Parametric vibrations of piezoelectric viscoelastic cylindrical panels taking into account transverse shear deformations

The paper presents a numerical-analytical approach to solving problems of parametric vibrations of layered hinged piezoelectric viscoelastic cylindrical panels under electromechanical harmonic loading. The mathematical model is constructed using mechanical hypotheses about layer-by-layer approximation of shear deformations by quadratic functions on the thickness of panel, which are supplemented by adequate hypotheses on the distribution of electric field quantities when the components of the electric field strength vector and the normal component of the electric induction vector are different from zero. The dissipative properties of materials are taken into account on the basis of the theory of linear viscoelectric elasticity. To solve the problems, a technique based on the use of the variation principle and the representation of the required quantities in the form of decomposition into double trigonometric series has been developed. This makes it possible to reduce the considered problems to Mathieu-Hill-type equations taking into account energy dissipation, which are solved by the method of harmonic linearization, which allows to determine the boundaries of the regions of dynamic instability.

A Hybrid Solution for Band-Gap Analysis of Vertical Vibration for Periodic Beam-Plate Coupled Systems Based on Variation Principle

The variation principle widely used in structural dynamics analysis allows us to transform the differential equation of the boundary value problem into a functional with extreme value. In recent years, it has been applied to the band-gap analysis of periodic structures. However, for periodic beam-plate composite structures with periodic and ordinary boundaries, it is relatively difficult for the traditional energy methods, such as the Rayleigh–Ritz method, to construct the displacement functions that satisfy boundary conditions. Hence, a hybrid solution is proposed in this paper to account for various boundary conditions of the periodic beam-plate composite structure. Specifically, the displacement functions constructed by the plane wave series can automatically satisfy the periodic boundary conditions. With the ordinary boundaries modeled by artificial springs, the spectral functions conforming to arbitrary boundary conditions are used to represent the displacement functions. The proposed solution is used to solve the band-gap problems of CRTS-III and CRTS-II slab ballastless tracks in China, and the accuracy of the solution is verified by comparing the calculated results with numerical simulations. In addition, through band-gap formation mechanism analysis, the frequency range of propagating flexural waves in each track component is accurately evaluated, which provides a theoretical basis for refined structural vibration reduction in the future. The solution proposed in this paper is flexible and convenient, which can be extended to a more complex band-gap analysis of periodic structures.

Adaptive vibration control of piezoelectric cantilever beams with uncertainties

Considering the stiffness characteristics of piezoelectric layer, the bending stiffness of piezoelectric cantilever beam is obtained by applying the first-order shear deformation theory. The finite element model of piezoelectric cantilever beam is established by Hamilton variation principle. At the maximum strain point, the sensors/actuators are equipped in pairs. Based on the uncertain dynamic model of piezoelectric cantilever beam, an adaptive sliding mode controller (ASMC) is designed by using backstepping technique. The correctness of the finite element model of cantilever beam established is verified by comparing the calculation results of ANSYS software. The effectiveness and superiority of the proposed the ASMC method are verified by the numerical simulations, in comparison with traditional linear quadratic regulator (LQR) control method.

Teacher-Based Assessment of Speaking in Cameroonian Secondary Schools: The Impact of Teacher Training

Speaking is an important language skill that deserves a place both in English language teaching and English language assessment. However, the assessment of speaking in Cameroonian secondary schools is still neglected in many teacher-based English language tests. Often, attempts made to assess the skill are done either almost always indirectly or informally, leaving a wide gap between tenets professed in the Competency-Based Approach (CBA) to English language teaching and practice in the field. In 2012, the government of Cameroon officially introduced the CBA as the pedagogic paradigm for the teaching of English as a Second Language (ESL), and by extension, assessment in secondary schools. Eight years down the line, little seems to have changed concerning the way speaking has always been assessed, even though the CBA requires that learners practically demonstrate knowledge, skills and values in testing situations. This article set out to evaluate the contribution of teacher training to the assessment of speaking. Data was collected through qualitative and quantitative methods. A total of 259 questionnaires were administered to examiners of the June 2019 marking session of the Cameroon General Certificate of Education (CGCE) as well as members of the Cameroon English Language and Literature Teachers’ Association (CAMELTA). Also, four interviews were conducted with the maximum variation principle in mind. The findings revealed that teacher training, both pre-service and in-service, is a major factor responsible for the neglect of speaking in assessments. It was recommended that teacher-training institutions introduce or expand courses on testing to include direct assessment of speaking and that opportunities be created for in-service teachers to acquire certification on assessment within the framework of the CBA to English language teaching.

Unethical evolution of social entities

Complex modern societies require an extended network of specialized workers and organizations (social entities) that play an active role in satisfying the demands of the community. Social entities compete with each other for specific resources (e.g., commercial companies for customers, politicians for votes, TV programs for rating, scientists for funding) with rules that mimic Darwinian natural selection. Social entities explore the landscape of possible strategies to survive (variation principle). Unsuccessful entities disappear as the winning ones drain the available resources (fitness principle). Fruitful strategies are copied and improved by competing entities (heredity principle). The struggle for resources forces the entities to explore all sorts of strategies that do not always follow ethical principles. Without clear limitations to the acceptable survival tactics, entities will explore fruitful unethical approaches depleting the available resources. Therefore, it is necessary to promote the elaboration of ethical codes for each specific social entity to limit the available strategies for competition.

