Recent Trends in Wave Mechanics and Vibrations

Natural frequencies of different thick triangular plates subject to classical boundary conditions are found based on a proposed shear deformation plate theory in this chapter. The stress distribution needs no shear correction factor in this proposed plate theory. The numerical formulation is performed by means of Rayleigh–Ritz method to obtain the generalized eigenvalue problem. The aim of this study is to find the effect of different physical and geometric parameters on natural frequencies. New results along with 3D mode shapes have been evaluated after the test of convergence and validation with the available results.

Sikkim Himalayan region lies between Nepal–India border in the west and the Bhutan Himalaya in the east. The region is known to be characterized by strike-slip motion on certain deep-rooted faults. In the past, the region has experienced several devastating earthquakes, namely April 25, 2015 Nepal earthquake (M: 7.8); September 18, 2011 Mangan (Sikkim) earthquake (M: 6.9); February 14, 2006 Sikkim earthquake (M: 5.3), and the like. The present study mainly focuses on few major shocks and their source mechanism to explain properly the process of tectonics. A numerically stable computational scheme, using method of eigenfunction expansion has been used in the study to compute surface response or theoretical seismogram in a layered vertically stratified media overlying a half-space. Simple dislocation source model has been considered. The transverse (SH) and vertical (P-SV) components of displacement field have been computed exactly as summed modes by propagator matrix approach using Runga–Kutta method of order 4. The present result has been compared with the observed seismograms. The overflow error appearing in the numerical computation has been prevented by approximating layer matrices suitably or using generalized R/T (Reflection and Transmission) coefficients. The numerical result has been represented here graphically. The study has an advantage to get an idea of real earth structure or seismic source model by an inverse iterative technique.

Flexible Robotic System (FRS) having multiple degrees of freedom has various challenging issues related to real-time control of inherent vibration. The paper addresses novel design semantics as well as vibration analysis of three degrees of freedom flexible robotic arm, fitted with a mini-gripper at its distal link. In this study, the design of a flexible robotic arm has been carried out along with the finite element analysis of the links and revolute joints a priori. Besides successful laboratory-based test hardware of the FRS, the paper focuses on new insight toward modeling of this inherent vibration of the FRS and brings out its effect on the associated dynamics of the FRS.

A revolute jointed robot having multiple grippers/end-effectors poses delicate issues in real-time control operation. The present paper reports the attributes of parametric design and dynamic simulation of the controller of a Multi-gripper Assistive Robot, along with results of test runs. The ensemble programming logic for the robot is developed toward controlling in-built vibration in real time. The hardware of the robotic manipulator has been accomplished in a way to minimize the inherent shaking of the manipulator’s arms. Two posture-driven strategies have been formulated, pertaining to two different phases of a graspable object, namely: (a) in-plane grasping and (b) off-plane lifting. The customized program module has been made interactive in order to systemize multiple grippers.

Explicit, analytical solutions are obtained for the flow of a non-Newtonian Reiner–Rivlin fluid between two coaxially rotating and radially stretching disks. The rotor–stator case and the cases of co- and counter-rotation are discussed elucidating the effects of various parameters of interest, such as stretching parameters, non-Newtonian parameter and Reynolds number.

The present paper aims to study the effects of nonuniform fluid viscosity and thermal conductivity on MHD flow and heat transfer of fluid in a vertical channel with heat source by considering thermal slip boundary conditions. Consideration of temperature-dependent viscosity, thermal conductivity, and magnetic parameter yields a highly nonlinear coupled system of partial differential equations. The coupled nonlinear partial differential equations governing the problem are reduced to a system of coupled highly nonlinear higher order ordinary differential equations by applying suitable similarity transformations. The system of higher order ordinary differential equations is then solved by employing Runge–Kutta sixth-order method.

The solution of displacement field to the problem of diffraction of SH waves generated by an impulsive point source due to a spherical cavity in a non-homogeneous elastic medium, has been obtained in integral forms. The integrals are evaluated asymptotically to obtain short time estimate of the motion near the wave front for large frequency. The displacement of impulsive waves are shown graphically for different values of inhomogeneity factor ‘$$q(0<q<1)$$’ with respect to observational point. It is observed that the displacement of diffracted SH-waves decreases as the arrival time increases for some fixed values of inhomogeneity of the medium. Also for fixed arrival time the displacement decreases as the inhomogeneity increases.

