Vibro-Acoustic Formulation of Elastically Restrained Shear Deformable Orthotropic Plates Using a Simple Shear Deformation Theory

A method is presented for vibro-acoustic analysis of elastically restrained orthotropic shear deformable plates subjected to excitation forces at different locations. The vibration of the shear deformable plate is formulated on the basis of the Ritz method and a simple first-order shear deformation theory in which 4 rather than 5 displacement components are used to simulate the deformation of the plate. The accuracy of the modal characteristics (natural frequency and mode shape) of an orthotropic plate predicted using the proposed method is verified by those obtained using other methods. The vibration responses of the plate are used in the first Rayleigh integral to construct the sound pressure level (SPL) curves of the plate subjected to excitation forces at different locations. The suitability of the present method for sound radiation analysis is validated by comparing the SPL curve obtained using the present method with those obtained using the other methods. The effects of different system parameters on the SPL curve of the plate are studied by means of several numerical examples. It has been shown that excitation location has significant effects on the smoothness of the SPL curve

Quantifying lumbar mobility using a single tri-axial accelerometer

Background: Lumbar mobility is regarded as important for assessing and managing low back pain (LBP). Inertial Measurement Units (IMUs) are currently the most feasible technology for quantifying lumbar mobility in clinical and research settings. However, their gyroscopes are susceptible to drift errors, limiting their use for long-term remote monitoring. Research question: Can a single tri-axial accelerometer provide an accurate and feasible alternative to a multi-sensor IMU for quantifying lumbar flexion mobility and velocity? Methods: In this cross-sectional study, 18 healthy adults performed nine repetitions of full spinal flexion movements. Lumbar flexion mobility and velocity were quantified using a multi-sensor IMU and just the tri-axial accelerometer within the IMU. Correlations between the two methods were assessed for each percentile of the lumbar flexion movement cycle, and differences in measurements were modelled using a Generalised Additive Model (GAM). Results: Very high correlations (r > 0.90) in flexion angles and velocities were found between the two methods for most of the movement cycle. However, the accelerometer overestimated lumbar flexion angle at the start (-4.7° [95 % CI -7.6° to -1.8°]) and end (-4.8° [95 % CI -7.7° to -1.9°]) of movement cycles, but underestimated angles (maximal difference of 4.3° [95 % CI 1.4° to 7.2°]) between 7 % and 92 % of the movement cycle. For flexion velocity, the accelerometer underestimated at the start (16.6°/s [95%CI 16.0 to 17.2°/s]) and overestimated (-12.3°/s [95%CI -12.9 to -11.7°/s]) at the end of the movement, compared to the IMU. Significance: Despite the observed differences, the study suggests that a single tri-axial accelerometer could be a feasible tool for continuous remote monitoring of lumbar mobility and velocity. This finding has potential implications for the management of LBP, enabling more accessible and cost-effective monitoring of lumbar mobility in both clinical and research settings

Quantifying lumbar mobility using a single tri-axial accelerometer

Background: Lumbar mobility is regarded as important for assessing and managing low back pain (LBP). Inertial Measurement Units (IMUs) are currently the most feasible technology for quantifying lumbar mobility in clinical and research settings. However, their gyroscopes are susceptible to drift errors, limiting their use for long-term remote monitoring. Research question: Can a single tri-axial accelerometer provide an accurate and feasible alternative to a multi-sensor IMU for quantifying lumbar flexion mobility and velocity? Methods: In this cross-sectional study, 18 healthy adults performed nine repetitions of full spinal flexion movements. Lumbar flexion mobility and velocity were quantified using a multi-sensor IMU and just the tri-axial accelerometer within the IMU. Correlations between the two methods were assessed for each percentile of the lumbar flexion movement cycle, and differences in measurements were modelled using a Generalised Additive Model (GAM). Results: Very high correlations (r > 0.90) in flexion angles and velocities were found between the two methods for most of the movement cycle. However, the accelerometer overestimated lumbar flexion angle at the start (-4.7° [95 % CI -7.6° to -1.8°]) and end (-4.8° [95 % CI -7.7° to -1.9°]) of movement cycles, but underestimated angles (maximal difference of 4.3° [95 % CI 1.4° to 7.2°]) between 7 % and 92 % of the movement cycle. For flexion velocity, the accelerometer underestimated at the start (16.6°/s [95%CI 16.0 to 17.2°/s]) and overestimated (-12.3°/s [95%CI -12.9 to -11.7°/s]) at the end of the movement, compared to the IMU. Significance: Despite the observed differences, the study suggests that a single tri-axial accelerometer could be a feasible tool for continuous remote monitoring of lumbar mobility and velocity. This finding has potential implications for the management of LBP, enabling more accessible and cost-effective monitoring of lumbar mobility in both clinical and research settings

Hierarchical Models for Failure Analysis of Plates bent by Distributed and Localized Transverse Loadings

The failure analysis of simply supported, isotropic, square plates is addressed. Attention focuses on minimum failure load amplitudes and failure locations. von Mises' equivalent stress along the plate thickness is also addressed. Several distributed and localized loading conditions are considered. Loads act on the top of the plate. Bi-sinusoidal and uniform loads are taken into account for distributed loadings, while stepwise constant centric and off-centric loadings are addressed in the case of localized loadings. Analysis is performed considering plates whose length-to-thickness ratio a/h can be as high as 100 (thin plates) and as low as 2 (very thick plates). Results are obtained via several 2D plate models. Classical theories (CTs) and higher order models are applied. Those theories are based on polynomial approximation of the displacement field. Among the higher order theories (HOTs), HOTsd models account for the transverse shear deformations, while HOTs models account for both transverse shear and transverse normal deformations. LHOTs represent a local application of the higher order theories. A layerwise approach is thus assumed: by means of mathematical interfaces, the plate is considered to be made of several fictitious layers. The exact 3D solution is presented in order to determine the accuracy of the results obtained via the 2D models. In this way a hierarchy among the 2D theories is established. CTs provide highly accurate results for a/h greater than 10 in the case of distributed loadings and greater than 20 for localized loadings. Results obtained via HOTs are highly accurate in the case of very thick plates for bi-sinusoidal and centric loadings. In the case of uniform and off-centric loadings a high gradient is present in the neighborhood of the plate top. In those cases, LHOTs yield results that match the exact solution