Calculation accuracy of mathematical homogenization method for thermo-mechanical coupling problems

The paper analyzes the thermo-mechanical couplinag phenomenon under the condition of sliding contact, establishes the finite element analysis continuous model of thermo-mechanical coupling, and proposes the system dynamic equilibrium equation and thermodynamic equilibrium equation. The article analyzes the contact conditions between the objects in the system and obtains the objects? contact conditions? mathematical expression. On this basis, the constraint function is used to express the mathematical homogenization. We apply the variation principle to the constraint function and form a non-linear equation group with the system balance equation solve the thermal-mechanical coupling problem. The example shows that we use the constraint function method to solve the thermo-mechanical coupling problem, which has good convergence, stable algorithm, and the calculation result can reflect the actual situation.

Principle and Model Block Diagrams of Cd Content Monthly Variation in Surface and Bottom Waters in Central Bay

According to survey data, in Jiaozhou Bay in 1992, the vertical distribution of Cd content and monthly changes in the surface and the bottom of the central sea area of Jiaozhou Bay were studied, and monthly changes, migration processes and variational principles of the Cd content in surface and bottom water were determined. In May, August, and October, the water body that the main sea current did not pass through were those in the center of the bay. Cd content in central surface water of Jiaozhou Bay was not transported from any source outside the bay from May to October. The results showed that Cd content transported by the main sea current changed from low to high in October, May and August; Cd content transported by the bay current changed from low to high: October, August and May; Cd content in surface water in the bay center changed from low to high in: August, May and October; Cd content in the bottom bay center changed from low to high in May, October and August. Thus, from May to October, monthly changes in these four parts were different. For this reason, the monthly variation principle of Cd content in the surface and bottom waters of the bay was proposed. In addition, the model block diagrams were established to show the change process and principle of Cd content deposition and migration. The principle shows that the bay current has no direct effect on the surface water in the center of the bay from May to October. However, the bottom water body in the center of Jiaozhou Bay was greatly affected, and the surface water body in the center of Jiaozhou Bay was further affected by the upwelling.

The Quantum Recipe

Introduction of the postulates of quantum mechanics: Wavefunctions, operators, observables, commutating operators, expectation values, probabilities, Heisenberg uncertainty. The postulates are then used to set up a ‘quantum recipe’, i.e. a straightforward recipe by which to write down the (nonrelativistic) quantum Hamiltonian of a system of particles. This chapter also discusses the representation of quantum operators as matrices, in reference to a set of ‘basis’ functions, and the variation principle. The idea of a particle trajectory must be abandoned in quantum mechanics. Observable properties of a particle correspond to eigenvalues of the associated quantum operators. The chapter concludes with a brief discussion of the Schrodinger’s cat paradox, quantum entanglement, and other oddities.

Dynamics and buckling loads for a vibrating damped Euler–Bernoulli beam connected to an inhomogeneous foundation

In this paper, the dynamics and the buckling loads for an Euler–Bernoulli beam resting on an inhomogeneous elastic, Winkler foundation are studied. An analytical, asymptotic method is proposed to determine the stability of the Euler–Bernoulli beam for various types of inhomogeneities in the elastic foundation taking into account different types of damping models. Based on the Rayleigh variation principle, beam buckling loads are computed for cases of harmonically perturbed types of inhomogeneities in the elastic foundation, for cases of point inhomogeneities in the form of concentrated springs in the elastic foundation, and for cases with rectangular inclusions in the elastic foundation. The investigation of the beam dynamics shows the possibility of internal resonances for particular values of the beam rigidity and longitudinal force. Such types of resonances, which are usually typical for nonlinear systems, are only possible for the beam due to its inhomogeneous foundation. The occurrence of so-called added mass effects near buckling instabilities under the influence of damping have been found. The analytical expressions for this “added mass” effect have been obtained for different damping models including space hysteresis types. This effect arises as a result of an interaction between the main mode, which is close to instability, and all the other stable modes of vibration.

Calculation of the energy eigenvalues of the Yukawa potential via variation principle

The Yukawa potential has an important and significant rule in some branches of physics such as nuclear, plasma and solid state. However, there is no analytical solution for Schrödinger equation with this potential without approximation, therefore, other ways, such as numerical, perturbation, variation and so on, are taken to deal with this potential. In this work, the variation principle is taken to obtain some of its energy eigenvalues. In the arbitrary [Formula: see text]-state, the Yukawa potentials with centrifugal term are taken together as effective potential and then by choosing the wave functions of the Hulthen potential as trial function which are obtained in this work from the Nikiforov–Uvarov method, and then by applying the variation principle, the energy eigenvalues are obtained. After that, the result is compared with the former numerical result. The comparison shows excellent agreement between our result and the former numerical ones.