A mathematical modeling of Love type surface waves propagating in a curved homogeneous isotropic layer lying over a curved homogeneous isotropic half-space has been considered. The variable separable and WKB methods are applied to solve the motion of differential equation of Love type surface waves propagation along with curved layer. Both the effects of two curvature of radii of curved layers which along and perpendicular to the propagation direction are taken into account. The analytical expression for Love type surface waves velocity and curvature of curved layer are obtained by setting the propagation of Love waves in plane layer as basis. The effect of radius of curvature on the phase velocity has been shown graphically.

Uncertainties play a major role in stochastic mechanics problems. To study the trajectory involved in stochastic mechanics problems generally, probability distributions are considered. Accordingly, the stochastic mechanics problems govern by stochastic differential equations followed by Markov process. However, the observation still lacks some sort of uncertainties, which are important but ignored. These imprecise uncertainties involved in the various factors affecting the constants, coefficients, initial, and boundary conditions. Hence, there may be a possibility to model a more reliable strategy that will quantify the uncertainty with better confidence. In this context, a computational method for solving fuzzy stochastic Volterra-Fredholm integral equation, which is based on the Block Pulse Functions (BPFs) using fuzzy stochastic operational matrix, is presented. The developed model is used to investigate a test problem of fuzzy stochastic Volterra integral equation and the results are compared in special cases.

Fractal dimension which is developed using linear regression method ($$log(area)-log(perimeter)$$) gives the overall shape of the landscape patches relating to their internal structure while the individual patch provides the geometrical complexity that can be obtained using the modified definition of fractal dimension. Here we have considered north-western part of Orissa, India as the sampled landscape. The fractal dimension as obtained from linear regression method indicates wasteland and agriculture patches with low fractal value but the forest patches have high fractal dimension, i.e., forest patches are more fragmented compared to the other. The modified definition of fractal dimension gives high values of fractal dimension for all the landscape patches and consequently geometrical complexity is reflected.

In this paper, the transverse vibration of axially travelling string is analysed. The axial velocity of the string is periodically varying about an average value. Applying direct perturbation method (MMS), an analytical solution is found. An analysis of principal parametric resonances is carried out when changing frequency of the axial velocity is zero, close to zero and twice the natural frequency. Mathematical analysis is carried out to determine the stability and instability zones. The results show that instability occurs when changing frequency of the axial velocity is close to two times the natural frequency, whereas no instability occurs when changing frequency is close to zero. A case study of bandsaw is discussed. The stability and instability zones are plotted for the first five natural frequencies.

This paper presents a procedure to identify uncertain structural parameters of multistorey shear buildings by interval functional link neural network. The structural parameters are identified using the response of the structure with both ambient and forced vibration. Here interval functional link neural network has been used to train interval data. The polynomials used in the functional link are Chebyshev polynomial. Different degrees of Chebyshev polynomial is used for training and further it is tested with interval Legendre polynomial using the stored converged weights of ChNN. These polynomials are taken in interval form. It is seen that by using interval functional link neural network the computational time is very less compared to interval neural network. Accordingly example problems of two and five-storey shear buildings have been analyzed for free and forced vibration case to show the efficiency of the IFLNN model.

The present paper assesses the safety of existing unreinforced building subjected to earthquake loading, considering uncertainty associated with various material properties. A static pushover analysis was carried out on an equivalent frame model of selected clay and fly ash brick masonry walls using two different load pattern as per ASCE/SEI 41-17. Uncertain material properties that affect the response significantly are identified through sensitivity analysis. The study shows the effect of brick type and mortar grade on the seismic performance of brick masonry wall. It was found from the study that masonry density, elastic modulus, Poisson’s ratio and shear bond strength are the most important material properties which affect the output response.

This stated manuscript is concerned with the propagation of surface waves in a dry sandy layer under initial stress. The analysis is based on Biot’s theory. The dispersion equation of phase velocity of this proposed layer has been derived using convenient second-order finite difference scheme, staggered-grid finite difference scheme, and higher order finite difference scheme where, in each case, second-order central difference operator has been used for temporal derivatives, but second, fourth, and higher order finite difference scheme are used for spatial derivatives, respectively. A comparison study using these three methods has been done and presented in graphs. It has been shown that staggered-grid finite difference scheme is more accurate than second-order finite difference scheme and higher order finite difference scheme is more accurate than second-order finite difference scheme and staggered-grid finite difference scheme both.

$$(\frac{G^\prime }{G})$$-expansion method is exercised to find out the wave solutions of some nonlinear evolution equations such as Chafee–Infante equation (CI), Gardner equation (GE), and Regularized long-wave equation (RLWE). This technique is straight forward and gives more new general solutions and various types of periodic and wave solutions, which were derived. We choose this method as it is straight, brief, elementary and compelling, and in agreement with many other nonlinear evolution equations (NLEEs).

