shell with PSDP is derived by the Lagrange equation. An experimental test is carried out on the cylindrical shell with PSDP to verify the vibration suppression ability of PSDP on the cylindrical shell and the correctness of the proposed model. Furthermore, the parameter analysis shows that determining the appropriate resistance value in the shunt circuit can achieve a good vibration suppression effect.

A convolution-type semi-analytic DQ approach to transient response of rectangular plates

The convolution-type Gurtin variational principle is known as the only variational principle that is, from the mathematics point of view, totally equivalent to the initial value problem system. In this paper, the equation of motion of rectangular thin plates is first transformed to a new governing equation containing initial conditions by using a convolution method. A convolution-type semi-analytical DQ approach, which involves differential quadrature （DQ） approximation in the space domain and an analytical series expansion in the time domain, is proposed to obtain the transient response solution. This approach offers the same advantages as the Gurtin variational principle and, at the same time, is much simpler in calculation. Numerical results show that it is very accurate yet computationally efficient for the dynamic response of plates.

Three-dimensional elasticity solutions for bending of generally supported thick functionally graded plates

Three-dimensional elasticity solutions for static bending of thick functionally graded plates are presented using a hybrid semi-analytical approach-the state-space based differential quadrature method （SSDQM）. The plate is generally supported at four edges for which the two-way differential quadrature method is used to solve the in-plane variations of the stress and displacement fields numerically. An approximate laminate model （ALM） is exploited to reduce the inhomogeneous plate into a multi-layered laminate, thus applying the state space method to solve analytically in the thickness direction. Both the convergence properties of SSDQM and ALM are examined. The SSDQM is validated by comparing the numerical results with the exact solutions reported in the literature. As an example, the Mori-Tanaka model is used to predict the effective bulk and shear moduli. Effects of gradient index and aspect ratios on the bending behavior of functionally graded thick plates are investigated.

New matrix method for response analysis of circumferentially stiffened non-circular cylindrical shells under harmonic pressure

Based on the governing equation of vibration of a kind of cylindrical shells written in a matrix differential equation of the first order, a new matrix method is presented for steady-state vibration analysis of a noncircular cylindrical shell simply sup- ported at two ends and circumferentially stiffened by rings under harmonic pressure. Its difference from the existing works by Yamada and Irie is that the matrix differential equation is solved by using the extended homogeneous capacity precision integration＇ approach other than the Runge-Kutta-Gill integration method. The transfer matrix can easily be determined by a high precision integration scheme. In addition, besides the normal interacting forces, which were commonly adopted by researchers earlier, the tangential interacting forces between the cylindrical shell and the rings are considered at the same time by means of the Dirac-δ function. The effects of the exciting frequencies on displacements and stresses responses have been investigated. Numerical results show that the proposed method is more efficient than the aforementioned method.

VIBRATION AND ACOUSTIC RADIATION FROM SUBMERGED STIFFENED SPHERICAL SHELL WITH DECK-TYPE INTERNAL PLATE

Based on the motion differential equations of vibration and acoustic coupling system for thin elastic spherical shell with an elastic plate attached to its internal surface,in which Dirac-δ functions are employed to introduce the moments and forces applied by the attachment on the surface of shell,by means of expanding field quantities as Legendre series,a semi-analytic solution is derived for the vibration and acoustic radiation from a submerged stiffened spherical shell with a deck-type internal plate,which has a satisfactory computational effectiveness and precision for an arbitrary frequency range.It is easy to analyze the effect of the internal plate on the acoustic radiation field by using the formulas obtained by the method proposed.It is concluded that the internal plate can significantly change the mechanical and acoustic characteristics of shell,and give the coupling system a very rich resonance frequency spectrum.Moreover,the method can be used to study the acoustic radiation mechanism in similar structures as the one studied here.

Boundary integrated neural networks and code for acoustic radiation and scattering

This paper presents a novel approach called the boundary integrated neural networks(BINNs)for analyzing acoustic radiation and scattering.The method introduces fundamental solutions of the time-harmonic wave equation to encode the boundary integral equations(BIEs)within the neural networks,replacing the conventional use of the governing equation in physics-informed neural networks(PINNs).This approach offers several advantages.First,the input data for the neural networks in the BINNs only require the coordinates of“boundary”collocation points,making it highly suitable for analyzing acoustic fields in unbounded domains.Second,the loss function of the BINNs is not a composite form and has a fast convergence.Third,the BINNs achieve comparable precision to the PINNs using fewer collocation points and hidden layers/neurons.Finally,the semianalytic characteristic of the BIEs contributes to the higher precision of the BINNs.Numerical examples are presented to demonstrate the performance of the proposed method,and a MATLAB code implementation is provided as supplementary material.

Folded novel accurate analytical and semi-analytical solutions of a generalized Calogero–Bogoyavlenskii–Schiff equation

This paper studies the analytical and semi-analytic solutions of the generalized Calogero–Bogoyavlenskii–Schiff(CBS)equation.This model describes the(2+1)–dimensional interaction between Riemann-wave propagation along the y-axis and the x-axis wave.The extended simplest equation(ESE)method is applied to the model,and a variety of novel solitarywave solutions is given.These solitary-wave solutions prove the dynamic behavior of soliton waves in plasma.The accuracy of the obtained solution is verified using a variational iteration(VI)semi-analytical scheme.The analysis and the match between the constructed analytical solution and the semi-analytical solution are sketched using various diagrams to show the accuracy of the solution we obtained.The adopted scheme’s performance shows the effectiveness of the method and its ability to be applied to various nonlinear evolution equations.

Localized collocation schemes and their applications

This paper presents a summary of various localized collocation schemes and their engineering applications.The basic concepts of localized collocation methods(LCMs)are first introduced,such as approximation theory,semianalytical collocation methods and localization strategies.Based on these basic concepts,five different formulations of localized collocation methods are introduced,including the localized radial basis function collocation method(LRBFCM)and the generalized finite difference method(GFDM),the localized method of fundamental solutions(LMFS),the localized radial Trefftz collocation method(LRTCM),and the localized collocation Trefftz method(LCTM).Then,several additional schemes,such as the generalized reciprocity method,Laplace and Fourier transformations,and Krylov deferred correction,are introduced to enable the application of the LCM to large-scale engineering and scientific computing for solving inhomogeneous,nonisotropic and time-dependent partial differential equations.Several typical benchmark examples are presented to show the recent developments and applications on the LCM solution of some selected boundary value problems,such as numerical wave flume,potential-based inverse electrocardiography,wave propagation analysis and 2D phononic crystals,elasticity and in-plane crack problems,heat conduction problems in heterogeneous material and nonlinear time-dependent Burgers’equations.Finally,some conclusions and outlooks of the LCMs are summarized.

Curve selection Lemma for semianalytic sets and conjugacy classes of finite order in Lie groups

Using a strong version of the Curve Selection Lemma for real semianalytic sets, we prove that for an arbitrary connected Lie group G, each connected component of the set E_n(G)of all elements of order n in G is a conjugacy class in G. In particular, all conjugacy classes of finite order in G are closed. Some properties of connected components of E_n(G) are also given.