Differential Transform Method for Axisymmetric Vibration Analysis of Circular Sandwich Plates with Viscoelastic Core

Demir, Özgür

doi:10.3390/sym14050852

Cited by 3 publications

(1 citation statement)

References 35 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…To explore the adjustable system dynamics, a direct numerical solution to the parameter-varying equations with random excitation is unsuitable for stochastic response statistics under various spatial parameters. An analytical solution to the equations is an alternative [22][23][24][25][26][27]. Therefore, the analysis method and dynamics adjustability of the partial and ordinary differential coupling system for the visco-elastomer sandwich plate coupled with supported masses under random excitation through spatial periodicity strategy need to be studied further for dynamic optimization or vibration control.…”

Section: Introductionmentioning

confidence: 99%

Response Adjustability Analysis of Partial and Ordinary Differential Coupling System for Visco-Elastomer Sandwich Plate Coupled with Distributed Masses under Random Excitation via Spatial Periodicity Strategy

Ying

Ruan

2022

Symmetry

View full text Add to dashboard Cite

Vibration control of composite structures coupled with distributed masses under random excitations is a significant issue. In this paper, partial and ordinary differential coupling equations are obtained from a periodic sandwich plate coupled with supported masses under random excitation. An analytical solution to the coupling equations is proposed, and the stochastic response adjustability of the system with various periodic distributions of geometrical and physical parameters is studied. Spatial periodic layer thickness and core modulus of the sandwich plate are considered based on the active–passive periodicity strategy. The periodically distributed masses are supported on the plate by coupling springs and dampers. Partial and ordinary differential coupling equations for the system including the periodic sandwich plate and supported masses are derived and then converted into unified ordinary differential equations for multi-mode coupling vibration. Generalized system stiffness, damping and mass are functions of the periodic parameters. Expressions of frequency response function and response spectral density of the system are obtained. Numerical results show the response adjustability via the spatially periodic geometrical and physical parameters. The results have the potential for application to dynamic control or optimization of sandwich structure systems.

show abstract

Section: Introductionmentioning

confidence: 99%

Response Adjustability Analysis of Partial and Ordinary Differential Coupling System for Visco-Elastomer Sandwich Plate Coupled with Distributed Masses under Random Excitation via Spatial Periodicity Strategy

Ying

Ruan

2022

Symmetry

View full text Add to dashboard Cite

show abstract

Stochastic Optimal Bounded Parametric Control of Periodic Viscoelastomer Sandwich Plate with Supported Mass Based on Dynamical Programming Principle

Ruan,

Ying,

Ying

et al. 2024

Buildings

View full text Add to dashboard Cite

The sandwich plate (SP) with supported mass can model structural systems such as platform or floor with installed vibration-sensitive apparatus under random loading. The stochastic optimal control (in time domain) of periodic (in space) viscoelastomer (VE) SP with supported mass subjected to random excitation is an important research subject, which can fully use VE controllability, but it is a challenging problem on optimal bounded parametric control (OBPC). In this paper, a stochastic OBPC for periodic VESP with supported mass subjected to random base loading is proposed according to the stochastic dynamical programming (SDP) principle. Response-reduction capability using the proposed OBPC is studied to demonstrate further control effectiveness of periodic SP via SDP. Controllable VE core modulus of SP is distributed periodically in space. Differential equations for coupling vibration of periodic SP with supported mass are derived and transformed into multi-dimensional system equations with parameters as nonlinear functions of bounded control. The OBPC problem is established by the system equations and performance index with bound constraint. Then, an SDP equation is derived according to the SDP principle. The OBPC law is obtained from the SDP equation under bound constraint. Optimally controlled responses are calculated and compared with passively controlled responses to evaluate control effectiveness. Numerical results on responses and statistics of SP via the proposed OBPC show further remarkable control effectiveness.

show abstract

Differential Transform Method and Neural Network for Solving Variational Calculus Problems

Brociek,

Pleszczyński

2024

Mathematics

View full text Add to dashboard Cite

The history of variational calculus dates back to the late 17th century when Johann Bernoulli presented his famous problem concerning the brachistochrone curve. Since then, variational calculus has developed intensively as many problems in physics and engineering are described by equations from this branch of mathematical analysis. This paper presents two non-classical, distinct methods for solving such problems. The first method is based on the differential transform method (DTM), which seeks an analytical solution in the form of a certain functional series. The second method, on the other hand, is based on the physics-informed neural network (PINN), where artificial intelligence in the form of a neural network is used to solve the differential equation. In addition to describing both methods, this paper also presents numerical examples along with a comparison of the obtained results.Comparingthe two methods, DTM produced marginally more accurate results than PINNs. While PINNs exhibited slightly higher errors, their performance remained commendable. The key strengths of neural networks are their adaptability and ease of implementation. Both approaches discussed in the article are effective for addressing the examined problems.

show abstract

Differential Transform Method for Axisymmetric Vibration Analysis of Circular Sandwich Plates with Viscoelastic Core

Cited by 3 publications

References 35 publications

Response Adjustability Analysis of Partial and Ordinary Differential Coupling System for Visco-Elastomer Sandwich Plate Coupled with Distributed Masses under Random Excitation via Spatial Periodicity Strategy

Response Adjustability Analysis of Partial and Ordinary Differential Coupling System for Visco-Elastomer Sandwich Plate Coupled with Distributed Masses under Random Excitation via Spatial Periodicity Strategy

Stochastic Optimal Bounded Parametric Control of Periodic Viscoelastomer Sandwich Plate with Supported Mass Based on Dynamical Programming Principle

Differential Transform Method and Neural Network for Solving Variational Calculus Problems

Contact Info

Product

Resources

About