The domain of Flexible Robotic Systems (FRS) is one of the unique ensembles of robotics research that deals with various modes of vibrations, inherent in the system. The vibration, so referred, is completely built-in type and thus it is designed invariant. By nature, the vibration in FRS is self-propagating and does not follow analytical modeling and rule-base in all applications. The asynchronous data fusion, emanating out of FRS is a challenging research paradigm till date, primarily due to the inherent characteristics in quantifying the output response of the system. Real-time assessment of vibration signature in FRS is a prerequisite for establishing a reliable control system for any real-life application. The paper focuses on a new approach of modeling this inherent vibration of the flexible robotic system and brings out its effect on the associated dynamics of the FRS. Besides, the paper dwells on modeling and theoretical analysis for a novel rheological rule-base, centering on the zone-based relative dependency of the finite numbered sensor units in combating the inherent vibration in the flexible robot. Besides, a new proposition is developed for assessing the decision threshold band, signaling the activation of the FRS-gripper, using a stochastic model.

The theory of Vegetative Radiative Transfer Equation (VRTE) in canopy scattering medium is the major mathematical tool enabling researchers to investigate and analyze mathematically essential ingredients to understand how to use remote sensing data for the canopy vegetative medium. VRTE involves geometry functions or G-functions associated with leaf normal distribution functions and a major constituent of the important Area Scattering Phase functions (ASPF) which governs the scattering pattern in any vegetative scattering medium. Almost all these functions are mathematically defined on the basis of Leaf Normal Distribution Function (LNDF), probability of distribution of normals to a particular leaf with respect to a particular direction, say, zenith direction. The VRTE started its evolution on the basis of four experimentally designed LNDF model with specific normalization conditions. In this article, we have presented various new models based on previous field survey but not reported in Biswas (JQSRT 108:197–219, 2007, [1]) and linear combinations of basic four models of LNDF with somewhat detailed mathematical sketch of these important mathematical functions and computer-generated simulations relevant for the realistic problems in these fields of study.

This paper presents an application of wavelet analysis for damage detection in steel structures. Wavelet analysis is a new mathematical and advanced signal processing tool that can be used to analyze the vibration data and the damage in the structure can be identified. It is found that spikes in the wavelet occurs either by damage or striking on the structure. The observed spikes in wavelet pattern are used for damage detection in multistory structures. A software application is developed that can process up to six sensors data and can locate the exact location of the damage. The application of Continuous Daubechies (Db8) wavelet in damage identification proved to be more robust in detecting the damage location. The experiments were conducted on a five-story steel structure at the CSIR-CBRI, Roorkee, India to verify the proposed method using two types of accelerometers.

To bridge the existing technological gap between age-old traditional methods and modern sophisticated cranes for material handling, the Central Building Research Institute (CSIR-CBRI) Roorkee previously developed mini climbing crane with a lifting capacity of 1000 kg at a maximum loading radius of one meter. The developed crane exhibits considerable saving in construction time besides a large saving in manpower. This machine has been awarded the best technology NRDC Award. In this paper, the kinematic model of the mini climbing crane has been developed. Crane workspace and boom tip trajectory are evaluated using MATLAB programming by varying different geometrical and motion parameters. Modal analysis of the full-scale mini climbing crane is performed for its overall stability. Further finite element model (FEM) of the crane shows the load-carrying capacity of the existing design of the mini climbing crane. The full-scale 3D CAD model of the crane is used in the finite element analysis (FEA) using ANSYS software. The study presented in this paper will help further in design and development of a newer version of mobile crane for fast civil construction work.

In nuclear industry, due to the presence of highly acidic and radioactive environment, all the handling and transferring operations of various systems and its components inside the hot cell are to be carried out remotely. For this remote handling operations, the in-cell crane is developed. During normal operation and under postulated seismic event, the structural integrity of the in-cell crane has to be maintained. Hence, as per the safety requirement, this system has to be seismically qualified. This paper highlights the finite element modelling of the in-cell crane for two different load configurations, load cases such as static and seismic; extraction of natural frequencies and mode shapes; mode combination using CQC (Complete Quadratic Combination) method. The seismic qualification of in-cell crane is done as per ASME Section III, Division 1, Subsection NF and its structural integrity is ensured.

Classification of seismic damage indices proposed in the published literature is popularly known as local damage indices and global damage indices. Multiple parameters for each of them are studied to predict the seismic performance of structures. Such a parameter is chosen in this study. For a building to fail by ground motion excitations, certain limiting values of the above-mentioned indices (performance-based limit states) are given in the codes and published literature. A review of a probabilistic detailed seismic analysis, carried out for a regular and geometrically irregular RC framed buildings subjected to typical site hazard, is presented in this paper. Natural ground motions are used to verify the probability of failure of such frames rather than using synthetic ground motion.

In this article, solution bounds for velocity and temperature of non-Newtonian nanofluid flow between two vertical flat plates due to natural convection have been investigated in uncertain environment. Governing differential equations of the titled problem contain a physical parameter, namely, nanoparticle volume fraction which is taken as uncertain in terms of interval. The considered problem has been solved by Galerkin’s method where Legendre polynomials are used to approximate the series solution. The terms in the assumed series solutions are orthogonalized by Gram–Schmidt orthogonalization process. The interval uncertainties are converted to crisp form by the help of parametric approach of intervals. The results obtained by proposed method are compared in special cases, viz., with the existing results and they are in good agreement.

In this paper, an imprecise radon diffusion transport through soil is investigated. As few such researchers have already studied Radon diffusion problems with crisp parameters. Due to various factors, there is a chance of impreciseness to occur in the involved parameters of the model while doing the experiment. So handling a differential equation with imprecise parameters is a challenging task. Accordingly, a second-order radon diffusion equation with imprecise parameters considered as intervals has been studied here. The solution of the considered diffusion equation is modeled by using modified Explicit Finite Difference Method (EFDM) along with parametric concept and for the validation, results are compared with the crisp solutions.

In this paper, efficient numerical methods for solving Bagley–Torvik (B-T) equations with variable coefficients and three-point boundary value conditions are considered. This model is considered as a viscoelastic behavior of geological strata, metal, and glasses using fractional differential equations. Many viscoelastic materials are proposed in which derivatives of fractional-order replace the usual time derivatives of integer order. An application of such a model is the prediction of the transient response of frequency-dependent materials. As such the titled problem is challenging to solve using the efficient method(s). The fractional derivative is described in the Caputo sense. First, a linearly independent set such as $$ \left\{ {1,x,x^{2} ,x^{3} , \ldots } \right\} $$ is converted to Boundary Characteristic Orthogonal Polynomials (BCOPS) by Gram–Schmidt Orthogonalization process then these are used in the Galerkin and Least Square methods to reduce B-T Equations to the linear or nonlinear system of algebraic equations. Example problems are addressed to show the powerfulness and efficacy of the method.

In general, dynamic analysis of a structure may lead to an eigenvalue problem. Accordingly, a novel mechanism for solving the corresponding eigenvalue problem has been proposed using Artificial Neural Network (ANN). In order to validate the ANN procedure, a few example problems, such as vibration analysis of a spring–mass system and a multistory shear building, have been examined. Further, inverse problem, viz., the stiffness of the spring–mass system problem with known mass has also been investigated with the help of ANN. Finally, the results obtained from the example problem for inverse problem have also been compared with the existing results in a special case.

The third- and fifth-order Korteweg–de-Vries (KdV) equations are the commonly used models for the study of various fields of science and engineering, viz., Shallow Water Waves (SWW) with surface tension and magnetoacoustic waves, etc. It is not easy to find the analytical solutions of physical models when they are highly nonlinear. As such, this article aims to find the numerical solutions of fifth-order KdV equations using Differential Quadrature Method (DQM). In DQM, shifted Legendre polynomials-based grid points have been used in finding the solution of two types of fifth-order KdV equations. The present results by DQM are compared with results obtained by other methods. Finally, error plot has also been incorporated and carried out to see the effect of number of grid points on the solution of fifth-order KdV equations.

This study present frequency parameters and mode shapes of nonuniform Single-Walled Carbon Nanotube (SWCNT) placed on Winkler elastic foundation. Eringen’s nonlocal theory is implemented in the Euler–Bernoulli beam to inquire size-dependent behavior of single-walled carbon nanotube. Here flexural stiffness is assumed to vary exponentially which is responsible for making it nonuniform since many nanoelectromechanical systems acquire geometrically nonuniform model. Differential Quadrature Method (DQM) is adopted and MATLAB code has been developed to explore the tabular and graphical results for different scaling parameters. All the standard boundary condition, viz, S-S, C-S, C-C, and C-F are taken into consideration, and obtained results are compared with the well-known results available in the literature showing excellent agreement. Also, the effects of various scaling parameters like nonuniform parameter, the nonlocal parameter, aspect ratio, and Winkler modulus parameter on frequency parameters are demonstrated using numerical as well as graphical results.

The purpose of the investigation is to handle the fractional vibration problem using the multilayer artificial neural network (ANN) method. Fractional calculus has found several applications in different fields of physical systems, viz., viscoelasticity, dynamics, and anomalous diffusion transport. Fractional derivatives are practically described viscoelasticity features in structural dynamics. In general, damping models involve ordinary integer differential operators that are relatively easy to handle. On the other hand, fractional derivatives give better models with respect to the vibration systems in comparison to classical integer-order models. Here, the fractional order in the damping coefficient has been considered. We have employed the multilayer feed-forward neural architecture and error back-propagation algorithm with unsupervised learning for minimizing the error function and modification of the parameters (weights and biases). The results obtained by the present method are compared with the analytical results and are found to be in good agreement.

Various science and engineering problems involve uncertainty with respect to parameters due to different causes. The uncertain parameters may be contemplated as closed intervals. Uncertain material parameters of structural vibration problems may produce interval mass matrices and interval stiffness matrices. In general, dynamic problems with interval uncertainty lead to generalized interval eigenvalue problems. Further, the inclusion of damping factor may transform the problem to a nonlinear interval eigenvalue problems, viz., quadratic and/or cubic eigenvalue problems. In this respect, affine arithmetic may be used to handle the uncertainties due to the overestimation problem occurred in some of the cases of interval arithmetic. Accordingly, this manuscript aims to deal with solving the nonlinear eigenvalue problems with interval parameters using affine arithmetic. Numerical examples have been worked out to illustrate the reliability and efficiency of the present approach.

Human speech which is generated through the vibration of the vocal cord gets affected by the emotional state of the speaker. Accurate recognition of different emotions concealed in human speech is a significant factor toward further improvement of the quality of Human–Computer Interaction (HCI). But the satisfactory level of accuracy is not yet achieved mainly because there is no well-accepted standard feature set. Emotions are hard to distinguish from speech even by human and that is why the standard feature set is difficult to extract. This paper presents a model to classify emotions from speech signals with high accuracy compared to the present state of the art. The speech dataset used in this experiment where speech recordings that are specifically labeled with different emotions of the speakers. A wavelet-based novel feature set is extracted from speech signals and then a Neural Network (NN) with a single hidden layer is trained on the feature set for classification of different emotions. The feature set is a newly introduced one and for the first time it is being tested with NN architecture and classification results are also compared with the results of other prominent classification techniques.

The equation of Radiative Transfer for coherent scattering atmosphere was developed by Woolley and Stibbs. The equation of Radiative Transfer for coherent scattering which is an integro-differential equation has been solved by various methods. The Double Interval Spherical Harmonic Method introduced effectively by Wilson and Sen has already been used by Ghosh and Karanjai to solve the equation of Radiative Transfer in coherent isotropic scattering atmosphere as well as coherent anisotropic scattering atmosphere with Pommraning phase function. The Double Interval Spherical Harmonic Method has been successfully used in this paper to solve the equation of Radiative Transfer for coherent anisotropic scattering atmosphere with planetary phase function.

The dynamical systems in various science and engineering problems are often governed by nonlinear equations (differential equations). Due to insufficiency and incompleteness of system information, the parameters in such equations may have uncertainty. Interval analysis serves as an efficient tool for handling uncertainties in terms of closed intervals. One of the major problems with interval analysis is handling “dependency problems” for computation of the tightest range of solution enclosure or exact enclosure. Such dependency problems are often observed while dealing with complex nonlinear equations. In this regard, initially, two test problems comprising interval nonlinear equations are considered. The Set Inversion via Interval Analysis (SIVIA) along with the Monte Carlo approach is used to compute the exact enclosure of the test problems. Further, the efficiency of the proposed approach has also been verified for solving nonlinear differential equation (Van der Pol oscillator) subject to interval initial conditions.